Calendars, and our Sun and Moon

last update: 18 August 2020


This text was written in the year 2020 according to the Gregorian calendar, however this year is also 2564 according to the Buddhist calendar, 5780-81 on the Hebrew calendar, 1441-42 on the Islamic calendar, and 12020 on the Holocene calendar.

According to Wikipedia the word
calendar comes from calendae, the first day of every month in the Roman calendar. Roman dates were counted inclusively forward to the next of three principal days: the first of the month (the calends), a day shortly before the middle of the month (the ides), and eight days (nine, counting inclusively) before this (the nones).

If we are going to start with the
Roman calendar then we are going to have to start by understanding the nundinal cycle, and the way the Romans initially adopted a lunar calendar before moving to a lunisolar calendar.

So on this webpage we will first look at 'Our Solar System', then the relationships 'Earth-Night Sky', 'Earth-Sun', and the 'Earth-Moon'.

Our Solar System

Solar Evolution

First we need to understand that the Sun is a nearly perfect sphere of hot plasma, and it's been burning for about the last 4.6 billion years (making it what is called a main sequence star). The Sun is more than 100 times bigger than Earth and has a mass of about 330,000 times that of Earth. Still today the Sun continues to convert more than 4 million tons of matter into energy every second, and this energy comes from fusing every second about 600 million tons of hydrogen into helium. Don't worry, so far the Sun has only lost about 0.03% of its total mass over the last 500 million years. This energy from fusion can take some time to escape the solar core, but it is the source of the sunlight that takes about 8 minutes 17 seconds to arrive from the Sun's surface to the Earth's surface. A photon (the basic unit of our sunlight) starts out in the Sun's core and, changing direction every time it encounters a charged particle, would take between 10,000 and 170,000 years to get the surface. So an extra 8-9 minutes is not that important.

The Sun started out, as did all stars, as a dense molecular cloud that collapsed due to gravitation. A molecular cloud consists mostly of molecular hydrogen and atomic helium produced by Big Bang nucleosynthesis, and is a type of interstellar cloud (also called a nebula). An interstellar cloud consists mostly of gas, plasma and cosmic dust, and is itself a specific type of interstellar medium, which is just a mix of matter and cosmic rays that exists between star systems. So interstellar clouds are where stars and planets are created, and at the same time are reservoirs of material collected from previous generations of stars.

Interstellar Molecules

In the above diagram we can see that once a star is born two options exist. Low-mass stars (like our Sun) convert elements up to carbon, oxygen, and nitrogen, and at the end of their life-cycle they will slowly expel the elements into the interstellar medium. High-mass stars do the same, but they eject mass as a supernova. And in a process called supernova nucleosynthesis they can synthesise up to 'iron peak' elements. The life cycle of stars is closely linked with the chemical evolution of the elements they eject back into the interstellar medium. Heavier elements are ejected in the form of small solid dust particles. Carbon and oxygen will appear as all kinds of silicates and oxides, and there will be a wide variety of molecules ranging from water through to acetylenic chain derivatives such as the cyanopolyynes.

Initially 'our'
molecular cloud would have been in equilibrium, but it is thought that a shock wave from a nearby supernova must have triggered the formation of the Sun by compressing the matter within the molecular cloud, causing certain regions to collapse under their own gravity. Stars can be formed by different types of instabilities in the molecular cloud, however the presence of extinct radionuclides, such as iron-60, in both meteorites and fossilised bacteria suggest that there were one or more supernovæ (stellar explosions) in the vicinity of our solar system. In fact our Sun is a heavy-element-rich star of the Population I type, with high abundances of heavy elements such gold and uranium.

Stars Lifecycle

The basic idea is that fragments were formed in the molecular cloud, and these fragments condensed into pre-stellar cores, one of which would become our solar system. Today if we include the Oort Cloud, our solar system has a diameter of around 3.75 light-years, but if we limit ourselves to the Kuiper Belt then it's only about 10 light-hours across. So to put things in perspective, the original molecular cloud was about 65 light-years across, the first fragments were nearly four light-years across, and a 'dense core' was probably about 0.2 light-years across. It has been suggested that our Sun was one of a cluster of between 1,000 and 10,000 stars formed over a volume of anywhere between 6.5 and 19.5 light-years across. The imperfect orbits of the planets around the Sun and the existence of detached objects suggests that the Sun interacted with close-passing stars during its infancy.


This is the Eagle Nebula (NGC 6611) home to the famous 'Pillars of Creation'. But this is just one example of a nebula, and there are 100's on the web, all different and spectacular. They might look quite dense, but they are just a cloud of gases and dust. A typical molecular cloud will contain roughly 100-100,000 particles per cubic centimetre, as compared with air on Earth which contains about 1019 particles per cubic centimetre. On the other hand, a typical molecular cloud is very, very big and can easily contain 10,000 to 1 million solar masses.

The irregularities in the
molecular cloud are amplified in an emerging interstellar clouds and we can see nebulæ with irregular, elongated shapes. Gravity exploits imperfections because it's an accelerative force that magnifies rapidly any irregularities. As nebulæ (interstellar clouds) collapse the molecular clouds start to rotate due to conservation of angular momentum. Whenever clumps of matter don't collide head-on, one or both can be set spinning, i.e. acquire an angular velocity (rotational/spin or orbital), and therefore angular momentum. In space the clumps will continue to spin unless something stops them, and if they coalesce with other spinning clumps there is a good chance they will increase their angular momentum. In fact everything spins, from galaxies down to individual stars and planets, and without a certain amount of angular momentum present at the beginning they simply could not have been created.

In reality acquiring angular momentum is not a challenge for interstellar clouds. The real challenge is to reduce angular momentum by 6-7 orders of magnitude so that main sequence stars can form. Initially the angular momentum is held in the form of rotation of the cloud, but the cloud can collapse transferred it to spin and orbital angular momenta of the fragments (and transferring thermal and rotational energy to gravitation energy). Successive cycles of collapse and fragmentation can yield objects with masses and specific angular momenta appropriate for the creation of main sequence stars.

Star Formation

As nebulæ collapse they spin faster (just like a figure skater pulling their arms in to spin faster). Much of the mass becomes concentrated in a central protostar, whereas the remaining gas and dust flattens out into a protoplanetary disk that will eventually give birth to the planets, moons, and asteroids. Moving from a pre-stellar core to a protostar is quite a quick process, taking about 400,000 years. The core (Sun) pulled in a lot of mass from the surrounding accretion disk, gradually compressing it, until nuclear fusion was eventually triggered (today the Sun represents 99.86% of the mass of the solar system). Moving from a pre-stellar core to a star requires a density increase of about 15 orders of magnitude.

As the
pre-stellar core pulled in more material the protoplanetary disk decreased in radius, and started to turn faster. The rotation causes the molecular cloud to flatten out and take the form of a disk. This occurs because centripetal acceleration from the orbital motion resists the gravitational pull of the star only in the radial direction, but the molecular cloud is free to collapse in the vertical direction. We can see the result of this today where all the planets sit close to the orbital plane of the Sun. Most are under 2° from the orbital plane, with Venus at 2.2°, and the odd-one-out Mercury with 6.3°.

Milky Way

These two images are a bit 'over-the-top' for this webpage, but they provide a fantastic overview of 'our' Milky Way. Above we have a view showing that the Milky Way is a barred spiral galaxy with a central bar-shaped structure of stars and four clearly defined and symmetrical spiral arms. Our Sun is in the less populated region just under the words 'Local arm'. Below we have the galactic plane of 'our' Milky Way. Reading from the top we have radio continuum (MHz), atomic hydrogen, radio continuum (GHz), molecular hydrogen, infrared, mid-infrared, near-infrared, optical, x-ray, and gamma-ray. This shows that not only our solar system collapsed into a flat disk, but the entire Milky Way with its billions of stars is also a flattish disk.

Combined View of Milky Way Plane

Within the remaining molecular cloud, electrostatic and gravitational interactions cause the cosmic dust and ice grains in the protoplanetary disk to accrete into lots of planetesimals (i.e. collide and stick together to form larger and larger bodies). The process competes against stellar winds driving the gases out of the system, and gravity pulling material into the core. Beyond a certain size (1 kilometre diameter) the planetesimals will start to attract each other, provoking collisions. They will slowly condense into moon-sized protoplanets, and these will slowly coalesced into a few planets (although it is thought that about 3.8 billion years ago most planetesimals were actually forcibly ejected from the solar system). So over hundreds of millions of years, the several hundred planetary embryos would have collided with each other, making ever-larger embryo planets, until a handful were left. Near the Sun volatile molecules like water and methane could not condense, but planets could form from compounds with higher melting points, such as metals (iron, nickel and aluminium) and silicates. These rocky bodies became the terrestrial planets (Mercury, Venus, Earth and Mars).

We tend to forget that metals such as iron, nickel, and aluminium and silica were not created on Earth but were produced during the collapse of supernovæ. In fact these elements are quite rare in the universe, so terrestrial planets could never grow very large. It is probable that terrestrial embryos would have rapidly ceased to accumulate matter, and todays planets would have been the result of collisions and mergers.

Planetary Compositions

giant planets (Jupiter, Saturn, Uranus, and Neptune) formed beyond the frost line, where it was cold enough for volatile compounds such as water, ammonia, methane, carbon dioxide, and carbon monoxide to condense into sold ice grains. The Nice Model explains how the solar system evolved, and in particular how the giant planets migrated from an initial compact configuration to their present positions.

As already mentioned initially there were several hundred
planetary embryos (Moon-sized or bigger) that would have collided and coalesced to form our four terrestrial planets. The Earth's Moon is thought to have been formed after a Mars-sized protoplanet (called Theia) obliquely impacted the proto-Earth some 30 million years after the formation of the solar system. The Moon is most likely to have coalesced from debris after the collision.

In our solar system the gas giants (Jupiter and Saturn) and the ice giants (Uranus and Neptune) spin more rapidly than the terrestrial planets, and they possess most of the solar system's angular momentum. The rotational angular momentum of the Sun is now less than 0.4% of the total angular momentum of the solar system, and Jupiter's orbital angular momentum alone accounts for over 60% of the total angular momentum of the solar system (the so-called "angular momentum problem" is important but not in the context of calendars).

In fact
the Sun rotates quite slowly, and in addition it rotates faster at its equator than at its poles. This is called differential rotation, and is 25.6 days at the equator and 33.5 days at the poles. We have to remember that the Sun cannot be viewed as a single large rotating solid mass, but as a kind of 'fluid' mass in which turbulent convective motion carries energy towards the surface through the mass movement of the plasma. This mass movement of plasma carries a portion of the angular velocity, and the angular momentum can become redistributed to different latitudes through meridional flow (along the axis north-south), which also means that different parts in the interior of the Sun also rotate at different speeds. In addition, our entire solar system, including our Sun, also orbits inside our galaxy, the Milky Way, completing one orbit in a galactic year, equivalent to 225-250 million years.

All eight
planets orbit the Sun virtually in the same plane and in the same direction as the Sun rotates, which is counter-clockwise when viewed from above the Sun's north pole. This is called 'prograde motion'. Six of the planets also rotate counter-clockwise about their axis, as does the Sun, so again they all have a prograde motion. The exceptions are Venus and Uranus which are considered to have a 'retrograde motion'. Uranus has an axial tilt of 97.77°, so its axis of rotation is almost parallel to the plane of the solar system. It is possible it acquired this skewed tilt from a collision with an Earth-sized protoplanet. Venus's axial tilt is 177°, meaning that it rotates almost exactly in the opposite direction to its orbit (opinions differ as to the reason for this).

Spinning Planets

Presenting a sensible graphic of the solar system to scale is an impossibly difficult challenge. Someone wrote "with Earth reduced to about the diameter of a pea, Jupiter would be about 300 metres away, and Pluto would be nearly 2 kilometres away and the size of a bacterium".

Above we can see
that all the planets orbit, tilt and rotate differently. We have mentioned above some of the more extreme angles between a planets rotational axis and its orbital axis. Experts love complicated words, so they call the tilt 'obliquity', and define 0° when the two axes point in the same direction, and are perpendicular to orbital plane. I've not found a well argumented explanation for these tilts, except the suggestion that Earth's tilt might have occurred at the same time it acquired the Moon. An alternative suggestion is the effect of a hypothetical Planet Nine.

Before moving on, it's important to note that there is a distinction between '
Earth's orbit' (around the Sun) and 'Earth orbit' which can mean the geocentric orbit of objects orbiting the Earth.

the Earth orbits the Sun, rotates about an axis, and has an axial tilt. Most people have heard of the fact that planetary orbits are not necessarily perfect circles, and some people will have heard of the elliptical orbits of comets such as Halley's Comet. Orbital eccentricity measures how much an orbit deviates from a perfect circle. However the reality is that our solar system is often presented with a tilted and distorted perspective, making the orbits look far more elliptical than is really the case. The Wikipedia diagram below is a case in point, even if they note that distances are exaggerated and not to scale.

Earths Orbit

orbit of Earth is almost circular, and that of Venus and Neptune have even lower eccentricities (Mercury's orbit is the most eccentric). The Earth's orbit actually only deviates from a perfect circle by a little more than 3%. The Moon has the most eccentric orbit of the large moons in the solar system, and is noticeably more eccentric than Earth's orbit around the Sun. The distance between the Earth and the Sun varies between about 147.5 million km in early January and 152.6 in early July.

Apsis denotes either of the two extreme points in a planetary orbit, both farthest and nearest points from the primary or 'host' body. When talking about the Sun (-helion, originally the Greek hḗlios), the prefix ap- (meaning 'away from') giving aphelion when the Earth is furthest from the Sun, and the prefix peri- (meaning 'near') gives perihelion when the Earth is nearest to the Sun. The same prefixes are used for the Earth (-gee, originally the Greek), giving apogee and perigee when the Moon is farthest and nearest to the Earth (the perigee is often referred to as a Supermoon). You find apogee also being used to indicate when an orbiting satellite is furthest from the Earth (figuratively apogee can just mean 'highest point').

Earth is always nearest to the Sun in early January (winter in the Northern Hemisphere) and furthest from the Sun in early July (summer). So we can see that it is the Earth's axial tilt that creates winter and summer, not Earth's orbit around the Sun. However, the Earth is moving slightly faster when nearest to the Sun (about 1 km/s faster on an average of 29.8 km/s), meaning that the winter season is the shortest (December solstice to March equinox). In fact winter in the Northern Hemisphere is usually nearly 5 days shorter than summer. So it is Earth's elliptical orbit that determines the length of the seasons, but not the warmest or coldest. In fact the Earth's orbital eccentricity only represents a 7% variation in the sunlight received over the different seasons.

As an aside, the Earth's orbital speed around the Sun is 29.8 km/s, which is the equivalent of about 107,280 km/h. Whereas (only) 1670 km/h is the speed of the Earth's surface at the equator (but fortunately its only about 1000 km/h in the UK). Finally, the orbital speed of our solar system around the Milky Way is about 200 km/s (720,000 km/h).

