According to the website http://aa.usno.navy.mil/faq/docs/GAST.php, a low-precision way of calculating the GMST is via the following formula:

GMST = 18.697374558 + 24.06570982441908 D

The website doesn't actually state where the numbers come from. Another website tries to do this:

"To compute of sidereal time with low precision use of the low precision formula: GMST = 18.697374558 + 24.06570982441908 D, where 18.697… is sidereal time of the reference time 2000-01-01 at 0 UT, 24.0657… is a ratio of synodic and sidereal periods of Earth and D is days (and its fractions) since the reference time."

but I don't understand what this 'ratio of synodic and sidereal periods' means. I know what the sidereal and synodic days are and their values, but how do we use those to end up with the number 24.0657...? If anyone could help me out that'd be much appreciated!

  • $\begingroup$ This is usually given the other way: a sidereal day is about 23h56m in "real time". This means one calendar day is 24.06570982441908 sidereal hours. $\endgroup$
    – user21
    Oct 6 '15 at 13:45

The number 18.697374558 was the value of GMST (in hours) at noon UT on 1 January, 2000. The number 24.06570982441908 reflects the fact that it takes slightly less than 24 hours (23.934469591898 hours to be precise) for a star to the appear to rotate by 360 degrees.

This is a consequence of the fact that the Earth orbits the Sun. Our 24 hour day is based on the time between two consecutive solar noons. Because the Earth moves a bit along its orbit, the Earth has to rotate by more than 360 degrees (with respect to the stars) to see the Sun rotate by 360 degrees.

Another way to look at it: The 23.934469591898 hour long sidereal day means that a solar day is 24.06570982441908 hours long expressed in sidereal hours.


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