Question

From Thesky6 programme I've calculated that the mean sidereal day is 86164.1207742 seconds. Not all numbers may be significant, but is there a more accurate calculation & from where?

Answer 1

You can calculate the mean sidereal day from the mean sidereal year.

Explanation:

The sidereal year is the time it takes the Earth to return to the same place with respect to the fixed stars. The mean sidereal year is `Y_s=365.256363` days. During this time the Earth rotates through 360° in its orbit.

Each mean solar day the Earth rotates about the Sun by `Y_s/360=0.9856` degrees. A mean solar day is the average time between successive solar noons where the Sun is at its highest in the sky. During this period the Earth rotates about its axis `360 +0.9856` degrees as it has to rotate the extra angle due to its change in orbital position.

A sidereal day is one complete rotation of the Earth about its axis with respect to the fixed stars. In a sidereal day the Earth rotates exactly 360° about its axis.

The mean solar day is 86400 seconds long. The mean sidereal day is therefore `86400-0.9856*86400/360=86163.4536` seconds.