One of the most interesting things about a 'general knowledge' topic is the opportunity to delve into an aside based upon nothing more than an odd word. In this case
apsis. So we are going to start by drawing a line of apsides, which is nothing more than the line connecting the two extremes of an ellipse (also called the major axis), in our case the aphelion and perihelion of Earth's orbit around the Sun. We also need to introduce the word 'periapsis' which is a generalisation of perihelion, in that it is simply the point in the path of an orbiting body that is nearest to the object about which it orbits, as 'apoapsis' is the equivalent for the furthest point.
Satellites require occasionally changes of orbit. For example, when moving to a final orbit from a parking orbit, or when a station-keeping is needed (to compensate for orbital perturbations), or just to correct injection errors. It is my understanding that 'orbital inclination change', or changing the orbit of a satellite, is best performed at places where the orbits intersect and for maximum efficiency where the orbital velocity is minimum, i.e. at the apoapsis or apogee. To save fuel this type of manoeuvre can actually involve raising the satellite to a higher orbit, changing the orbit at an apogee, and then lowering the satellite back to its original altitude.
Turning to
celestial mechanics, apsidal precession is the gradual rotation of the line of apsides of an objects orbit. The apsidal precession is the first time derivative of the argument of periapsis, one of the six main orbital elements of an orbit. Apsidal precession is considered positive when the orbit's axis rotates in the same direction as the orbital motion. An 'apsidal period' is the time interval required for an orbit to precess through 360°. Newton included in his works a theorem on revolving orbits, and he applied it to the orbit of the Moon, however the theorem remained undeveloped and unused. In the mid-19th Century the apsidal precession of Mercury was detected. A very small different (42.98 arcseconds per century) was found between the measurements and the predicted apsidal precession using Newtonian mechanics. A difference that was accounted for by Einstein's general theory of relativity.
A final thought on the
line of apsides goes as follows. There was a suggestion made that a maximum of oceanic tides would occur when the line of apsides of the Sun-Earth and Earth-Moon were aligned. An analysis performed in 1974 by D.E. Cartwright of the National Oceanography Centre discussed in detail how the alignment of the Sun and Moon affects tides on Earth.

We have already mentioned that all the planets, including Earth, orbit the Sun, rotate about an axis, and have an axial tilt. We have noted that the Earth rotates eastward on its own axis, in prograde motion. We also know that a day is "the period of time during which the Earth completes one rotation around its axis". How do we determine that one rotation has been completed? A simple sundial can measure the length of a day by using the Sun's altitude or azimuth (or both). As the Sun moves across the sky, shadows change in direction and length. When they are again found to look identical it means that the Sun is in an identical position, and that means the Earth has completed one rotation. You can decide that it's noon (12:00) when the shadow of the gnomon points exactly north, or when the Sun reaches its highest position, or when the shadow is the shortest. But generally it's easiest for us to define noon as the moment when the Sun is at its highest point in the sky. You then wait until the same condition is found again, and decide that it is again noon, and that 24 hours have passed. However, the second noon is in fact only a local apparent noon (solar noon).

Technically this "highest point in the sky" is called a local meridian, which is an imaginary great circle on the 'celestial sphere'.

Sidereal Day

Wikipedia has the above graphic. In position 1 (day 1) the Sun is exactly overhead, and 24 hours later (day 2) you would expect it to be again in position 1. This is an ideal case where the Earth only rotates about its axis. However the Earth also orbit's the Sun, so on day 2 the Sun will be in position 3, a bit further along on its orbit around Sun. If you had a device that determined independently when the Earth had completed exactly one complete orbit you would not again see the Sun exactly overhead. You would have to wait just a bit longer to find the Sun exactly overhead (i.e. in line again with your local meridian). This is because your relative position with respect to the Sun has changed because of Earth's orbit. Just an extra 1° (more exactly 0.986°) and you will again be perfectly aligned, and the Sun will be exactly overhead.

Now returning to the above diagram, there was also a position 2. We saw above that position 1 and position 3 represented a little bit more that just one full rotation of the
Earth. Nevertheless we have defined that period as one day, and have separated it into 24 hours, and with minutes and seconds. And all this despite the fact that it actually represents a rotation of nearly 361°.

However we can also measure a full
day based upon the Earth's rate of rotation relative to the fixed stars. We consider the stars fixed because they are very far away and don't appear to move relative to each other even when we are orbiting the Sun (which is not the case for our Sun and the planets). The idea is always the same, you fix on a specific location and wait until the Sun or a particular star reappears at the same place. If you are looking for the reappearance of particular star, it will be perfectly aligned at position 2. So in position 2 the observer will correctly conclude that the Earth has completed one 360° rotation. But as we can see in the diagram the observer has not had to wait that extra time for that extra 1° of rotation (as per alignment with the Sun). Therefore by aligning on a star they have complete one full rotation of the Earth in less than 24 hours, or 23 hours, 56 minutes and 04 seconds.

We mentioned above hours, minutes and seconds, but in reality everything is defined in the unit of seconds. Dividing hours and minutes in 60 parts dates from the 3rd millennium BC (the so-called sexagesimal system). Since 1967 a 'second' has been defined using an 'atomic clock' based upon the Caesium standard. What that means is a second is defined as the frequency (number of oscillations/second) of the unperturbed ground-state hyperfine transition of the Caesium-133 atom, the only stable isotope of Caesium. These clocks are said to accurate to 1 second in 138 million years. Now that the second can be measured with incredible accuracy, small differences are found with civil time, and occasionally a leap second is added to 're-set' solar time.

By aligning with the
Sun we have defined a day according to an apparent solar time, and aligning with a star we have defined a day according to sidereal time (sidus is Latin for star, and it's a measure of time used to locate celestial objects). And the difference is nearly 4 minutes.

But in addition the
Earth has a slightly eccentric orbit with respect to the Sun and on top of that it has an axial tilt. This means that the exact distance and direction of Earth-Sun is constantly changing, and even position 3 is not a constant.
If we use the number of swings of a
pendulum as a reference unit of time we will see that a '24 hour' period is shorter (less swings) in September and longer (more swings) in December. This difference can vary from -21 seconds to +29 seconds.
In practice what we end up doing is fixing an imaginary 'mean
Sun' that matching the real Sun's average rate of movement over the year. This we define as solar time.
Our observer saw the apparent motion of the actual
Sun move from position 1 to position 3, which are both defined using a local geographic meridian (the Sun passing over a high point on the horizon, or the Sun at it highest point in the sky). They defined that period as 'true solar time' or 'apparent solar time' because it is based upon the apparent movement of the Sun across the sky. So apparent solar time tracks what is called the diurnal motion of the Sun, or the apparent motion of the Sun (or the stars).

In addition to
apparent solar time there is also 'mean solar time', which follows this imaginary 'mean Sun', and thus establishes a 'mean solar day', which is nearly constant, unlike the 'apparent solar day'.

Why is it 'nearly constant' as mentioned above? The reality is that the Earth's axial rotation is slowing down because of tidal forces, the Moon's gravitational pull on the Earth. This means that every 100 years both the solar day and the sidereal day gain 1.7 milliseconds. Because the Earth's axial rotation is slowing down, some additional angular momentum is transferred to the Moon, meaning that it is pulling away from the Earth at about 3 cm per year.

Why is the exact distance and direction of
Earth-Sun constantly changing? First, due to the eccentricity of Earth's orbit, and where the Earth moves faster when it is nearest the Sun (perihelion) and slower when it is farthest from the Sun (aphelion). Second, due to Earth's axial tilt (known as the obliquity of the ecliptic), the Sun's annual motion is along a great circle (the ecliptic) that is tilted to Earth's celestial equator. When the Sun crosses the equator at both equinoxes, the Sun's daily shift (relative to the background stars) is at an angle to the equator, so the projection of this shift onto the equator is less than its average for the year. When the Sun is farthest from the equator at both solstices, the Sun's shift in position from one day to the next is parallel to the equator, so the projection onto the equator of this shift is larger than the average for the year (see tropical year). In June and December when the Sun is farthest from the celestial equator a given shift along the ecliptic corresponds to a large shift at the equator. So 'apparent solar days' are shorter in March and September than in June or December.

The so-called '
equation of time' describes the difference between apparent solar time and the mean solar time (even if it's not an actual mathematical equation).

Later on this webpage we will look in more detail both at this
equation of time and at the idea of a celestial sphere with its celestial equator and its celestial poles.

Earth Tilt

We have already mentioned that all the planets, including Earth, orbit the Sun, rotate about an axis, and have an axial tilt. We introduced the ideas of diurnal motion, apparent solar time, mean solar time, and sidereal time. And we found that Earth's elliptical orbit determines the length of the seasons, but it is Earth's axial tilt that creates winter and summer.

When we write "
creates winter and summer", what does that really mean? Above we can see that the Earth's axis of rotation is tilted with respect to its orbital plane, and today that angle is approximately 23.4 degrees. This tilt is also known as "obliquity of the ecliptic", and the ecliptic plane is Earth's orbital plane around the Sun.

Earth Seasons

The above diagram is important because it shows why we have
seasons, but people generally have lots of questions about this diagram. Let's look at what we are seeing, and try to answer some of the questions.
We see
Earth orbiting the Sun, and we see it rotates about an axis and tilts. In addition we see that the Earth is always inclined in the same direction, and does not change direction during the year. It is just because Earth is always inclined in the same direction, that we have seasons.
However, even the word
season needs defining, and there are at least three different ways to look at it.

Seasonal Lag

There are meteorological seasons where three month periods are defined by a prevalent weather on land in the region. In a large part of Europe temperature is used as a key determinant, with spring starting on 1 March, summer on 1 June, autumn on 1 September, and winter on 1 December. However, in other regions winter, pre-monsoon, monsoon, and post-monsoon are used. Yet other regions might want to include an Atlantic hurricane season, a flood season, or planting and harvesting seasons.
There are the
astronomical seasons determined by the solstices (when the Sun reaches its most northerly or southerly sun path) and the equinoxes (when the Sun is directly overhead at the equator).
And there are the
solar seasons, determined by the mid-points of the solstices and equinoxes, which equate to the minimum and maximum insolation respectively.

In the above diagrams we can see that the
Northern Hemisphere experiences more direct sunlight during May, June, and July, as the hemisphere faces the Sun. It is Earth's axial tilt that causes the Sun to be higher in the sky during the summer months, which increases the solar flux. However, due to seasonal lag, June, July, and August are the warmest months in the Northern Hemisphere.

Solar irradiance is also called solar flux or simply solar radiation, but it is just a measure of the electromagnetic radiation in a specific wavelength range, received from the Sun. It can be measured in space or on the Earth's surface after atmospheric scattering and absorption. It's measured in watt per square metre, W/m2 (i.e. power per square metre). The terms power and energy are often confused. Energy is a conserved quantity which cannot be created or destroyed, but only converted from one form to another (e.g. conversion of radiant energy into thermal energy). Power is the rate at which energy is generated or consumed, and is measured in watts representing energy per unit time. When you want to integrate solar irradiance over time you obtain radiant energy, which is measured in joules (i.e. J/m2 which is the same as watt-second). You tend to see the intensity of sunlight written in terms of watts per square metre.

Sun has a small core with an estimated temperature of about 15.7 million kelvin (°K), but the surface has an effective temperature of about 5780 °K. Below we will mention that the solar irradiance is about 1362 W/m2 above Earth's atmosphere. We can determine how much power is being emitted into the solid angle subtended by Earth, and this is 170 peta-watts, or about 6.3 x 107 W/m2. We can then determine that the total energy radiated by the Sun in all directions, is about 3.85 x 1026 joules per second. Man has been able to build lasers with peta-watt levels of power output, but only for picoseconds. This means that the total energy output was about 600 joules per second.

Before looking more closely at the issue of
seasonal lag, lets first look at the amount of solar radiation reaching the ground. Different seasons are the result of variations in this solar radiation. Below we have the composite 'Total Solar Irradiance' (TSI), with the running mean. This is the amount of solar radiative energy incident on the Earth's upper atmosphere. The variations you see are linked to the averaged 28-day solar-rotation, and the formation of sunspots (visibly darker regions) and faculae (bright spots). Sunspots are cooler areas that can range in size from 20 km to 150,000 km in diameter, and they can last just a few days or several months. In a sunspot the temperature can drop by up to 2500°C, and this can produce a drop of solar luminosity of up to 0.3%. You can also clearly see the nearly periodic 11-year solar cycle, where levels of solar radiation and ejection of solar material, as well as the number and size of sunspots, solar flares, and coronal loops, appear to be all synchronised. Faculae are short-lived areas several thousand kilometres across that can appear and disappear in minutes, but which produce brighter areas on the Sun's surface. Faculae can appear by themselves, but they also always appear alongside sunspots. Oddly enough in a sunspot cycle faculae can win out over the sunspots and make the Sun look up to 0.1% brighter.

Composite Total Solar Irradiance

Looking at the moving average you can see that total solar irradiance varies between a minimum of 1361 W/m2 and a maximum of 1364 W/m2. The minimum is usually used as a reference point, and it represents the period when the number of sunspots is at a minimum. This figure is wavelength-integrated, so it's for all types of solar irradiance, not just visible light, and it's the figure for solar irradiance above the Earth's atmosphere (so its extraterrestrial solar irradiance).

Solar Constant

The averaged solar irradiance per unit area is called the solar constant, and is a measure of the flux density or electromagnetic power (energy per unit time) passing through a one square metre surface situated 'above' the Earth's atmosphere (this is one representation of the Poynting vector). Not visible in the graphic of solar irradiance is the annual variation due to the Earth's orbital eccentricity, with an increase to 1412 W/m2 in early January and a decrease to 1321 W/m2 in early July for a total fluctuation off about 6.9% (see perihelion and aphelion). In fact, the results are all normalised to 1362 W/m2 at a standard distance from the Sun of 1 astronomical unit (150 million kilometres).

Spectral Irradiance and Photon Flux

The Sun's core generates 99% of its fusion power, converting about 600 million tons of hydrogen into helium nuclei every second. Despite the Sun's emitting a broad spectrum of wavelengths and energies, from X-rays to radio waves, the irradiance peaks in the visible wavelengths. A common unit for irradiance (also called spectral flux density) is W m-2 nm-1, which is the same as joules per second per square metre of a surface that is illuminated per nm of wavelength (e.g. between 300 nm and 301 nm). This is irradiance as a function of wavelength, but the total irradiance in W/m2 can be found by integrating over all wavelengths. We need to know more about the how sunlight is distributed over wavelengths and photon energies because the interaction of sunlight with the Earth's atmosphere is not a simple linear relationship. The above spectra are called 'air mass zero' spectra meaning that they were measured with no air between the instrument and the Sun. The shape of the spectra are different because long wavelength photons have a lower energy than photons with a shorter wavelength.
The first two graphs above are for
irradiance as a function of photon wavelength and photon energy, and the second pair of graphs are for photon flux (number per area per time or cm-2 s-1) again as a function of photon wavelength and photon energy. The photon flux can even be quantified as an equivalent electric current when every photon is converted into a free electron-hole pair (100% efficiency). Looking at the photon flux we can see that more than half of all the photon are in the infrared region. Later we will see how the Earth's atmosphere affects the solar spectrum.

The Sun's rays are attenuated as they pass through the Earth's atmosphere. At any given moment the Earth's surface receives about 1050 W/m2 directly from the Sun at its zenith on a cloudless day at sea level (this is called direct normal irradiance). This takes into consideration atmospheric losses due to absorption and scattering (penetrating a think layer of clean, dry, cloudless air). This increases to around 1120 W/m2 for a horizontal surface at sea level, always for the Sun at its zenith on a cloudless day. This second figure takes into consideration radiation scattered and/or re-emitted by the atmosphere and surroundings (so both direct and indirect radiation sources).

