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.

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.

One full rotation of the Earth around its axis with respect to the fixed stars is known as a sidereal day, during which the Earth rotates precisely 360 degrees around its axis.

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

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Answer 2

Lydia Allen

A more accurate calculation of the mean sidereal day can be obtained from astronomical databases, such as the International Earth Rotation and Reference Systems Service (IERS). They provide precise measurements of Earth's rotation parameters, including the length of the mean sidereal day. These measurements are constantly refined and updated to maintain accuracy.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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 &amp; from where?

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?