# 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?

Mar 21, 2016

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&deg; 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&deg; about its axis.

The mean solar day is 86400 seconds long. The mean sidereal day is therefore $86400 - 0.9856 \cdot \frac{86400}{360} = 86163.4536$ seconds.