Dry air of the Earth's atmosphere consists of nitrogen (78.08%), oxygen (20.95%), and argon (0.93%). In addition water vapour can vary from ppm's up to 5% for hot, humid air. The Earth's atmosphere is divided into four distinct layers:-
Troposphere (0 to between 6,000 and 18,000 metres) - contains 75% of the atmosphere's mass and 99% of water vapour and aerosols - temperature decreases with altitude and can be -17°C at 5,000 metres and can be -56°C at 18,000 metres - this layer is home to trade winds and clouds
Tropopause is the boundary between the troposphere and the stratosphere (between 9,000 and 17,000 metres) - jet streams (winds west to east) are located near the tropopause
Stratosphere (from between 7,000-20,000 metres and up to 50,000-55,000 metres) - airliners cruise in lower reaches of stratosphere (9,000-12,000 metres) - temperature increases from -50°C to -15°C (temperature inversion) caused by ultraviolet radiation - can be home to very strong winds (up to 220 km/h) - contains the ozone layer (15,000 to 35,000 metres)
Mesosphere - (50 to 100 kilometres) - sometimes termed 'near space' - aerodynamics no longer applies but is still too low for orbital spacecraft - temperature decreases again down to -100°C
Mesopause separates the mesosphere from the thermosphere, and at about 100,000 metres there is the turbopause below which turbulent mixing of chemical species dominates
Thermosphere (80 to 500 kilometres) - hard vacuum - the concept of temperature become meaningless in a vacuum - ultraviolet radiation constantly breaks molecules into ions (e.g. ionosphere between 60 and 1,000 kilometres) - solar winds are located here - International Space Station orbits at 410 kilometres
Thermopause separates the thermosphere from the exosphere and sits 500 to 1,000 kilometres above sea level.
In addition there is the
exosphere (from 600 to 10,000 kilometres) where the remaining molecules (mostly hydrogen and carbon dioxide) are still bound by gravity, and where the majority of satellites are found.

However there are few practical problems with the figure 1361
W/m2. Firstly this figure will vary with both the Sun's angle (i.e. the tilt of the Earth's surface with respect to the Sun's position above the horizon) and atmospheric conditions (e.g. cloud cover, moisture content, dust, etc.). When the Sun is closer to the horizon the sunlight shines on the Earth at a lower angle (large solar zenith angle), so the energy is spread over a larger area. Another problem is the 'cloudless day' presumption. Even thin wispy cirrus clouds will reduce by 50% the solar irradiance actually reaching the Earth's surface. And cloud cover can easily exceed 50%, and is dependent upon the optical depth of the cloud. Global dimming by particulates and aerosols may be responsible for an additional 4-20% reduction of solar irradiance. The figure of 1361 W/m2 is only for the areas with the Sun directly overhead. The radiation received as you move away from the zenith will decrease due to the curvature of the Earth, and in addition at any given time half the Earth's surface is hidden from the Sun (night). So the total energy received by the Earth is dependent upon its cross section, but it is actually distributed over the entire surface area of a sphere that rotates. It is for this reason that the average incoming solar radiation is ¼ of the solar constant, i.e. about 340 W/m2.

Above we saw that the solar constant (1361 W/m2) was the average radiation intensity (flux density) falling on an imaginary surface, perpendicular to the Sun's rays and at the edge of the Earth's atmosphere. And we understood that solar constant is not a constant, because it varies by nearly 7% due to the Earth's orbital eccentricity, and by around ± 0.3% due to sunspot cycles. So for any specific day the solar constant (I0) would need to be re-calculated.
The value of I
0 is the same for any place on the Earth's surface, provided they are perpendicular to the Sun's rays. However not all places on the Earth's surface are perpendicular to the Sun's rays, and we need to calculate the solar irradiance incident on another imaginary surface that is parallel to a horizontal plane anywhere on the Earth's surface, knowing that it will be less than I0.

The Cosine Effect

Above we can see that I0 corresponds to a place P', as if the Earth's atmosphere had no effect on the incident radiation. We can see the horizontal Plane A at some other point P on the Earth's surface, and the horizontal Plane B being parallel to Plane A at the edge of the Earth's atmosphere. Plane C is a surface perpendicular to the Sun's rays, and usually called the 'normal plane'. The θz is the solar zenith angle and using the simple law of cosines we can obtain the I0h, the extraterrestrial irradiance intensity on any horizontal plane (Plane B) facing the Sun. We have used I0 and I0h to represent solar irradiance as measured in unit of power per unit area (watt per square metre or W/m2), but many texts use radiant energy (called irradiation H0) as measured in joules per square metre (J/m2).

We have already mentioned that I0 varies throughout the year dependent upon Earth's orbital eccentricity and Earth's axial tilt (and sunspot cycles), but it is a constant for any specific latitude. However for any specific latitude the radiant energy H0 and H0h will vary throughout the year. The reason is that radiant energy (J/m2 or watt-second) is an integral of solar irradiance (watt-second), and is dependent upon the total time of exposure. Which means that even if I0 is a constant for any specific latitude, H0 is not. It will change from latitude to latitude because the length of the days change (i.e. period of exposure change). The most obvious case is near the Earth's poles where for longer periods they are exposed to either 24 hours of daylight or 24 hours of darkness.

The next step is to understand better what happens to
solar irradiance as it passes through the Earth's atmosphere. There are two generic process, i.e. scattering and absorption.
Scattering as a generic process where an incident particle is deviated from a straight trajectory when it interacts with another particle. These particles can be molecules, atoms, electrons, photon, etc., and scattering processes can be either elastic or inelastic. These two options have quite technical definitions, but it is sufficient to say that 'elastic' means that the total kinetic energy in the collision is conserved even if the directions are modified. In the case of generic inelastic scattering the energy of the incident particle is reduced or increased. What we are interested in is the scattering of photons from the Sun with the contents of the Earth's atmosphere, which includes nitrogen, oxygen, argon, carbon dioxide, water vapour, etc., and even particulates such as aerosols, droplets or solids in the form of dust, etc. The reality is that an individual scattering even is quite a random event, but in real life radiation will be scattering many time, and can be modelled as a diffusion process.
Absorption is about how matter (typically atoms) absorbed the energy of a particle (typically a photon) transforming the radiant energy into internal energy (often thermal energy). Absorption is often see in the form of attenuation, the gradual loss of photon flux through the air. The first thing to note is that attenuation is an exponential function of the path length through the medium. It is a kind of macroscopic measure of absorption and includes lots of different physical processes that result in photons not arriving at their destination, e.g. diffuse reflection as well as different forms of selective absorption. Photons of specific wavelengths can be absorbed at the atomic level, or they can be absorbed into a molecules vibrational states or into the chemical bonds (see photodissociation), and (for example) the energy converted into thermal energy.

We have already mentioned that the
Sun emits a broad spectrum of wavelengths and energies, from X-rays to radio waves, however the irradiance peaks in the visible wavelengths. In fact 99% of the Sun's energy is emitted in the region between 100 nm and 4000 nm (400-750 nm for the visible spectrum and 750-5000 nm for the near infrared region). We have already looked at irradiance and photon flux as a function of photon wavelength and photon energy, but now we will start by looking in more detail at that irradiance at TOA (Top of Atmosphere) as a function of wavenumber.

Total Solar Irradiance

The above graph comes from NASA and plots the solar irradiance with some narrow absorption bands associated with cool gaseous molecules in the Sun's outer atmosphere (photosphere). The red line dates from 1992 and black line from an earlier period. The solar constant is the integral over the curve, and was found to be 1366.91 W/m2. Oddly I've not found a better graph than this one. It is still used in publications today, even through solar irradiance spectra are being logged every day.
For many people the wavenumber (1/wavelengths) might be new, but it has provided a useful way of looking at many closely packed spectral lines. For example, the difference in wavelengths between two lines might be only 0.073 nm, but expressed as a wavenumber this would be 10 cm-1. The wavenumber provides an easy to understand linear scale where higher wavenumber's mean higher energies and higher frequencies. The wavenumber being directly proportional to energy (including vibrational energy), a comparison of wavenumber's directly compares energies, and in addition a wavenumber is a smaller whole number and avoids using lots of decimal places. For example, it's easier (for some people) to express the range of visible radiation as between 12500-25000 cm-1, and not between 400-800 x 10-9 metres.

Looking at
solar irradiance it possible to see spectral lines which result from the emission or absorption of light, and they can be used to identify the presence of different atoms and molecules. In particular spectral absorption lines are named Fraunhofer lines, and they were originally observed as dark features in the optical spectrum of the Sun. Joseph von Fraunhofer (German, 1787-1826) gave his name to these dark lines in 1814. It was in 1885 that Johann Jakob Balmer (Swiss, 1825-1898) gave his name to the spectral line emissions of the hydrogen atom (corresponding to the H-series in the above graph). The importance of the absorption lines was only realised after the discovery of the emission lines. Below we can see that the emission lines and absorption lines of hydrogen are situated at the same wavelengths. So the emission lines for known chemical elements or chemical compounds helped determine the composition of distant stars.

Hydrogen Spectrum

Why does hydrogen have both emission and absorption spectra? In fact we are looking at two different things. Let's take an emission nebula consisting of ionised gases emitting light at various wavelengths, but mostly high-energy ultraviolet photons. Low density interstellar gas clouds are primarily composed of hydrogen, with its relatively low energy of ionisation. The high-energy ultraviolet photons break the neutral hydrogen atoms into hydrogen nuclei and free electrons, which later recombine to form hydrogen in excited states. As the excited atoms return to their lowest energy levels they emit photons with well defined energies characteristic of the allowed excited states of hydrogen (e.g. the famous red line at 656.3 nm give emission nebula their characteristic red colour). It is these emitted photons with well defined energies that make up the Balmer series. But what happens if these photons with well defined energies now go through a gas composed of neutral hydrogen atoms. The hydrogen atom will absorb the photon and become excited. Initially scientists through that they were looking at stars composed of different chemical elements, but they then found that spectral lines of stars look different simply because they have different temperatures. And that most stars have nearly the same composition as the Sun. In fact absorption lines of hydrogen are not seen in the hottest and coolest stars. In the hottest stars, all the hydrogen atoms are completely ionised into hydrogen nuclei and free electrons and can't produce absorption lines. In the coolest stars the neutral hydrogen atoms are in unexcited or ground states. They can absorb photons and become excited, but those type of photons lie in the ultraviolet part of the spectrum, and there are very few ultraviolet photons in cold stars. The emission lines of hydrogen (the Balmer series) are strongest in stars with a temperature of about 10,000 °K. At this temperature many hydrogen atoms are in an excited state, but can rise to still-higher excited states, producing hydrogen absorption lines. So in the case of our Sun its outer atmosphere (photosphere) is at a much cooler temperature than the inner layers. The cooler gases in the photosphere absorb photons at specific wavelengths corresponding to its chemical composition. The excited atoms do relax back to their ground states and do re-emit characteristic photons but in random directions, so what an observer sees is just the characteristic absorption lines.

The composition of the
photosphere can be measured as a percentage of the total mass or as a percentage of the total number of atoms (in parenthesis), and starts with hydrogen 71% (91.2%), helium 27.1% (8.7%), oxygen 0.97% (0.078%), carbon 0.40% (0.043%), followed by traces of nitrogen, silicon, magnesium, neon, iron, sulphur, … For example, magnesium is one of the easiest elements to find in many types of stars, with Mg-I visible over a wide range of temperatures and even in metal-poor stars (see metallicity). The Ca-II triplet is known to be strongly dependent upon the temperature of the stars.
The observation of the
spectral lines of stars allowed scientists to sort them into spectral classes, based upon the stars surface temperature. From hottest to coldest, we have seven spectral classes, O, B, A, F, G, K, and M. Other classes have been added, i.e. W, carbon stars C, S for cool giants, D for degenerate gases, as well as L, T and Y for even cooler objects. Each of the seven original spectral classes can be dived into hottest '0' through to coolest '9', so a B3 is hotter than a B4 (most classes appear to have sub-classes and many have sub-sub-classes). So our Sun is called a G2V star. G-type main-sequence stars have prominent Ca-II spectral lines, and most prominent in G2 stars. The 'V' indicates the luminosity class for main sequence stars, which is a group of stars that have a particular combination of colour index and brightness (absolute magnitude) largely conditioned by their mass, chemical composition and age (and they are the most numerous true stars in the universe). Below we can see the relative importance of the absorption lines for different stars of different temperatures, along with the spectral classes. The only problem you have to look out for is that astronomers call anything heavier than helium a metal, even if it has no metallic properties.

Absorption by Spectral class

In a very simplistic way, if you had a star with hydrogen absorption lines that were weaker than in a known A-class star then it might be a B-class star or a G-class star, but if the absorption lines also showed the presence of ionised iron and other metals, then it must be a G-class star. In fact our Sun is a type of star thought to have formed from an interstellar cloud that had previously been enriched in heavier elements from other stars, and as such is metal-rich with up to 2-3% of heavy elements. As far as I know astronomers have detected 67 chemical elements in the Sun.

So far we have looked at what is happening at the TOA (Top of Atmosphere), but now our solar irradiance has to pass through the Earth's atmosphere. From the Sun, photons travelled though the almost perfect vacuum of outer space. Entering the Earth's atmosphere they will 'encounter' billions of atoms and molecules. They will be scattered or absorbed depending upon the photon energy (or wavelength) and the type of atom and molecule encountered. This process of propagation of radiation through a medium is called radiative transfer, and there are many models of this process ranging from the very simple to the extremely complex. The temperature, pressure and chemical composition of the Earth's atmosphere changes a lot with altitude, and the Sun cannot always be assumed to be overhead (at the zenith). Different types of electromagnetic radiation (e.g. radio waves, infrared, visible light, ultraviolet, X-rays, etc.) will react different as they penetrate the Earth's atmosphere.

Solar Spectrum

In the above graph we can see two new features, in addition to the (smoothed and simplified) solar irradiance spectrum (at TOA) that we already discussed (yellow).
The first new feature is that the measured
solar irradiance spectrum is very similar to the emission spectrum of a black body of the temperature (black line).

The second new feature is
solar irradiance at sea level with the Sun directly overhead (the red area). This is a highly simplified graphic, but the key message is the appearance of absorption bands. We can immediately see that the Earth's atmosphere is reasonably transparent in the visible part of the spectrum, opaque in the ultraviolet (UV) region, and has several important absorption bands in the infrared region. So what is happening? In very simple terms photons are disappearing in specific wavelength bands. We know that the molecules bonds can be dissociated when they absorb photons, this is called a photochemical reaction (actinism is the property of solar radiation that leads to photochemical reactions). It is also possible that the molecule becomes excited, and return to their ground states through a process of fluorescence or phosphorescence, both photo-physical processes in the sense that they don't involve any chemical change. However some photo-physical processes can transfer energy to other molecules that do undergo secondary photochemical reactions. These molecules will undergo chemical change but typically would not have undergone a (light-absorbing) photochemical reaction.

