Another way to look at it is that the Sun has made one full circuit of 360 degrees along the ecliptic in a year of 365.24 days (very close to 1 degree per day). The result is that between two consecutive meridian crossings of the Sun, the Earth has to turn nearly 361 degrees, not 360 degrees, in 24 hours. This makes the length of time for one solar day to be a little more than the true rotation rate of 23 hours 56 minutes with respect to the background stars.
Note that the Earth's rotation axis is always pointed toward the Celestial Poles. Currently the North Celestial Pole is very close to the star Polaris. The figure above shows this view of the Earth's nearly circular orbit from slightly above the orbital plane (hence, the very elliptical appearance of the orbit).
Imagine that at noon there is a huge arrow that is pointing at the Sun and a star directly in line behind the Sun. The observer on the Earth sees the Sun at its highest point above the horizon: on the arc going through the north-zenith-south points, which is called the meridian. The observer is also experiencing local noon. If the Sun were not there, the observer would also see the star on the meridian.
Now as time goes on, the Earth moves in its orbit and it rotates from west to east (both motions are counterclockwise if viewed from above the north pole). One sidereal period later (23 hours 56 minutes) or one true rotation period later, the arrow is again pointing toward the star. The observer on the Earth sees the star on the meridian. But the arrow is not pointing at the Sun! In fact the Earth needs to rotate a little more to get the arrow lined up with the Sun. The observer on the Earth sees the Sun a little bit east of the meridian. Four minutes later or one degree of further rotation aligns the arrow and Sun and you have one solar day (24 hours) since the last time the Sun was on the meridian. The geometry of the situation also shows that the Earth moves about 1 degree in its orbit during one sidereal day. That night the Earth observer will see certain stars visible like those in Taurus, for example. (Notice that the Earth's rotation axis is still pointed toward Polaris.) A half of a year later Taurus will not be visible but those stars in Scorpius will be visible. (Again, notice that the Earth's rotation axis is still pointed toward Polaris.) The extra angle any planet must rotate on its axis to get the Sun back to the meridian equals the angle amount the planet moved in its orbit in one sidereal day.
The Earth's sidereal day is always 23 hours 56 minutes long because the number of degrees the Earth spins through in a given amount of time stays constant. If you are careful, you will find that the solar day is sometimes slightly longer than 24 hours and sometimes slightly shorter than 24 hours. The reason for this is that the Earth's orbit around the Sun is elliptical and that the Sun's motion is not parallel to the celestial equator. The effects of this are explained fully in the Equation of Time section below. The value of 24 hours for the solar day is an average for the year and is what our time-keeping system is based on.
The precession of the Earth's rotation axis introduces another difference between sidereal time and solar time. This is seen in how the year is measured. A year is defined as the orbital period of the Earth. However, if you use the Sun's position as a guide, you come up with a time interval about 20 minutes shorter than if you use the stars as a guide. The time required for the constellations to complete one 360ƒ cycle around the sky and to return to their original point on our sky is called a sidereal year. This is the time it takes the Earth to complete exactly one orbit around the Sun and equals 365.2564 solar days.
The slow shift of the star coordinates from precession means that the Sun will not be at exactly the same position with respect to the celestial equator after one sidereal year. The tropical year is the time interval between two sucessive vernal equinoxes. It equals 365.2422 solar days and is the year our calendars are based on. After several thousand years the 20 minute difference between sidereal and tropical years would have made our summers occur several months earlier if we used a calendar based on the sidereal year.
| local noon | sidereal day | sidereal year |
|---|---|---|
| tropical year |
It used to be that every town's clocks were set according to their local noon and this got very confusing for the railroad system so they got the nation to adopt a more sensible clock scheme called time zones. Each person within a time zone has the same clock time. Each time zone is 15 degrees wide, corresponding to 15ƒ/minute × 4 minutes/degree = 60 minutes = 1 hour worth of time. Those in the next time zone east of you have clocks that are 1 hour ahead of yours. The Pacific timezone is centered on 120ƒ W longitude, the Mountain timezone is centered on 105ƒ longitude, etc.
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Another effect to consider is that the Earth's orbit is elliptical so when the Earth is at its closest point to the Sun (at perihelion), it moves quickest. When at its farthest point from the Sun (at aphelion), the Earth moves slowest. Remember that a solar day is the time between meridian passages of the Sun. At perihelion the Earth is moving rapidly so the Sun appears to move quicker eastward than at other times of the year. The Earth has to rotate through a greater angle to get the Sun back to local noon. This effect alone accounts for up to 10 minutes difference between the actual Sun and the mean Sun. |
However, the maximum and minimum of these two effects do not coincide so the combination of the two (called the Equation of Time) is a complicated relation shown in the figure below. The Equation of Time explains why, according to your clock, the earliest sunset and latest sunrise is not at the winter solstice. Yet, the shortest day is at the winter solstice. Rather than resetting our clocks every day to this variable Sun, our clocks are based on a uniformly moving Sun (the mean Sun) that moves along the celestial equator at a rate of 360 degrees/365.2564 per day. Aren't you glad that your watch keeps track of time for you?
