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Is it by pure random chance that Mars and the Earth have nearly the same day duration (Mars day is barely 40 minutes longer, which is just 3% difference), or there is some causal relationship between the two?

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The length of the day on Earth has been changing ever since it was formed due to the influence of the Moon, so the current near equality is an accident of timing. Go back or foward a few billion years and the day lengths would be more different.

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is there some way to know the duration of Mars a few billion years ago? –  lurscher Jan 25 '13 at 15:42
    
A good question and one that I deliberately avoided! :-) As far as I know there are no observations to tell how the length of the day on Mars has changed. However the main reason the day length changes on Earth is the tidal force from the Moon and the moons of Mars are too small to raise any significant tides. Tidal forces from the Sun will have some effect, but these are a lot lower on Mars, partly because they vary as $r^{-3}$ and partly because Mars has no oceans and much less energy is dissipated in tidal movements on land. So ... –  John Rennie Jan 25 '13 at 16:21
    
... although we don't know if the day length has changed on Mars it seems likely any change will be much less than the change on Earth. –  John Rennie Jan 25 '13 at 16:22
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