Perrin-Jablonski Diagram

These photo-physical and photochemical processes are often presented in what is called a Perrin-Jabloński diagram. It is a way of illustrating the electronic states of a molecule and the (quantised) transitions between them. Firstly we can see the energy levels S0 the singlet ground state of the molecule, then we have the Sn excited singlet states and Tn the excited triplet states (see intersystem crossing). A singlet state is simply one in which the electron does not flip its spin when excited. The straight arrows are the radiative transitions involving the absorption or (spontaneous) emission of a photon. The undulating arrows are non-radiative transitions between two molecular states without the absorption or emission of a photon. The simplest kind of transition is where the photon is absorbed and the molecule acquires vibrational energy and moves to an excited singlet state. The molecule will look to dissipate the acquired energy and return to its singlet ground state. The easiest way is through vibrational relaxation (yellow arrows), either intramolecular or intermolecular. An alternative (purple arrows) is internal conversion followed by vibrational relaxation, a form of 'radiationless de-excitation'. Photon emission S1 to S0 is called fluorescence (green arrows), whereas the photon emission T1 to S0 is known as phosphorescence (red arrows). The reality is that phosphorescence requires the electron's spin to be flipped, and this has a very low probability.
So we have both photo-physical and photochemical processes that can absorb photons and proceed down a variety of photochemical pathways. And it is evident that everything will be depend upon the photon energy and therefore on the wavelengths.

How can we best summarise the impact of these
absorption bands on the solar irradiance entering the Earth's atmosphere? We can look at it as a general question of transparency and translucency. Just how much light passes through the Earth's atmosphere without appreciable scattering (i.e. transparency), or eventually allowing for some scattering where the refractive index changes (i.e. translucency). Or perhaps we can look at the opacity of the Earth's atmosphere, which might better describe the effect of photons being adsorbed or scattered.

The best overall presentation I've found pulls together
spectral intensity and total adsorption, along with the adsorption for major components in the Earth's atmosphere. We can see that between 70% and 75% solar irradiance gets through the Earth's atmosphere but only some of that warms the Earth's surface (some of that 70% will also be reflected back by clouds and highly-reflective surfaces such as ice). However when the Earth's surface is warmer than the Earth's atmosphere it also re-emits infrared radiation, but at a longer wavelength. But only 15% to 30% of that escapes the Earth's atmosphere, the rest being reflected back to the Earth's surface. In very simple terms, the more infrared radiation is reflected back by greenhouse gases, the more the Earth's surface warms up (resulting in climate change).

Atmospheric Transmission

One of the nicest things about this graphic is that it includes both the optical window (shortwave window) and the infrared window (longwave window), as well as the ozone layer.

Let's first look
water in the Earth's atmosphere. It can be found as water vapour, liquid water in clouds, rain and fog, and solid water in the form of snow, ice (at least 19 different phases) and hail. Water molecules last about 9 days in the Earth's atmosphere, and they are the main absorbers of solar irradiance and a major greenhouse gas. However, without atmospheric water vapour, the Earth would be in a permanent ice age. The Earth's atmosphere holds about 13 trillion tons of water, and water is responsible for about 70% of all atmospheric absorption, mainly in the infrared region. We have already mentioned the importance of the absorption bands in the infrared region, but, as we can see in the graph, it also is a major absorber at longer wavelengths. Ice, snow, and clouds will reflect, absorb, and transmit photons, and a lot will depend upon grain size (for snow), bubbles and brine inclusions (depending on where the ice is found), and impurities, dust and soot (in clouds). In very simple terms water molecules in water vapour have a very small moment of inertia on rotation which gives rise to a rich combination of vibrational-rotational spectra producing thousands of individual absorption lines which overlap and make up the absorption bands.

In the earlier graph of the spectrum of
solar irradiance

photon absorption by water, which will be dependent upon the photon energy (wavelength) and the physical state of the water.

absorbance changes dramatically depending upon the physical state of the water,
water vapour). We can see that water is responsible for absorption bands in the near-infrared

Water vapor is a greenhouse gas in the Earth's atmosphere, responsible for 70% of the known absorption of incoming sunlight, particularly in the infrared region, and about 60% of the atmospheric absorption of thermal radiation by the Earth known as the greenhouse effect.[25] It is also an important factor in multispectral imaging and hyperspectral imaging used in remote sensing[12] because water vapor absorbs radiation differently in different spectral bands. Its effects are also an important consideration in infrared astronomy and radio astronomy in the microwave or millimeter wave bands. The South Pole Telescope was constructed in Antarctica in part because the elevation and low temperatures there mean there is very little water vapor in the atmosphere.[26]
Similarly, carbon dioxide absorption bands occur around 1400, 1600 and 2000 nm,[27] but its presence in the Earth's atmosphere accounts for just 26% of the greenhouse effect.[25] Carbon dioxide gas absorbs energy in some small segments of the thermal infrared spectrum that water vapor misses. This extra absorption within the atmosphere causes the air to warm just a bit more and the warmer the atmosphere the greater its capacity to hold more water vapor. This extra water vapor absorption further enhances the Earth's greenhouse effect.[28]
In the atmospheric window between approximately 8000 and 14000 nm, in the far-infrared spectrum, carbon dioxide and water absorption is weak.[29] This window allows most of the thermal radiation in this band to be radiated out to space directly from the Earth's surface. This band is also used for remote sensing of the Earth from space, for example with thermal Infrared imaging.
As well as absorbing radiation, water vapour occasionally emits radiation in all directions, according to the Black Body Emission curve for its current temperature overlaid on the water absorption spectrum. Much of this energy will be recaptured by other water molecules, but at higher altitudes, radiation sent towards space is less likely to be recaptured, as there is less water available to recapture radiation of water-specific absorbing wavelengths. By the top of the troposphere, about 12 km above sea level, most water vapor condenses to liquid water or ice as it releases its heat of vapourization. Once changed state, liquid water and ice fall away to lower altitudes. This will be balanced by incoming water vapour rising via convection currents.
Liquid water and ice emit radiation at a higher rate than water vapour (see graph above). Water at the top of the troposphere, particularly in liquid and solid states, cools as it emits net photons to space. Neighboring gas molecules other than water (e.g. Nitrogen) are cooled by passing their heat kinetically to the water. This is why temperatures at the top of the troposphere (known as the tropopause) are about -50 degrees Celsius.

Figure 2 shows the absorption in a real atmosphere measured during my PhD, in units of optical depth, which is just a measure of how opaque the atmosphere is. So, looking at Figure 2, if water vapour absorbs more radiation than CO2, then why are we worried so much about CO2? The issue here is to do with what we call climate forcings and climate feedbacks. A forcing can be thought of as due to something outside of the climate system causing a change in its properties, while a feedback is the result of the climate system responding to a forcing.
In this context, CO2 contributes to the forcing (we emit CO2, which causes the atmosphere to heat up) and water vapour is a feedback (higher temperature leads to more water vapour in the atmosphere from evaporation of the oceans). This means that as CO2 heats up the Earth, it also causes an increase in the water vapour absorption, trapping much more radiation than the CO2 would alone, amplifying the overall effect on the climate by a factor of 2-3.

Jargon changes and you often see TOA (Top of Atmosphere) changed to AM0 meaning air mass coefficient, which is a ratio relative to the optical path length vertically upwards, i.e. at the zenith. So AM0 is the same as TOA, but AM1 describes a place on the Earth's surface with the Sun directly overhead. You will also see AM1.5, which describes an optical path through the Earth's atmosphere equivalent to 1.5 times AM1. This terminology is often uses in evaluating the performance of solar cell installations.

Since the creation of the Earth its atmosphere has changed quite dramatically. Initially the Earth's atmosphere would have consisted of hydrogen, helium, and some hydrogenated compounds such as methane, ammonia and water (this is sometimes called the 'primary atmosphere'). There was no molecular oxygen or reactive oxides. If hydrogen and helium are the most common chemical elements in the universe, why are they so rare in the Earth's atmosphere? The simple fact is that hydrogen and helium was travelling too fast (due to the high surface temperature) and the Earth was too small (gravity too weak). Jeans Escape just means that molecules can reach escape velocity and leave the atmosphere. And that's what happened, over time hydrogen and helium escaped from the Earth's atmosphere. It is possible that a collision between two planetesimals would have be enough to raise the thermal velocity of a hydrogen-rich atmosphere above the escape velocity (see Giant-Impact Hypothesis). Some hydrogen was retained because it was bonded into heavier compounds. However helium was light and not very reactive, so most of it was lost into space. It would appear that neon and argon went the same way, whereas nitrogen and sulphur, being reactive, were retained in heavier compounds. It was Francis William Aston (English, 1877-1945) who first concluded that the noble gases were abnormally scarce on the Earth compared to other elements (the noble gases are part of a strongly depleted group called the atmophile elements). A well argued view is that the events that led to the creation of the Moon about 4.5 billion years ago also established the bulk properties of the Earth and probably determined its overall composition and the sizes of its atmospheres and oceans.
Along with the remaining
hydrogen and helium the other elements grouped into rocky materials. Initially it was thought that early volcanic activity produced a new secondary atmosphere (sometimes called a 'primordial atmosphere') composed of water, carbon dioxide and nitrogen molecules with traces of carbon monoxide and molecular hydrogen. But with no methane or ammonia, and no free oxygen and therefore no dioxygen which today provides an important protect again ultraviolet radiation through the creation of ozone layer. However it is now thought that 'icy' material in the form of comets, etc. also became trapped in the mantle (see the Late Heavy Bombardment and crater counting). The icy materials included water, carbon dioxide, methane, ammonia, and sulfur dioxide. At the time experiments were being performed that showed that a wide range of amino acids and other prebiotic molecules could be formed by electric discharges (or ultraviolet radiation) in a highly reduced atmosphere containing methane, ammonia, and water. The idea is that the icy materials were turned into gases in the warm mantle and released to the surface to produce a secondary atmosphere. Today it is thought that Earth's 'primordial' atmosphere consisted of methane, ammonia, dioxygen, water, and dinitrogen, along with smaller quantities of sulfur dioxide, hydrogen sulphide, hydrochloric acid, nitrogen dioxide, and the noble gases.
Earth the temperature was just right for the formation of liquid water in the form of early oceans, and because the Earth had a reduced atmosphere the carbon dioxide was dissolved in the liquid water to produce carbonate rocks. Most of the oxygen would have been locking in the liquid water, but some oxygen would have been released by photodisintegration of water vapour in the upper atmosphere. The original secondary atmosphere would have been nitrogen and carbon dioxide rich. Most of today's oxygen comes from photosynthesis, but the first appearance of molecular oxygen (dioxygen) has been associated with the Great Oxidation Event around 2.4 billion years ago and the appearance of cyanobacteria.
atmospheric escape is name for the collective loss of Earth's atmosphere to outer space. It has been estimated that the Earth's oceans have lost about a quarter of their original mass, i.e. through a process of methanogenesis hydrogen was released and then lost from the Earth's atmosphere. And even today it has been estimated that the Earth is still losing nearly 100,000 tons of hydrogen per year. For anyone interested in comparative planetology this article on "Earth's Earliest Atmospheres" is a good starting point.

Simulated vertical optical depth of the targeted constituents for 55°N around 10 a.m. The strong absorbers are plotted in the upper part and the relevant weak absorbers in the middle part. In the lower part, the vertical optical depth due to Rayleigh scattering, aerosol extinction and absorption is given. Note the large dynamic range of the differential absorption structures used for retrieval of the constituents. (Courtesy: IUP-IFE, University of Bremen)

Seasonal average of SCIAMACHY UV Aerosol Index for July-September 2005. Blue indicates absorbing aerosols (mineral dust, biomass burning smoke); red/orange indicate weakly absorbing but scattering aerosols (sulphate and secondary organic aerosols) and remaining clouds. Only pixels with cloud fraction smaller than 5% are included in the average. (Courtesy : M. Penning de Vries, MPI for Chemistry, Mainz)

Saharan desert dust outbreak to the Atlantic on 25 July 2004. Shown is the SCIAMACHY AAI at 9:15 UTC of that day overlaid on a MODIS RGB picture, acquired around 11:10 UTC (right side of the plot) and 12:50 UTC (left side of the plot). High SCIAMACHY AAI values coincide with the dust plume, visible as a yellow haze on the MODIS image. (Courtesy: de Graaf et al. 2007)

Absorbed Aerosol Index AAI


Main article: Raman scattering
When a photon is the incident particle, there is an inelastic scattering process called Raman scattering. In this scattering process, the incident photon interacts with matter (gas, liquid, and solid) and the frequency of the photon is shifted towards red or blue. A red shift can be observed when part of the energy of the photon is transferred to the interacting matter, where it adds to its internal energy in a process called Stokes Raman scattering. The blue shift can be observed when internal energy of the matter is transferred to the photon; this process is called anti-Stokes Raman scattering.
Inelastic scattering is seen in the interaction between an electron and a photon. When a high-energy photon collides with a free electron and transfers energy, the process is called Compton scattering. Furthermore, when an electron with relativistic energy collides with an infrared or visible photon, the electron gives energy to the photon. This process is called inverse Compton scattering.

  • In Rayleigh scattering a photon penetrates into a medium composed of particles whose sizes are much smaller than the wavelength of the incident photon. In this scattering process, the energy (and therefore the wavelength) of the incident photon is conserved and only its direction is changed. In this case, the scattering intensity is proportional to the fourth power of the reciprocal wavelength of the incident photon.

The key two parameters are time of exposure and
Sun angle, and also the thickness of the atmosphere that solar radiation has to pass through also plays a role.

In meteorological terms, the
solstices (the maximum and minimum insolation) do not fall in the middle of summer or winter. The heights of these seasons can occur up to 7 weeks later.’s-climate-history.html

Regardless of the time of year, the northern and southern hemispheres always experience opposite seasons. The two instants when the Sun is directly overhead at the Equator are the equinoxes. Also at that moment, both the North Pole and the South Pole of the Earth are just on the terminator, and hence day and night are equally divided between the two hemispheres. Around the March equinox, the Northern Hemisphere will be experiencing spring as the hours of daylight increase, and the Southern Hemisphere is experiencing autumn as daylight hours shorten.

The effect of axial tilt is observable as the change in day length and altitude of the Sun at solar noon (the Sun's culmination) during the year. The low angle of Sun during the winter months means that incoming rays of solar radiation are spread over a larger area of the Earth's surface, so the light received is more indirect and of lower intensity. Between this effect and the shorter daylight hours, the axial tilt of the Earth accounts for most of the seasonal variation in climate in both hemispheres.

In astronomical reckoning by hours of daylight alone, the solstices and equinoxes are in the middle of the respective seasons. Because of seasonal lag due to thermal absorption and release by the oceans, regions with a continental climate, which predominate in the Northern Hemisphere, often consider these four dates to be the start of the seasons as in the diagram, with the cross-quarter days considered seasonal midpoints. The length of these seasons is not uniform because of Earth's elliptical orbit and its different speeds along that orbit

In addition the
Earth's axial tilt is not fixed, there is an axial precession, so that the axial tilt oscillates between 22.1° and 24.5° over a period of 26,000 years. Now this might appear to be a trivial detail, but is it?
So the Earth orbits, spins, and precesses. A lot of people don't know that the Earth precesses, but those who are passionate about observing the night sky do. We will come back to axial precession later, but for the time being all we need to know is that it exists and is caused by

Tidal locking occurs when an orbiting body (anything from a star to a planet to a moon) always has the same face towards the object it is orbiting. So the orbiting body takes just as long to rotate around its own axis as it does to complete one orbit around its partner. The Moon is tidally locked, because it always present the same hemisphere (face) to the Earth.
It is obvious that the Moon will also affect the rotation and orbit of the Earth, but to a lesser degree. In fact, as revealed in the fossil record, over the last ca. 4.5 billion years the Sun and the Moon acting together have lengthened the Earth day from about 6 hours to the current 24 hours. To be more precise the Earth rotates once every 23 hours, 56 minutes, and 4 seconds, with respect to distant stars. The tidal effects of the Moon is still slowing down Earth's rotation by about 1.7 milliseconds every century.

tropical year

The assumption is that the
Sun revolves around a stationary Earth on what is called a celestial sphere, which rotates every 24 hours about an axis that connects the celestial poles.