Two popular theories are often stated to explain the temperature differences of the seasons: 1) the different distances the Earth is from the Sun in its elliptical orbit (at perihelion the Earth is 147.1 million kilometers from the Sun and at aphelion the Earth is 152.1 million kilometers from the Sun); and 2) the tilt of the Earth's axis with respect to its orbital plane. If the first theory were true, then both the north and south hemispheres should experience the same seasons at the same time. They don't. Using the scientific method discussed in chapters 1 and 2, you can reject the distance theory.
A popular variation of the distance theory says that the part of the Earth tilted toward the Sun should be hotter than the part tilted away from the Sun because of the differences in distances. If you continue along with this line of reasoning, then you conclude that the night side of the Earth is colder than the daylight side because the night side is farther away from the Sun. This ignores the more straightforward reason that the night side is directed opposite the Sun, so the Sun's energy does not directly reach it. But let's examine the tilt-distance model a little more. The 23.5ƒ tilt of the Earth means that the north pole is about 5080 kilometers closer than the south pole toward the end of June. This is much, much smaller than the 152 million kilometer distance between the Sun and the Earth's center at that time. The amount of energy received decreases with the square of the distance.
If you calculate (152,000,000 + 5080)2/(152,000,000 - 5080)2, you will find that the north pole would get slightly over 1/100th of one percent more energy than the south pole. This is much too small a difference to explain the large temperature differences! Even if you compare one side of the Earth with the opposite side, so you use the Earth's diameter in place of the 5080 kilometers in the calculation above, you get 3/100th of one percent difference in energy received. Clearly, distance is not the reason for the large temperature differences. Notice that I used the aphelion value for the distance between the Earth and Sun. That is because the Earth is near aphelion during the northern hemisphere's summer! This is known by measuring the apparent size of the Sun. You can safely assume that the Sun's actual size does not vary with a period that depends on the orbital period of a planet thousands of times smaller than it, or that it would choose the Earth's orbital period as its pulsation cycle.
Even though the distance model (in any variation) is incorrect, it is still a ``good'' scientific theory in that it makes testable predictions of how the temperature should change throughout the year and by how much. However, what annoys scientists, particularly astronomy professors, is ignoring those predictions and the big conflicts between predictions and what is observed. Let's take a look at a model that correctly predicts what is observed.
The tilt theory correctly explains the seasons but the reason is a little more subtle than the distance theory's explanation. Because the Earth's rotation axis is tilted, the north hemisphere will be pointed toward the Sun and will experience summer while the south hemisphere will be pointed away from the Sun and will experience winter. During the summer the sunlight strikes the ground more directly (closer to perpendicular), concentrating the Sun's energy. This concentrated energy is able to heat the surface more quickly than during the winter time when the Sun's rays hit the ground at more glancing angles, spreading out the energy.
Also, during the summer the Sun is above the horizon for a longer time so its energy has more time to heat things up than during the winter.
The rotational axes of most of the other planets of the solar system are also tilted with respect to their orbital planes so they undergo seasonal changes in their temperatures too. The planets Mercury, Jupiter, and Venus have very small tilts (3ƒ or less) so the varying distance they are from the Sun may play more of a role in any seasonal temperature variations. However, of these three, only Mercury has significant differences between perihelion and aphelion. Its extremely thin atmosphere is not able to retain any of the Sun's energy. Jupiter's and Venus' orbits are very nearly circular and their atmospheres are very thick, so their temperature variations are near zero.
Mars, Saturn, and Neptune have tilts that are similar to the Earth's, but Saturn and Neptune have near zero temperature variation because of their very thick atmospheres and nearly circular orbits. Mars has large temperature changes because of its very thin atmosphere and its more eccentric orbit places its southern hemisphere closest to the Sun during its summer and farthest from the Sun during its winter. Mars' northern hemisphere has milder seasonal variation than its southern hemisphere because of this arrangement. Since planets move slowest in their orbits when they are furthest from the Sun, Mars' southern hemisphere has short, hot summers and long, cold winters.
Uranus' seasons should be the most unusual because it orbits the Sun on its side---its axis is tilted by 98 degrees! For half of the Uranian year, one hemisphere is in sunlight and the other is in the dark. For the other half of the Uranian year, the situation is reversed. The thick atmosphere of Uranus distributes the solar energy from one hemisphere to the other effectively, so the seasonal temperature changes are near zero. Pluto's axis is also tilted by a large amount (122.5 degrees), its orbit is the most elliptical of the planets, and it has an extremely thin atmosphere. But it is always so far from the Sun that it is perpetually in deep freeze (only 50 degrees above absolute zero!).
| aphelion | Equation of Time | mean Sun |
|---|---|---|
| perihelion | time zone |
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last update: 25 January 1999
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