Solar and Sidereal Day
My watch is based on a solar day equal in time to 24 hours. If you read a good
Astronomy textbook, you will learn that the Earth rotates on its axis in 23
hours and 56 minutes. "But hold on there a minute, Dr. Franke!" you
might say. "How can our watch time be different from a sundial time."
The fact that our clocks are based on the solar day and the Sun appears to drift
eastward with respect to the stars (or lag behind the stars) by about 1 degree
per day means that if you look closely at the positions of the stars over a
period of several days, you will notice that according to our clocks, the stars
rise and set 4 minutes earlier each day. Our clocks say that the day is 24 hours
long, so the stars move around the Earth in 23 hours 56 minutes. This time period
is called the sidereal day because it is measured with respect to the stars.
This is the true rotation rate of the Earth and stays the same no matter where
the Earth is in its orbit---the sidereal day = 23 hours 56 minutes on every
day of the year. One month later (30 days) a given star will rise 2 hours earlier
than it did before (30 days × 4 minutes/day = 120 minutes). A year later
that star will rise at the same time as it did today.
here to cause these changes? Look at the image to your left. If we were to place
a huge arrow in the ground, pointing high and straight into the sky, we would
take note of when the sun was aimed directly under the point of the arrow. We
could also know to which star behind the sun the arrow was pointing. One sidereal
day later (23 hours and 56 minutes), the Earth will have completed a 360 degree
spin, but if we looked up along the pole's arrow, the sun and background star
would not be under the point. We would have to wait 4 minutes for the correct
alignment. This dilemma is solved when we realize that the Earth has moved slightly
in its orbit around the sun, and requires the additional 4 minutes to have our
planet spin back into sun-star alignment. The length of rotation for 360 degrees
is 23 hours and 56 minutes, but the length of time for the sun to make a complete
circuit in the sky is 24 hours. This 4 minutes of daytime to have 1 degree of
motion bring Earth-Sun-Star alignment coincides with the 1 degree that Earth
moves in its orbit during a day.
The same principle applies for all of the other planets as well. The sidereal
time of any planet is equal to the time required to make one complete revolution
of 360 degrees. The extra angle any planet must rotate to get the Sun back into
alignment with the stars is equal to the angle amount the planet has moved in
its orbit in one day.
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