Tidal interactions

Over millions of years, Earth's rotation has been slowed significantly by tidal acceleration through gravitational interactions with the Moon. Thus angular momentum is slowly transferred to the Moon at a rate proportional to
is the orbital radius of the Moon. This process has gradually increased the length of the day to its current value, and resulted in the Moon being tidally locked with Earth.
This gradual rotational deceleration is empirically documented by estimates of day lengths obtained from observations of tidal rhythmites and stromatolites; a compilation of these measurements found that the length of the day has increased steadily from about 21 hours at 600 Myr ago to the current 24-hour value. By counting the microscopic lamina that form at higher tides, tidal frequencies (and thus day lengths) can be estimated, much like counting tree rings, though these estimates can be increasingly unreliable at older ages.
Resonant stabilization

A simulated history of Earth's day length, depicting a resonant-stabilizing event throughout the Precambrian era.

The current rate of tidal deceleration is anomalously high, implying Earth's rotational velocity must have decreased more slowly in the past. Empirical data tentatively shows a sharp increase in rotational deceleration about 600 Myr ago. Some models suggest that Earth maintained a constant day length of 21 hours throughout much of the Precambrian.[42] This day length corresponds to the semidiurnal resonant period of the thermally-driven atmospheric tide; at this day length, the decelerative lunar torque could have been canceled by an accelerative torque from the atmospheric tide, resulting in no net torque and a constant rotational period. This stabilizing effect could have been broken by a sudden change in global temperature. Recent computational simulations support this hypothesis and suggest the Marinoan or Sturtian glaciations broke this stable configuration about 600 Myr ago; the simulated results agree quite closely with existing paleorotational data.
Global events
Some recent large-scale events, such as the 2004 Indian Ocean earthquake, have caused the length of a day to shorten by 3 microseconds by reducing Earth's moment of inertia Post-glacial rebound, ongoing since the last Ice age, is also changing the distribution of Earth's mass, thus affecting the moment of inertia of Earth and, by the conservation of angular momentum, Earth's rotation period
The length of the day can also be influenced by manmade structures. For example, NASA scientists calculated that the water stored in the Three Gorges Dam has increased the length of Earth's day by 0.06 microseconds due to the shift in mass.

Most of the largest
natural satellites are tidally locked, with one face permanently turned towards their parent planet. The expression 'natural satellite' includes 'regular satellites' and 'irregular moons', with the following definitions:-
natural satellite
regular satellite
irregular moon


In the previous discussions I vaguely referred to the period of the moon's phases as "a month". In fact, the Moon repeats its phases in 29.5 days, which is called the synodic period.

  • This means that the period of the phases is almost, but not quite, synchronous with our calendar months of 28, (29), 30 or 31 days.
  • The lack of perfect synchronization means that the actual days of the month on which certain phases occur shifts systematically throughout the year, and from one year to the next.
However, the actual period of the Moon's orbit around the Earth (and its resonant period of rotation on its axis) is NOT 29.5 days, but rather 27.3 days with respect to the stars. As you might expect, this is called the Moon's sidereal period.

Why do the sidereal and synodic periods differ? In analogy with the difference between a solar day and a sidereal day, the difference between a synodic month and a sidereal month has to do with the fact that while the Moon is orbiting the Earth, the Earth-Moon system is orbiting the Sun.

  • A sidereal month is the time for the Moon to orbit the Earth with respect to the stars.
  • A synodic month is the time for the Moon to orbit the Earth with respect to the Sun, and is the time for one complete cycle of phases.
  • In the figure the Moon starts off at New Moon phase.
  • In a sidereal period (27.3 days) of the Moon's revolution about the Earth, when the Moon returns to the same position in the sky with respect to the stars, the Earth has actually advanced (27.3 / 365.24) ~ 1/13 of one revolution in its orbit around the Sun. This amount of revolution about the Sun is about 27o.
  • But at this point, the Moon has not yet returned to the New Moon phase, and has therefore not completed one full cycle of phases or one revolution with respect to the Sun. To do so, the Moon must orbit an extra 27o in its orbit.
  • Thus, one synodic period, i.e., cycle of phases, corresponds to a true 387o of revolution around the Earth, and this extra amount of motion requires an extra 2.2 days.
  • The motion of the Moon with respect to the Sun and stars is now easily understood:
    • In one day, the Moon circles (1/27.3) of its orbit around the Earth, which is equivalent to 13o around EASTWARD compared to the stars.
    • However, the Sun appears to move about 1o EASTWARD with respect to the stars as well, so, compared to the Sun, the Moon appears to go only a net 12o EASTWARD per 24 hour, human day.
    • This 12o per day eastward motion of the Moon with respect to the stars corresponds to the moon rising, transiting and setting about 50 minutes later per day.
    • Because the Moon moves 13 degrees per day eastward with respect to the stars, but is itself a half degree wide, this means it moves 26 moon diameters with respect to the stars in a day, or its own diameter in little less than about an hour.

    In the above I've tried very rapidly to introduce how the solar system, with the Sun and its planets and moons, was formed. For a different perspective, have a look at these impressive videos on YouTube:-
    National Geographic with
    Origins of the Universe 101, Solar System 101 and Sun 101
    Naked Science with
    Birth of the Universe and Birth of the Earth
    The Origin of the Earth
    Simulating Solar System Formation
    And to finish with
    Real Images from the Solar System.

    And just before we (finally) start to look at
    calendars take a look at this really cool visualisation about the true scale of our solar system and some of the stars in our night sky.

    The next step is to introduce a lot of new vocabulary associated with what we see when we look at the
    Sun, the stars in our night sky, and the Moon.

    Earth-Night Sky

    Axis Tilt Celestial Sphere

    We have said that the Earth orbits, spins, and precesses. Let's start with the celestial equator and the celestial poles.

    Firstly, the
    equator is defined with a latitude of 0° and is equidistant from the geographic poles (latitude 0° is also known as a great circle). Besides the equator there are four other notable circles of latitude, namely the polar circles and the tropical circles:-
    Arctic Circle - ca. 66° 33' North of the equator
    Tropic of Cancer - ca. 23° 26' North of the equator
    Equator - 0°
    Tropic of Capricorn - ca. 23° 26' South of the equator
    Antarctic Circle - ca. 66° 33' South of the equator
    As you can probably guess the Tropic of Cancer was named because at that time the Sun was positioned in the Cancer constellation during the June solstice (20-22 June), and likewise the Tropic of Capricorn were named because the Sun was in the constellation Capricorn during the December solstice (20-22 December). One report says the naming existed some 2,000 years ago, although another source stated that the term Tropic of Cancer was first used in 1623 and Tropic of Capricorn in 1625.
    The choice of 23° 33' corresponds to the tilt of the
    Earth (today 23° 25'), and between the two tropical circles is where it is physically possible to find the Sun directly overhead at noon. Beyond the two limits the Sun cannot appear overhead. The two tropical circles define the boundary between the tropical zone and the temperate zone (everything between the polar circles and the tropical circles).

    The Arctic Circle covers about 4% of the Earth's surface and is home to about 4 million people living in Russia (Karelia), Norway, Finland, Sweden, Greenland (Denmark), Iceland, US (Alaska), and Canada (Yukon). Places that come to mind are Lapland (in both Finland and Sweden), Baffin Island (in Canada, and the fifth-largest island in the world) and the Barents Sea (Norway and Russia). Alert (82° north) in Canada is the northernmost permanently inhabited place in the world (but no permanent residents). The Antarctic Circle also covers about 4% of the Earth's surface, but there are no permanent residents.
    About 30% of the world's population lives in the
    Southern Hemisphere, but only about 3% of the world's population lives south of the Tropic of Capricorn.
    There are also some historically famous
    latitudes, namely:-
    17th Parallel North was the demarcation line between North and South Vietnam established in 1954
    Missouri Compromise Line (36° 30' N) was established in 1820 and prohibited slavery north on the line, but permitted it south of the line
    38th Parallel North was the border between North and South Korea prior to the Korean War
    Mason-Dixon Line (39° 34' N) was ratified in 1865 and became the border between the US slave states and free states
    49th Parallel North represents a substantial part of the Canada-US border
    60th Parallel North and the 60th Parallel South are half as long as the Equator line

    The North and South Poles are where the Earth's axis of rotation meets the surface. Looking down on the Earth's North Pole, the planet turns counter-clockwise. The North Pole is quite distinct from the North Magnetic Pole.

    The celestial equator and the celestial poles are imaginary indefinite extensions beyond the Earth's surface which intersect with the celestial sphere, an abstract sphere concentric to Earth. The idea is that all objects in the sky are projected on to the celestial sphere and the centre of the sphere is the observer. Because everything appears to be placed on the same single 'transparent' celestial sphere there is nothing to tell us how far away the different planets and stars are. The overall impression is that all objects seem equally far away, and fixed inside a sphere which rotates overhead from east to west, while the Earth seems to stand still. So the celestial sphere helps us visualise the motion of celestial bodies in the entire sky around Earth, and you can find star maps that can be used to identify and locate constellations and stars that you can see from any place on the Earth's surface and for any night of the year.

    Star Chart

    Now let's assume an observer is standing somewhere looking up at the
    night sky. They will not see the complete celestial sphere, but only a celestial hemisphere. And what they see will depend upon their exact location, and the exact time and date. So the celestial hemisphere is the observers local sky. Below we can see the observers visible part of the sky (Z in the zenith the highest point on the celestial sphere, CEq the celestial equator, and NCP/SCP the celestial poles).

    Local Sky

    They will see the Sun rise in the East and set in the West, and that will be followed by the stars rising in the East and later setting in the West. This is an apparent motion across our sky, because in fact the observer is moving in front of a fixed sky (with a fixed Sun and fixed stars) as the Earth orbits the Sun and rotates around its own axis. The apparent motion of celestial bodies around the two celestial poles is called diurnal motion.

    Equatorial Coordinate System

    To identified what we are seeing we will need to use a celestial coordinate system so we can give a location to every star that we can see. Wikipedia tells us that the equatorial coordinate system is the most widely used because it pinpoints all the visible objects in the night sky wherever the observer is located on the Earth's surface. It uses the celestial equator (an extension of the equator), the primary direction towards the March equinox (spring equinox or vernal equinox), and a right-handed convention (i.e. positive values going north and towards the east). A star's spherical coordinates can be expressed as a pair, right ascension and declination, without a distance coordinate.
    Right ascension (RA) is

    TWhile we use a physical location on Earth as our reference for longitude, what reference do we use for right ascension? Where is the 0° mark in the sky separating east from west? Astronomers use the spot the Sun arrives at on the first day of spring, called the vernal equinox. Presently, it's located in the constellation of Pisces, the Fish. The sky can be treated as a clock, since it wheels by as Earth rotates, so the zero point of right ascension is called "0h" for "zero hours." Unlike longitude, right ascension is measured in just one direction — east. Because there are 24 hours in a day, each hour of right ascension measured along the equator equals 1/24th of a circle (360° divided by 24) or 15°. That's a little more than one-half the width of the W-shaped constellation Cassiopeia.

    Declination (Dec.) is the angle measured north (positive) or south (negative) of the celestial equator, at a given point on the hour circle. The declination is equivalent to a latitude and is measured degrees (°), etc. on a sexagesimal base (base-60).
    So RA and Dec. (such as RA 2h 41m 39s, Dec. +89° 15' 51" for Polaris the North Star) unlocks the exact location of any particular star, provided you taken into consideration that stars circle the sky every 24 hours, so RA ranges from 0h to 24h.

    Winter Sky

    Here is an example of the night sky as you would have seen it in Cyprus (35° N) at midnight on 1 January 2011. The main point of orientation would have be the Big Dipper/Plough in the constellation Ursa Major (Great Bear), and Orion (the Hunter) would have been the main focus of attention. Also Sirius (the Dog Star) would have been the brightest star in the night sky. At this location the entire night sky would have rotated around a point near Polaris, a 2nd-magnitude star. Because Polaris is very close to the north celestial pole, it is currently the northern pole star, and is usually called the 'North Star' or 'Pole Star'.
    This means that a straight line dropped from the
    Polaris/North Star to the horizon would have pointed due north, and the altitude of the Polaris/North Star above the horizon was equal to the observers latitude north of the equator.
    spring the Big Dipper/Plough would have swung high overhead and would have been near the centre of the star chart. It would move to the northwest in the summer, and swinging out of view in autumn, before reappearing in the winter. To see the Big Dipper/Plough all year around (so-called circumpolar), you would need to be north of 40° N.

    Given that a
    star is very far away from Earth its direction remains unchanged. However, a star's position in the night sky will depend upon where the observer is located on the Earth's surface, and it will continually change as the Earth orbits and rotates. If an observer returns some weeks or months later to the exact same position and at exactly the same time, they will not see the same night sky.

    Earth rotates daily on its axis, so during the night all the star's will move across the observers celestial hemisphere from east to west. The star's will appear to move in circular paths around one of the celestial poles, this is called diurnal motion. Star's far from the celestial pole appear to rotate in large circles, whereas star's located very near to the celestial pole rotate in small circles and don't appear to have any diurnal motion at all.
    The observer will usually see some
    star's near the celestial pole that never set below the horizon. These are called circumpolar stars, and they all lie within a relative circumpolar circle. A circle centred on the celestial pole and with a radius equals the observer's latitude. Star's outside the circumpolar circle will dip below the horizon for some part of their daily circular path (naturally other star's remain permanently below the horizon). With the north celestial pole directly overhead all visible star's are circumpolar stars. At the equator the celestial pole will lie on the horizon and none will be circumpolar stars.
    So whether a
    star is a circumpolar star depends upon the observers latitude. Also the daily motion of a star across the sky is called diurnal motion, and takes the form of a diurnal circle, which may or may not be fully visible depending upon the observers latitude.
    As you might guess a
    circumpolar constellation is a constellation where none of the participants star's set below the horizon, as viewed from the observers latitude.

    Earth Rotation

    Above we have the very famous long-exposure photograph showing the apparent paths of the star's as the Earth rotates. We see that the only stationary point is the north celestial pole and each arc captures the motion of each individual celestial body. So the long-exposure has captured what is called diurnal motion. National Geographic has a video of time-lapse scenes, including some impressive ones of the night sky.

    Earth orbits the Sun, and if our observer stays at the same location on the Earth's surface and looks at the night sky at the same time every night, they will see that all the star's in their celestial hemisphere shift slowly from west to east. Let's say that our observer is watching for a particular star to rise. If our observer is looking at exactly the same place as yesterday, the star will appear 3 minutes 34 seconds earlier. If our observer decided to look for the star at exactly the same time as yesterday, they will find that it has moved to the west by about 1°. And each night the star will rise 3 minutes 34 seconds earlier than the day before. What has really happened is that the Earth has moved slightly as it orbits the Sun. So our observer is at same physical location on the Earth's surface, but that location relative to the star's in the night sky has moved. If our observer looks for their star through a full year they will think that it has made one full 360° circle of the Earth in 365 days (whereas what they have really done is to complete a full orbit of the Sun).

    Night Sky

    What we have describe about is true, but it's not the whole story. What our observer will actually see is very dependently upon where they are on the Earth's surface. If you look at the long-exposure photograph again you can see that those star's near the celestial pole complete a full circle, so they never actually rise or set. Other star's further away from the celestial pole will rise and set, and as a last (trivial) conclusion, there will be star's that always remain below the horizon and are never seen from that particular location on the Earth's surface. The star's seen all year round (from that specific location or latitude) are called circumpolar stars.

