Guess what is the formula that links the sidereal day of a planet and its solar day

[Nazalassa]

Quick explanation:

Sidereal time vs solar time. Above left: a distant star (the small orange star) and the Sun are at culmination, on the local meridian m. Centre: only the distant star is at culmination (there has been a mean sidereal day since above left). Right: a few minutes later the Sun is on the local meridian again. There has been a solar day since above left. (from Wikipedia)

As you can see, the sidereal day is the time that a planet takes to do exactly one rotation around its rotation axis, whereas the solar day is the time between the moment of two consecutive days when the Sun (or the planet's star) is the higher in the sky.

 

So the question is, how do you calculate the length of the sidereal day of a planet, if we know the length of its year in days (Earth is 365.26 days) and the length of its day?
Try to guess! Also please put your explanations, if you post any, in spoilers.

 

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WARNING, this is the answers! Do not go further if you haven't answered!

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Oh, really?

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There goes another one.

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If you haven't answered yet, please do not continue to not kill the fun!

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Answers:

1. (length of day) * (length of year) / (length of year + 1)  --> answer 3
2. (length of day) * (length of year) / (length of year - 1)  ---> answer 2
3. 5 h  59 min  9.4 s  -----------------------------------------------------> answer 3

 

[imcute]

oops did the division wrong enough to round up to the second answer instead of the third in the third qu