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When I only know the sidereal rotation period, how do I determine the true length of day on a body?

We know the Earth's sidereal day doesn't have full 24 hrs unlike the true length of day. It's similar on Mars where the sidereal day isn't as long as a Sol (about 24 hrs 40 min) either. So how do we calculate the true length of day on a planet?

Let's do it on the example of the planetoid Ceres: its sidereal rotation period is 9 hrs 4 min and 27 sec. How do we calculate the true length of day on Ceres?

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    $\begingroup$ You mean the mean Solar day? You would have to know the period around the star $\endgroup$
    – Tosic
    Jan 29, 2020 at 12:40
  • $\begingroup$ Note that the "true" or apparent day length (the time from one high noon to the next) generally differs from that of the mean solar day. See en.wikipedia.org/wiki/Equation_of_time and physics.stackexchange.com/a/469884/123208 $\endgroup$
    – PM 2Ring
    Jan 29, 2020 at 17:33
  • $\begingroup$ @PM2Ring I was asking on the mean solar day however, what on Earth is 24 hrs and on Mars about 24 hrs 40 min. $\endgroup$
    – user30007
    Jan 30, 2020 at 6:29

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If you know the length of a sideral day and the length of a year, you can determine the length of a solar day.

From Wikipedia:

enter image description here

After one year, there will have been one more solar day than sideral day. Therefore :

solar day = sideral day / (1 - (sideral day/orbital period))

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  • $\begingroup$ From this I conclude that the farther the object is from the Sun, the smaller the difference between the length of the sidereal and of the solar day? $\endgroup$
    – user30007
    Jan 29, 2020 at 13:18
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    $\begingroup$ @user30007 Yes, indeed. $\endgroup$
    – usernumber
    Jan 29, 2020 at 14:45

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