    Main articles: Fluctuations in the length of day and ΔT

    Earth's axial tilt is about 23.4°. It oscillates between 22.1° and 24.5° on a 41,000-year cycle and is currently decreasing.

    In rotational axis[edit]
    Earth's rotation axis moves with respect to the fixed stars (inertial space); the components of this motion are precession and nutation. It also moves with respect to Earth's crust; this is called polar motion.
    Precession is a rotation of Earth's rotation axis, caused primarily by external torques from the gravity of the Sun, Moon and other bodies. The polar motion is primarily due to free core nutation and the Chandler wobble.
    In rotational velocity[edit]
    Tidal interactions[edit]
    Over millions of years, Earth's rotation has been slowed significantly by tidal acceleration through gravitational interactions with the Moon. Thus angular momentum is slowly transferred to the Moon at a rate proportional to
    is the orbital radius of the Moon. This process has gradually increased the length of the day to its current value, and resulted in the Moon being tidally locked with Earth.
    This gradual rotational deceleration is empirically documented by estimates of day lengths obtained from observations of tidal rhythmites and stromatolites; a compilation of these measurements[41] found that the length of the day has increased steadily from about 21 hours at 600 Myr ago[42] to the current 24-hour value. By counting the microscopic lamina that form at higher tides, tidal frequencies (and thus day lengths) can be estimated, much like counting tree rings, though these estimates can be increasingly unreliable at older ages.[43]
    Resonant stabilization[edit]
    The current rate of tidal deceleration is anomalously high, implying Earth's rotational velocity must have decreased more slowly in the past. Empirical data[41] tentatively shows a sharp increase in rotational deceleration about 600 Myr ago. Some models suggest that Earth maintained a constant day length of 21 hours throughout much of the Precambrian.[42] This day length corresponds to the semidiurnal resonant period of the thermally-driven atmospheric tide; at this day length, the decelerative lunar torque could have been canceled by an accelerative torque from the atmospheric tide, resulting in no net torque and a constant rotational period. This stabilizing effect could have been broken by a sudden change in global temperature. Recent computational simulations support this hypothesis and suggest the Marinoan or Sturtian glaciations broke this stable configuration about 600 Myr ago; the simulated results agree quite closely with existing paleorotational data.[44]
    Global events[edit]

    Deviation of day length from SI based day

    Some recent large-scale events, such as the 2004 Indian Ocean earthquake, have caused the length of a day to shorten by 3 microseconds by reducing Earth's moment of inertia.[45] Post-glacial rebound, ongoing since the last Ice age, is also changing the distribution of Earth's mass, thus affecting the moment of inertia of Earth and, by the conservation of angular momentum, Earth's rotation period.[46]
    The length of the day can also be influenced by manmade structures. For example, NASA scientists calculated that the water stored in the Three Gorges Dam has increased the length of Earth's day by 0.06 microseconds due to the shift in mass.[47]

    How does the fact the
    Earth has moved slightly as it orbits the Sun affect what our observer sees? Let's say that our observer is watching for a particular star to rise and set. The reality is that star's don't rise and set, it's simply the setting and rising of the Sun that renders them 'invisible' during the day. And of course the Sun does not rise and set, it is the Earth rotation that causes the Sun to appear and disappear in our celestial hemisphere.

    At first glance, it seems like these ought to be the same.  If the Earth spins around 360°, then wouldn't both the stars and the Sun appear to go around 360° in our sky?  It turns out that the stars do (that's really just the definition of a sidereal day), but the Sun does not.  The Earth actually has to spin about an extra degree (for a total of 361°) for the Sun to appear back in its original location.
    The reason for this extra degree is that during the same time the Earth is spinning around 360° on its axis, it is also busy moving along its orbit around the Sun.  It takes the Earth about 365.25 days to orbit once around the Sun.  And one complete orbit is 360°.  So the Earth moves about 1° (really 360°/365.25636 or about 0.98561°) per (solar) day.  This 1° difference holds for Earth only, based on its sidereal day and orbital periods.  For other planets (and moons), the difference may be much more or less than 1 degree, based on their unique sidereal days and orbital periods.  Figure 1, below, shows the general case for any planet orbiting the Sun (or really, for any moon orbiting a planet as well; but we'll get back to that later).
    Since the Earth takes 4 minutes to rotate 1° (24h * 60min/hr = 1440min, so 1440min/360° = 4min/1°), a given star will, on average(5), rise about 4 minutes earlier each night.  Over the course of a 30-day month, that adds up to 4min*30 = 120 minutes.  That's 2 hours, which is how much earlier a given star rises each month (in Earth's sky, anyway).

    Cause and significance[edit]

    Sirius is the fixed star with the greatest apparent magnitude and one which is almost non-variable. The Pleiades, a key feature of Taurus shown across Orion in the same photograph also experience an annual period of visibility ("rising and setting").

    Relative to the other stars, the Sun appears to drift eastward (about 1365.24219 of Earth's orbit—hence almost one degree—per solar day) along a path called the ecliptic (specifically appearing in front of 12 constellations considered the zodiac constellations from a total of 88 modern constellations) which is, by definition, the plane of the earth's orbit. While the Sun appears in front of (or south or north of) a relatively small group of stars they can no longer be seen either before dawn, during daytime or after sunset[a]—their appearance coincides with that of the Sun above the horizon.
    Depending on the observer's latitude many stars are subject to annual heliacal risings and settings. Rising means the local latitude of the earth has moved along its orbit such that the star, star cluster or galaxy emerges for part of the year to within months be visible for the whole night and then for the early portion of the night. Thus the star's first emergence, an annual rise, is immediately before dawn. The risen status of each star is easiest considered day-on-day in the tropics where the time of dawn varies less.
    The rising of a star which has had its annual rising ("heliacal rising"), typically over months, rises earlier at night and so at dawn figures more toward its annual highest point (meridian) and then in later dawns more toward the west all by about 1182 of its arc (about 1365 of the circle) per day, until, observing the western sky after sunset, it has already disappeared. This is called the cosmical setting.[4] The same star will reappear in the eastern sky at dawn approximately one year after its previous rising. For zodiac and near-zodiac constellations (near the ecliptic, the apparent daily path of the Sun), Earth's precession means the date of their rising decreases gradually, completing one cycle in about 26,000 years (for example at the March Equinox, the position of the Sun relative to the stars—at which Right Ascension is calibrated as zero, the First Point of Aries, is in the preceding constellation of Pisces.)[5]
    Non-application to circumpolar stars[edit]
    Some stars, when viewed from latitudes not at the equator, do not rise or set. These are circumpolar stars, which are either always in the sky or never. For example, the North Star (Polaris) is not visible in Australia and the Southern Cross is not seen in Europe, because they always stay below the respective horizons.
    The term circumpolar is somewhat localised as between the Tropic of Cancer and the Equator, the Southern polar constellations have a brief spell of annual visibility (thus "heliacal" rising and "cosmic" setting) and the same applies as to the other polar constellations in respect of the reverse tropic.

    Axial tilt

    As a thought exercise, let's imagine that the
    Earth did not have an axial tilt between its rotational axis and its orbital axis. Assuming a perfectly circular orbit this would mean that each area of the exposed surface of the Earth would always get the same amount of sunlight depending upon its declination.

    Axial Precession

    In rotational axis[edit]
    Earth's rotation axis moves with respect to the fixed stars (inertial space); the components of this motion are precession and nutation. It also moves with respect to Earth's crust; this is called polar motion.
    Precession is a rotation of Earth's rotation axis, caused primarily by external torques from the gravity of the Sun, Moon and other bodies. The polar motion is primarily due to free core nutation and the Chandler wobble.

    Unlike Earth coordinates, celestial coordinates change due to the slow wobble of Earth's axis called precession. Precession causes the equinox points to drift westward at a rate of 50.3 arcseconds annually. As the equinox shifts, it drags the coordinate grid with it. That's why star catalogs and software programs have to be updated regularly to the latest "epoch." This is done every 50 years. Most catalogs and software currently use Epoch J2000.0 coordinates (for the year 2000). The next major update will happen in 2050.


    Polar Motion



    Earth's rotation period relative to the International Celestial Reference Frame, called its stellar day by the International Earth Rotation and Reference Systems Service (IERS), is 86,164.098 903 691 seconds of mean solar time (UT1) (23h 56m 4.098 903 691s, 0.997 269 663 237 16 mean solar days).[33][n 3] Earth's rotation period relative to the precessing mean vernal equinox, named sidereal day, is 86,164.090 530 832 88 seconds of mean solar time (UT1) (23h 56m 4.090 530 832 88s, 0.997 269 566 329 08 mean solar days).[33] Thus, the sidereal day is shorter than the stellar day by about 8.4 ms.[35]
    Both the stellar day and the sidereal day are shorter than the mean solar day by about 3 minutes 56 seconds. This is a result of the Earth turning 1 additional rotation, relative to the celestial reference frame, as it orbits the Sun (so 366.25 rotations/y). The mean solar day in SI seconds is available from the IERS for the periods 1623–2005[36] and 1962–2005.[37]
    Recently (1999–2010) the average annual length of the mean solar day in excess of 86,400 SI seconds has varied between 0.25 ms and 1 ms, which must be added to both the stellar and sidereal days given in mean solar time above to obtain their lengths in SI seconds (see Fluctuations in the length of day).


    We have said that the Earth
    orbits, spins, and precesses.

    moving night sky day by day

    The Analemma (part 2)

    Solar day , solar time

    Periods [edit]

    Starry circles arc around the south celestial pole, seen overhead at ESO's La Silla Observatory.[23]

    True solar day[edit]
    Main article: Solar time
    Earth's rotation period relative to the Sun (solar noon to solar noon) is its true solar day or apparent solar day. It depends on Earth's orbital motion and is thus affected by changes in the eccentricity and inclination of Earth's orbit. Both vary over thousands of years, so the annual variation of the true solar day also varies. Generally, it is longer than the mean solar day during two periods of the year and shorter during another two.[n 2] The true solar day tends to be longer near perihelion when the Sun apparently moves along the ecliptic through a greater angle than usual, taking about 10 seconds longer to do so. Conversely, it is about 10 seconds shorter near aphelion. It is about 20 seconds longer near a solstice when the projection of the Sun's apparent motion along the ecliptic onto the celestial equator causes the Sun to move through a greater angle than usual. Conversely, near an equinox the projection onto the equator is shorter by about 20 seconds. Currently, the perihelion and solstice effects combine to lengthen the true solar day near 22 December by 30 mean solar seconds, but the solstice effect is partially cancelled by the aphelion effect near 19 June when it is only 13 seconds longer. The effects of the equinoxes shorten it near 26 March and 16 September by 18 seconds and 21 seconds, respectively.[24][25][26]
    Mean solar day[edit]
    Main article: Solar time § Mean solar time
    The average of the true solar day during the course of an entire year is the mean solar day, which contains 86,400 mean solar seconds. Currently, each of these seconds is slightly longer than an SI second because Earth's mean solar day is now slightly longer than it was during the 19th century due to tidal friction. The average length of the mean solar day since the introduction of the leap second in 1972 has been about 0 to 2 ms longer than 86,400 SI seconds.[27][28][29] Random fluctuations due to core-mantle coupling have an amplitude of about 5 ms.[30][31] The mean solar second between 1750 and 1892 was chosen in 1895 by Simon Newcomb as the independent unit of time in his Tables of the Sun. These tables were used to calculate the world's ephemerides between 1900 and 1983, so this second became known as the ephemeris second. In 1967 the SI second was made equal to the ephemeris second.[32]
    The apparent solar time is a measure of Earth's rotation and the difference between it and the mean solar time is known as the equation of time.
    Stellar and sidereal day[edit]

    On a prograde planet like Earth, the stellar day is shorter than the solar day. At time 1, the Sun and a certain distant star are both overhead. At time 2, the planet has rotated 360° and the distant star is overhead again but the Sun is not (12 = one stellar day). It is not until a little later, at time 3, that the Sun is overhead again (13 = one solar day).

    Earth's rotation period relative to the International Celestial Reference Frame, called its stellar day by the International Earth Rotation and Reference Systems Service (IERS), is 86,164.098 903 691 seconds of mean solar time (UT1) (23h 56m 4.098 903 691s, 0.997 269 663 237 16 mean solar days).[33][n 3] Earth's rotation period relative to the precessing mean vernal equinox, named sidereal day, is 86,164.090 530 832 88 seconds of mean solar time (UT1) (23h 56m 4.090 530 832 88s, 0.997 269 566 329 08 mean solar days).[33] Thus, the sidereal day is shorter than the stellar day by about 8.4 ms.[35]
    Both the stellar day and the sidereal day are shorter than the mean solar day by about 3 minutes 56 seconds. This is a result of the Earth turning 1 additional rotation, relative to the celestial reference frame, as it orbits the Sun (so 366.25 rotations/y). The mean solar day in SI seconds is available from the IERS for the periods 1623–2005[36] and 1962–2005.[37]
    Recently (1999–2010) the average annual length of the mean solar day in excess of 86,400 SI seconds has varied between 0.25 ms and 1 ms, which must be added to both the stellar and sidereal days given in mean solar time above to obtain their lengths in SI seconds (see Fluctuations in the length of day).

    As a thought exercise, let's imagine that the
    Earth did not have an axial tilt between its rotational axis and its orbital axis. Assuming a perfectly circular orbit this would mean that each area of the exposed surface of the Earth would always get the same amount of sunlight depending upon its declination. Experts have argued that it would be too cold in the higher latitudes, and man would have been forced to live in the Earth's tropical mid-section. However, both hot-humid and hot-dry environments have low agricultural productivity, and neither would have been able to support large, complex societies.

    In the cycle of Earth's seasons, the equatorial plane runs through the Sun twice per year: on the equinoxes in March and September. To a person on Earth, the Sun appears to travel above the equator (or along the celestial equator) at these times. Light rays from the Sun's center are perpendicular to Earth's surface at the point of solar noon on the equator.
    Locations on the equator experience the shortest sunrises and sunsets because the Sun's daily path is nearly perpendicular to the horizon for most of the year. The length of daylight (sunrise to sunset) is almost constant throughout the year; it is about 14 minutes longer than nighttime due to atmospheric refraction and the fact that sunrise begins (or sunset ends) as the upper limb, not the center, of the Sun's disk contacts the horizon.
    Earth bulges slightly at the equator; the "average" diameter of Earth is 12,750 km (7,920 mi), but the diameter at the equator is about 43 km (27 mi) greater than at the poles.[2]


    The Earth's rotation around its axis, and revolution around the Sun, evolve over time due to gravitational interactions with other bodies in the Solar System. The variations are complex, but a few cycles are dominant.[1]
    The Earth's orbit varies between nearly circular and mildly elliptical (its eccentricity varies). When the orbit is more elongated, there is more variation in the distance between the Earth and the Sun, and in the amount of solar radiation, at different times in the year.
    In addition, the rotational tilt of the Earth (its obliquity) changes slightly. A greater tilt makes the seasons more extreme. Finally, the direction in the fixed stars pointed to by the Earth's axis changes (axial precession), while the Earth's elliptical orbit around the Sun rotates (apsidal precession). The combined effect is that proximity to the Sun occurs during different astronomical seasons.
    Milankovitch studied changes in these movements of the Earth, which alter the amount and location of solar radiation reaching the Earth. This is known as solar forcing (an example of radiative forcing). Milankovitch emphasized the changes experienced at 65° north due to the great amount of land at that latitude. Land masses change temperature more quickly than oceans, because of the mixing of surface and deep water and the fact that soil has a lower volumetric heat capacity than water.
    Orbital eccentricity[edit]
    Main article: Orbital eccentricity
    The Earth's orbit approximates an ellipse. Eccentricity measures the departure of this ellipse from circularity. The shape of the Earth's orbit varies between nearly circular (with the lowest eccentricity of 0.000055) and mildly elliptical (highest eccentricity of 0.0679).[2] Its geometric or logarithmic mean is 0.0019. The major component of these variations occurs with a period of 413,000 years (eccentricity variation of ±0.012). Other components have 95,000-year and 125,000-year cycles (with a beat period of 400,000 years). They loosely combine into a 100,000-year cycle (variation of −0.03 to +0.02). The present eccentricity is 0.017 and decreasing.
    Eccentricity varies primarily due to the gravitational pull of Jupiter and Saturn. However, the semi-major axis of the orbital ellipse remains unchanged; according to perturbation theory, which computes the evolution of the orbit, the semi-major axis is invariant. The orbital period (the length of a sidereal year) is also invariant, because according to Kepler's third law, it is determined by the semi-major axis.

    Effect on temperature[edit]
    The semi-major axis is a constant. Therefore, when Earth's orbit becomes more eccentric, the semi-minor axis shortens. This increases the magnitude of seasonal changes.[3]
    The relative increase in solar irradiation at closest approach to the Sun (perihelion) compared to the irradiation at the furthest distance (aphelion) is slightly larger than four times the eccentricity. For Earth's current orbital eccentricity, incoming solar radiation varies by about 6.8%, while the distance from the Sun currently varies by only 3.4% (5.1 million km or 3.2 million mi or 0.034 au).
    Perihelion presently occurs around January 3, while aphelion is around July 4. When the orbit is at its most eccentric, the amount of solar radiation at perihelion will be about 23% more than at aphelion. However, the Earth's eccentricity is always so small that the variation in solar irradiation is a minor factor in seasonal climate variation, compared to axial tilt and even compared to the relative ease of heating the larger land masses of the northern hemisphere.
    Effect on lengths of seasons[edit]

    Season durations[4]







    NorthernSouthernDate: Season
    2005Winter Summer solstice21 December 2005 18:3588.99 days
    2006Spring Autumn equinox20 March 2006 18:2692.75 days
    2006Summer solsticeWinter solstice21 June 2006 12:2693.65 days
    2006Autumn equinoxSpring equinox23 September 2006 4:0389.85 days
    2006Winter solsticeSummer solstice22 December 2006 0:2288.99 days
    2007Spring equinoxAutumn equinox21 March 2007 0:0792.75 days
    2007Summer solsticeWinter solstice21 June 2007 18:0693.66 days
    2007Autumn equinoxSpring equinox23 September 2007 9:5189.85 days
    2007Winter solsticeSummer solstice22 December 2007 06:08 
    The seasons are quadrants of the Earth's orbit, marked by the two solstices and the two equinoxes. Kepler's second law states that a body in orbit traces equal areas over equal times; its orbital velocity is highest around perihelion and lowest around aphelion. The Earth spends less time near perihelion and more time near aphelion. This means that the lengths of the seasons vary.
    Perihelion currently occurs around January 3, so the Earth's greater velocity shortens winter and autumn in the northern hemisphere. Summer in the northern hemisphere is 4.66 days longer than winter, and spring is 2.9 days longer than autumn.
    Greater eccentricity increases the variation in the Earth's orbital velocity. However, currently, the Earth's orbit is becoming less eccentric (more nearly circular). This will make the seasons more similar in length.
    Axial tilt (obliquity)[edit]
    Main article: Axial tilt
    The angle of the Earth's axial tilt with respect to the orbital plane (the obliquity of the ecliptic) varies between 22.1° and 24.5°, over a cycle of about 41,000 years. The current tilt is 23.44°, roughly halfway between its extreme values. The tilt last reached its maximum in 8,700 BCE. It is now in the decreasing phase of its cycle, and will reach its minimum around the year 11,800 CE.
    Increased tilt increases the amplitude of the seasonal cycle in insolation, providing more solar radiation in each hemisphere's summer and less in winter. However, these effects are not uniform everywhere on the Earth's surface. Increased tilt increases the total annual solar radiation at higher latitudes, and decreases the total closer to the equator.
    The current trend of decreasing tilt, by itself, will promote milder seasons (warmer winters and colder summers), as well as an overall cooling trend. Because most of the planet's snow and ice lies at high latitude, decreasing tilt may encourage the onset of an ice age for two reasons: There is less overall summer insolation, and also less insolation at higher latitudes, which melts less of the previous winter's snow and ice.

    Axial precession[edit]
    Main article: Axial precession
    Axial precession is the trend in the direction of the Earth's axis of rotation relative to the fixed stars, with a period of 25,771.5 years. This motion means that eventually Polaris will no longer be the north pole star. It is caused by the tidal forces exerted by the Sun and the Moon on the solid Earth; both contribute roughly equally to this effect.
    Currently, perihelion occurs during the southern hemisphere's summer. This means that solar radiation due to (1) axial tilt inclining the southern hemisphere toward the Sun and (2) the Earth's proximity to the Sun, both reach maximum during the southern summer and both reach minimum during the southern winter. Their effects on heating are thus additive, which means that seasonal variation in irradiation of the southern hemisphere is more extreme. In the northern hemisphere, these two factors reach maximum at opposite times of the year: The north is tilted toward the Sun when the Earth is furthest from the Sun. The two effects work in opposite directions, resulting in less extreme variations in insolation.
    In about 13,000 years, the north pole will be tilted toward the Sun when the Earth is at perihelion. Axial tilt and orbital eccentricity will both contribute their maximum increase in solar radiation during the northern hemisphere's summer. Axial precession will promote more extreme variation in irradiation of the northern hemisphere and less extreme variation in the south.
    When the Earth's axis is aligned such that aphelion and perihelion occur near the equinoxes, axial tilt will not be aligned with or against eccentricity.
    Apsidal precession[edit]
    Main article: Apsidal precession

    In addition, the orbital ellipse itself precesses in space, in an irregular fashion, completing a full cycle every 112,000 years relative to the fixed stars.[5] Apsidal precession occurs in the plane of the ecliptic and alters the orientation of the Earth's orbit relative to the ecliptic. This happens primarily as a result of interactions with Jupiter and Saturn. Smaller contributions are also made by the sun's oblateness and by the effects of general relativity that are well known for Mercury.
    Apsidal precession combines with the 25,771.5-year cycle of axial precession (see above) to vary the position in the year that the Earth reaches perihelion. Apsidal precession shortens this period to 23,000 years on average (varying between 20,800 and 29,000 years).[5]

    As the orientation of Earth's orbit changes, each season will gradually start earlier in the year. Precession means the Earth's nonuniform motion (see above) will affect different seasons. Winter, for instance, will be in a different section of the orbit. When the Earth's apsides (extremes of distance from the sun) are aligned with the equinoxes, the length of spring and summer combined will equal that of autumn and winter. When they are aligned with the solstices, the difference in the length of these seasons will be greatest.
    Orbital inclination[edit]
    Main article: Orbital inclination
    The inclination of Earth's orbit drifts up and down relative to its present orbit. This three-dimensional movement is known as "precession of the ecliptic" or "planetary precession". Earth's current inclination relative to the invariable plane (the plane that represents the angular momentum of the Solar System, approximately the orbital plane of Jupiter) is 1.57°.
    Milankovitch did not study planetary precession. It was discovered more recently and measured, relative to Earth's orbit, to have a period of about 70,000 years. However, when measured independently of Earth's orbit, but relative to the invariable plane, precession has a period of about 100,000 years. This period is very similar to the 100,000-year eccentricity period. Both periods closely match the 100,000-year pattern of glacial events.[6]
    Theory constraints[edit]
    Tabernas Desert, Spain: Cycles can be observed in the colouration and resistance of different strata of sediments.
    Materials taken from the Earth have been studied to infer the cycles of past climate. Antarctic ice cores contain trapped air

    The Babylonians were the first to realize that the Sun's motion along the ecliptic was not uniform, though they were unaware of why this was; it is today known that this is due to the Earth moving in an elliptic orbit around the Sun, with the Earth moving faster when it is nearer to the Sun at perihelion and moving slower when it is farther away at aphelion.[1]
    In the 17th century, Johannes Kepler discovered that the orbits along which the planets travel around the Sun are ellipses with the Sun at one focus, and described this in his first law of planetary motion. Later, Isaac Newton explained this as a corollary of his law of universal gravitation.


    By astronomical convention, the four seasons are determined by the solstices (the two points in the Earth's orbit of the maximum tilt of the Earth's axis, toward the Sun or away from the Sun) and the equinoxes (the two points in the Earth's orbit where the Earth's tilted axis and an imaginary line drawn from the Earth to the Sun are exactly perpendicular to one another). The solstices and equinoxes divide the year up into four approximately equal parts. In the northern hemisphere winter solstice occurs on or about December 21; summer solstice is near June 21; spring equinox is around March 20; and autumnal equinox is about September 23.[7] The effect of the Earth's axial tilt in the southern hemisphere is the opposite of that in the northern hemisphere, thus the seasons of the solstices and equinoxes in the southern hemisphere are the reverse of those in the northern hemisphere (e.g. the northern summer solstice is at the same time as the southern winter solstice).
    In modern times, Earth's perihelion occurs around January 3, and the aphelion around July 4 (for other eras, see precession and Milankovitch cycles). The changing Earth–Sun distance results in an increase of about 6.9% [8] in total solar energy reaching the Earth at perihelion relative to aphelion. Since the southern hemisphere is tilted toward the Sun at about the same time that the Earth reaches the closest approach to the Sun, the southern hemisphere receives slightly more energy from the Sun than does the northern over the course of a year. However, this effect is much less significant than the total energy change due to the axial tilt, and most of the excess energy is absorbed by the higher proportion of surface covered by water in the southern hemisphere.[9]
    The Hill sphere (gravitational sphere of influence) of the Earth is about 1,500,000 kilometers (0.01 AU) in radius, or approximately four times the average distance to the Moon.[10][nb 2] This is the maximal distance at which the Earth's gravitational influence is stronger than the more distant Sun and planets. Objects orbiting the Earth must be within this radius, otherwise they may become unbound by the gravitational perturbation of the Sun.

    Astronomical timing as the basis for designating the temperate seasons dates back at least to the
    Julian calendar used by the ancient Romans. It continues to be used on many modern Gregorian calendars worldwide, although some countries like Australia, New Zealand, Pakistan and Russia prefer to use meteorological reckoning. The precise timing of the seasons is determined by the exact times of transit of the sun over the tropics of Cancer and Capricorn for the solstices and the times of the sun's transit over the equator for the equinoxes, or a traditional date close to these times.[19]
    The following diagram shows the relation between the line of solstice and the line of apsides of Earth's elliptical orbit. The orbital ellipse (with eccentricity exaggerated for effect) goes through each of the six Earth images, which are sequentially the perihelion (periapsis—nearest point to the sun) on anywhere from 2 January to 5 January, the point of March equinox on 19, 20 or 21 March, the point of June solstice on 20 or 21 June, the aphelion (apoapsis—farthest point from the sun) on anywhere from 4 July to 7 July, the September equinox on 22 or 23 September, and the December solstice on 21 or 22 December.

    These "astronomical" seasons are not of equal length, because of the
    elliptical nature of the orbit of the Earth, as discovered by Johannes Kepler. From the March equinox it currently takes 92.75 days until the June solstice, then 93.65 days until the September equinox, 89.85 days until the December solstice and finally 88.99 days until the March equinox.
    Variation due to calendar misalignment[edit]
    The times of the equinoxes and solstices are not fixed with respect to the modern Gregorian calendar, but fall about six hours later every year, amounting to one full day in four years. They are reset by the occurrence of a leap year. The Gregorian calendar is designed to keep the March equinox no later than 21 March as accurately as is practical. Also see: Gregorian calendar seasonal error.
    The calendar equinox (used in the calculation of Easter) is 21 March, the same date as in the Easter tables current at the time of the Council of Nicaea in AD 325. The calendar is therefore framed to prevent the astronomical equinox wandering onto 22 March. From Nicaea to the date of the reform, the years 500, 600, 700, 900, 1000, 1100, 1300, 1400 and 1500, which would not have been leap years in the Gregorian calendar, amount to nine days, but astronomers directed that ten days be removed.
    Currently, the most common equinox and solstice dates are March 20, June 21, September 22 or 23 and December 21; the four-year average slowly shifts to earlier times as the century progresses. This shift is a full day in about 128 years (compensated mainly by the century "leap year" rules of the Gregorian calendar) and as 2000 was a leap year the current shift has been progressing since the beginning of the last century, when equinoxes and solstices were relatively late. This also means that in many years of the twentieth century, the dates of March 21, June 22, September 23 and December 22 were much more common, so older books teach (and older people may still remember) these dates.
    Note that all the times are given in UTC (roughly speaking, the time at Greenwich, ignoring British Summer Time). People living farther to the east (Asia and Australia), whose local times are in advance, will see the astronomical seasons apparently start later; for example, in Tonga (UTC+13), an equinox occurred on September 24, 1999, a date which will not crop up again until 2103. On the other hand, people living far to the west (America) whose clocks run behind UTC may experience an equinox as early as March 19.
    Change over time[edit]
    Over thousands of years, the Earth's axial tilt and orbital eccentricity vary (see Milankovitch cycles). The equinoxes and solstices move westward relative to the stars while the perihelion and aphelion move eastward. Thus, ten thousand years from now Earth's northern winter will occur at aphelion and northern summer at perihelion. The severity of seasonal change — the average temperature difference between summer and winter in location — will also change over time because the Earth's axial tilt fluctuates between 22.1 and 24.5 degrees.
    Smaller irregularities in the times are caused by perturbations of the Moon and the other planets.

    Solar timing is based on insolation in which the solstices and equinoxes are seen as the midpoints of the seasons. It was the method for reckoning seasons in medieval Europe, especially by the Celts, and is still ceremonially observed in Ireland and some East Asian countries. Summer is defined as the quarter of the year with the greatest insolation and winter as the quarter with the least.
    The solar seasons change at the cross-quarter days, which are about 3–4 weeks earlier than the meteorological seasons and 6–7 weeks earlier than seasons starting at equinoxes and solstices. Thus, the day of greatest insolation is designated "midsummer" as noted in William Shakespeare's play A Midsummer Night's Dream, which is set on the summer solstice. On the Celtic calendar, the start of the seasons corresponds to four Pagan agricultural festivals - the traditional first day of winter is 1 November (Samhain, the Celtic origin of Halloween); spring starts 1 February (Imbolc, the Celtic origin of Groundhog Day); summer begins 1 May (Beltane, the Celtic origin of May Day); the first day of autumn is 1 August (Celtic Lughnasadh).

    The second thing to understand is that as the
    Moon orbits the Earth, we see the sunlit part of the Moon.

    Moon Phases

    In order to understand the Roman calendar we need to understand the lunar phases. In the above diagram the Sun is on the right, and the Earth is in the centre. In the middle, the dotted line represents a line of sight when you are on the Earth looking up at the Moon. The larger image of the Moon is what you would see.

    There are eight phases of the Moon in each month:-
    We start with a
    New Moon, where the side of the Moon facing us is not illuminated by the Sun. At this time the Moon is not up at night, but it is up duding the day (we just can't see it). Solar eclipse can occur during the New Moon, depending upon how the Sun, Earth, and Moon line up.
    As the
    Moon waxes (grows) into its crescent phase, it begins to show up as silvery-crescent in the night sky right after sunset. The site facing the sunset direction will be lit up.
    days after the New Moon, the Moon is in First Quarter. Only half of it is visible for the first half of the evening, and then it sets.
    After First Quarter, the Moon appears to grow into a gibbous shape (
    Waxing Gibbous). Most of it is visible, except for a dark sliver that shrinks over the next seven nights. The Moon is usually visible during the afternoon.
    During the
    Full Moon, the Sun lights up the entire surface of the Moon that faces Earth. It rises just as the Sun sets and diapers beneath the western horizon when the Sun rises the next morning. The Moon's orbit around the Earth is not perfectly symmetrical, and at times the Moon will look slightly larger than normal because it is little nearer to the Earth. Lunar eclipse occur only at Full Moons because the Moon is passing directly between Earth and the Sun in its orbit, but not every Full Moon results in an eclipse.
    After the Full Moon, the lunar shape starts to wane (get smaller), called
    Waning Gibbous. It is visible later at night and into the early morning, and we see a steadily shrinking shape of the lunar surface that's being lit up. The side that is lit up is facing toward the Sun, in this case, the sunrise direction. During this phase the Moon can often be seen in the morning sky.
    Last Quarter, is where we see exactly half of the sunlit surface of the Moon. It can be seen in the early morning and daytime sky.
    The last phase of the Moon before retiring to New Moon is called the
    Waning Crescent, and it is a steadily shrinking crescent phase. We can see only a small sliver from Earth. It's visible in the early morning, and by the end of the 28-day lion cycle, it has vanished almost entirely.

    calends signified the start of a new lunar phase, and on this day the pontiffs (priests) would announce, or 'call out', the number of days until the next month. In addition debts inscribed in the 'kalendaria' had to be paid on this day.

    Romans would count days differently, i.e. April 22 would be the 10th of the calends of May, meaning that it was the 10th day before the announcement of May. In fact they would add 2 days to 8 remaining days in the 28-day month.

    The original calendar consisted of ten months beginning in spring with
    March; winter was left as an unassigned span of days. These months ran for 38 nundinal cycles, each forming an eight-day week (nine days counted inclusively, hence the name) ended by religious rituals and a public market. The winter period was later divided into two months, January and February. The legendary early kings Romulus and Numa Pompilius were traditionally credited with establishing this early fixed calendar, which bears traces of its origin as an observational lunar one. In particular, the kalends, nones, and ides seem to have derived from the first sighting of the crescent moon, the first-quarter moon, and the full moon respectively. The system ran well short of the solar year, and it needed constant intercalation to keep religious festivals and other activities in their proper seasons. This is a typical element of lunisolar calendars. For superstitious reasons, such intercalation occurred within the month of February even after it was no longer considered the last month.

    Moon 101
    Earth 101

    Lunar Eclipse 101
    Solar Eclipse 101

    Gregorian calendar

    The Gregorian calendar, as used for civil and scientific purposes, is an international standard. It is a solar calendar that is designed to maintain synchrony with the mean tropical year (Dobrzycki 1983, p. 123). It has a cycle of 400 years (146,097 days). Each cycle repeats the months, dates, and weekdays. The average year length is 146,097/400 = 365
    97400 = 365.2425 days per year, a close approximation to the mean tropical year of 365.2422 days (Seidelmann 1992, pp. 576–81).
    The Gregorian calendar is a reformed version of the Julian calendar. By the time of the reform in 1582, the date of the vernal equinox had shifted about 10 days, from about March 21 at the time of the First Council of Nicaea in 325, to about March 11. According to North (1983), the real motivation for reform was not primarily a matter of getting agricultural cycles back to where they had once been in the seasonal cycle; the primary concern of Christians was the correct observance of Easter. The rules used to compute the date of Easter used a conventional date for the vernal equinox (March 21), and it was considered important to keep March 21 close to the actual equinox (North 1983, pp. 75–76).
    If society in the future still attaches importance to the synchronization between the civil calendar and the seasons, another reform of the calendar will eventually be necessary. According to Blackburn and Holford-Strevens (who used Newcomb's value for the tropical year) if the tropical year remained at its 1900 value of 365.24219878125 days the Gregorian calendar would be 3 days, 17 min, 33 s behind the Sun after 10,000 years. Aggravating this error, the length of the tropical year (measured in Terrestrial Time) is decreasing at a rate of approximately 0.53 s per century. Also, the mean solar day is getting longer at a rate of about 1.5 ms per century. These effects will cause the calendar to be nearly a day behind in 3200. The number of solar days in a "tropical millennium" is decreasing by about 0.06 per millennium (neglecting the oscillatory changes in the real length of the tropical year).[2] This means there should be fewer and fewer leap days as time goes on. A possible reform would be to omit the leap day in 3200, keep 3600 and 4000 as leap years, and thereafter make all centennial years common except 4500, 5000, 5500, 6000, etc. But the quantity ΔT is not sufficiently predictable to form more precise proposals (Blackburn & Holford-Strevens 2003, p. 692).

    Julian calendar

    Christian calendar

    Most of the world's Christians mark time on the solar Gregorian calendar, a late medieval correction of the much-older Julian calendar. Julius Caesar had initiated the calendar named after him in 46 b.c.e., but it was based on some miscalculations. In 1582, Pope Gregory XIII shortened the Julian year by ten days and added a day to February every fourth or "leap" year. Some Eastern Christian churches still use the Julian calendar, so that their major feasts fall just less than two weeks later than those of the Western churches. Until the Gregorian reform, Christians considered March 25 the beginning of the year, since that was judged to be the day on which Gabriel announced to Mary that she would give birth to Jesus. March 25, which had in ancient times been mistakenly calculated as the spring equinox, the first day of spring, remains the Feast of the Annunciation.
    For centuries Christians continued to observe the timing of traditional Jewish feasts, which were movable within limits of specific agricultural seasons (such as planting and harvest times). Using the Jewish seven-day week, Christians gradually added fixed feasts, such as those of saints and martyrs. The custom of designating Sunday as a day of religious observance began during the first generation after Jesus' death and Emperor Constantine decreed it a day of rest in 321. Wednesdays and Fridays had anciently been days of fasting, a practice now surviving largely on the first day of Lent, Good Friday, and other Fridays during Lent. For most Christians the year consists of three liturgical seasons, Advent and Christmastide, Lent and an Eastertide that ends with Pentecost Sunday, and "Ordinary" time until the first Sunday of the following Advent. Some Christians in Egypt and Ethiopia still use the solar Coptic calendar, based on the ancient Egyptian reckoning. Recent recalculations suggest that Jesus was actually born closer to 4 b.c.e. than to the year 1.

    Jewish calendar

    The Jewish calendar is lunisolar--that is, it is regulated by the positions of both the moon and the sun. There are twelve alternating lunar months of twenty-nine and thirty days each. The year totals 353, 354, or 355 days. Leap years are introduced to conform to the solar year of 365.25 days. Leap years contain either 383, 384, or 385 days and occur seven times in every nineteen-year period. This is called the Metonic cycle. The first month of the year is that in which the Exodus began. But tradition dictates that certain feasts must occur during certain seasons, so the calendar has to be adjusted every so often to prevent the lunar months from straying too far from the agricultural, or solar, cycle. To make it work, an extra month, called Adar Sheni (Second Adar), is added during seven out of every nineteen years. Thus, the number of days in a given year is not fixed and may vary from 353 to 385 days, and the first day of the month can fall on any day of the week and will vary from year to year. The Jewish lunar months are called Tishri (September/October), Cheshvan (October/November), Kislev (November/December), Tevet (December/January), Shevat (January/February), Adar (February/March), Adar Sheni (Second Adar, inserted only in "leap years"), Nisan (March/April), Iyyar (April/May), Sivan (May/June), Tammuz (June/July), Av (July/August), and Elul (August/September). With the leap year provision, the lunar months slide back or forward but remain within the solar months indicated in parentheses.

    Muslin calendar

    Muslims follow a lunar calendar whose twelve months add up to 354 days. In a cycle of thirty lunar years, eleven are leap years, with one day added to the last month. During Muhammad's time the lunar months were associated with seasons (Ramadan means "extreme heat," Rabi' "rainy season," and Jumada "dry season," for example). As in the Jewish calendar, the pre-Islamic year maintained its connection with agricultural cycles and seasons by the intercalation of a whole month in certain years. Since the practice of intercalation ended around Muhammad's time, the Islamic lunar year rotates backward eleven days each year in relation to the Gregorian solar year. If Ramadan, for example, begins on January 12 this year, next year it will begin on January 1, and so on. Certain practical results of this backward rotation are worth noting because of the way timing can affect religious practice. When Ramadan (the ninth month) occurs in the dead of winter, when days are shortest, the fast from sunrise to sunset is less arduous than when Ramadan falls during the height of summer. Pilgrimage to Mecca can also be more strenuous when the season of Hajj (in the twelfth month) occurs during the hottest season. Muslims the world over therefore must learn to work with two different systems of marking special times. Muslims begin their count of years with the Hijra of 622. Approximately every thirty-three years the beginnings of the Islamic lunar and Gregorian solar years roughly coincide.

    Hindu calendar

    Combining lunar months with seasons of the solar year, the Hindu calendar functions somewhat like the Jewish. About every three years it inserts an extra month after a month with two new moons. Hindu lunar months vary from twenty-nine to thirty-two days. The names of the months, with the roughly corresponding Gregorian months in parentheses, are as follows: Chaitra (March/April), Vaishakha (April/May), Jyaistha (May/June), Asadhe (June/July), Shravana (July/August), Bhadrapada (August/September), Ashvina (September/October), Karttika (October/November), Margasivsa (November/December), Pansa (December/January), Magha (January/February), and Phalguna (February/March). Leap months take the name of the month preceding them.

    For ritual purposes, each month is divided into its dark and light halves, with associated celebrations, and the moment of the full moon is a time of celebration each month. And some festivals and observances fall each year on the same solar date. Each year is likened to a day in the life of the deities, with the solar solstices symbolizing sunrise and sundown. In addition to the complexity introduced by the blending of solar and lunar reckonings, systems vary still further from region to region in India. Historically, the greater Hindu religious calendar has been so full that virtually every day some Hindu community has celebrated some feast somewhere in the subcontinent. Hinduism is not unlike Roman Catholic and Eastern Orthodox traditions in that respect, except that the majority of the Christian religious feasts are those of saints, rather than of the deity as such. All of this makes for an immensely rich sense of the intersection of sacred times and places. Every day is appropriate for religious observance, and no one day of the week is set aside as an especially sacred time.

    Buddhist calendar

    Since Buddhism has long been identified with so many different cultural settings, there is some variation in the ways Buddhists keep track of sacred times. The basic religious calendar remains tied, at least nominally, to the ancient Hindu combination of lunar and solar reckoning, but many Buddhists now observe some festivities on fixed dates. The earliest Buddhists apparently did not concern themselves with marking special occurrences on their calendar. But within a generation or so, India's growing and spreading Buddhist communities began to incorporate religious social occasions into ordinary life. As Buddhist communities arose outside of India they naturally tended to blend religious observances imported by Buddhist missionaries with the indigenous festivities of the land. In most places where Buddhism is an important presence today, the reckoning of years begins with the date of the Buddha's entry into nirvana (which coincided with his death). In any given year, Buddhists observe various festal occasions. Some commemorate major events in the life of the Buddha, others celebrate different institutional features of the tradition, others are tied to seasonal festivities, and still others are linked to events only in certain countries.


    Whether Daoist, CCT, Buddhist, or Confucian, all Chinese have historically acknowledged the same overall reckoning of time. Official Confucian and CIT events were traditionally set by a Board of Astrology and promulgated by a Ministry of Rites. In overall structure, the Chinese lunar calendar consists of twelve months of twenty-nine or thirty days, since the time between new moons is about twenty-nine and a half days. The lunar year dovetails with the solar, with the intercalation of an extra month approximately every six years or when five additional days per year total thirty. Reckoning began around 2637 b.c.e., so that the year 2000 marked the year 4637. Each of the twelve animals of the Chinese zodiac is associated with a particular quality or event and gives its name to every twelfth year, beginning with the Rat (industry and prosperity) and proceeding in order through Ox (spring planting), Tiger (valor), Hare (longevity), Dragon (power and good fortune), Snake (cunning), Horse (perseverance), Sheep (filial piety) or Goat, Monkey (health), Rooster (protection), Dog (fidelity), and Pig (home and family). The year 2000 was the Year of the Dragon, 2001 that of the Snake, 2002 that of the Horse, and so on. Five full cycles, each named after one of the five elements (wood, fire, earth, metal and water) equals sixty years, an important interval for ritual purposes. Major annual markers are the winter (maximum Yin) and summer (maximum Yang) solstices and vernal and autumnal equinoxes when Yin and Yang are in balance. During each month, the most important times are the moments of new and full moon.


    Shinto reckoning of ritual time has been much influenced by Chinese traditions. As early as 675 c.e., religious Daoism had made a significant impact on the Japanese imperial court, which formally adopted many Daoist practices. Most importantly, the court set up a bureau of divination, called the Onmyoryo ("Office of Yin-Yang"), based on Daoist principles. One of the Onmyoryo's chief functions was to establish a liturgical calendar that patterned earthly life on the rhythms of the cosmos. This lunar calendar retains all the main features of its Chinese model, including the cycles of sixty years based on the combinations of twelve "branches" and ten "stems" (see the sections on Daoism and Confucianism). The Japanese call their Chinese version of the lunar calendar Kyureki, as distinct from the modern solar calendar adopted in 1872, the Shinreki. An early formal cycle of annual observance, called the nenchu gyoji, literally "year-round-discipline-rituals," developed as early as the tenth century c.e. Imperial authorities promulgated it in a vast historical record called the Engi-shiki ("Institutes of the Engi Era," 901-923 c.e.), an essential source of information about Shinto ritual in general. Japan's lunar calendar needs to tuck in an extra month every three years or so.

    Prior to the nineteenth century, many Shinto shrines maintained their own calendars of events, including uniquely regional and local festivities. Today some major events still take place according to various ways of adapting the lunar calendar to fit the solar. For example, some festivals now occur on the same numbered day within the same numbered month, but transferred to the solar reckoning. In other words, a festival that fell on the seventh day of the seventh lunar month now falls on July 7. Some festivals are now dated by keeping the day date but adding a solar month, so that a celebration once held on the seventh day of the seventh month now occurs on August 7. Finally, and more rarely, a few days retain their lunar dating completely, so that they rotate backward against the solar year. From the solar point of view, therefore, these are moveable feasts. Since the late nineteenth century, the timing of the major festivals has been coordinated so that all the larger shrines observe them at the same time. But there are still many distinctive local and regional festivities attached to individual shrines, such as the rituals dedicated to the patron deities of particular places. In addition to the liturgical calendar, an important related feature is the Japanese custom of dividing history according to imperial reigns or epochs. Emperor Hirohito died in 1989, ending the Showa era, and his son Akihito's accession inaugurated the Heisei epoch.