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Is there a way to calculate the rotational speed (or day length) of a planet?

If not then what are the factors? I mean what affects the speed? Is it just the distance from Sun (like period of a planet) or mass, density and other things are also important?

And of course by planet, I meant solid planets.

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closed as unclear what you're asking by user36790, Bill N, Gert, HDE 226868, ACuriousMind Nov 5 '15 at 1:39

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Welcome to Physics.SE @Omur. Try to provide more clarifying details in your questions so it's easier to understand what you're trying to understand. $\endgroup$ – DilithiumMatrix Nov 4 '15 at 16:46
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    $\begingroup$ I just want to know if there is a way to calculate the day length of a solid planet. That's all. I hope the question is clear enough. $\endgroup$ – Omur Nov 4 '15 at 16:48
  • $\begingroup$ Are you asking for a first-principles way to calculate the axial rotation rate of an arbitrary planet? Or are you asking for a first-principles way to calculate the orbital period? In the first case, the fact that Earth and Venus have very different axial rotation periods (and Venus rotates in the opposite direction) would clearly suggest that it is not possible. $\endgroup$ – Jon Custer Nov 4 '15 at 16:55
  • $\begingroup$ @JonCuster By rotational speed I meant spin rate of a planet. And by day length I meant orbital period. Won't they be completely related to each other?? $\endgroup$ – Omur Nov 4 '15 at 17:12
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    $\begingroup$ If you research the periods of rotation you will find no correlation between them and other factors (period of revolution, mass, etc). The length of daylight at a point on the surface of a planet is related to axial tilt, latitude, rotational period, revolutionary period, and direction of rotation. But @JonCuster is correct in saying that the you can't predict rotational period from first principles. $\endgroup$ – Bill N Nov 4 '15 at 20:55
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Rotational speeds of planets cannot be calculated/predicted because planet formation seems to be highly chaotic. The spin of planets (both rocky and gas) is determined by many factors, including:

  • the angular momentum of the material which was accreted on the planet,
  • gravitational interactions with other planets,
  • the history of collisions as the planet formed
  • tidal interactions with the host star (if the planet is close in) and the gaseous and debris disks while the planet was forming.

In the solar system, for example, Mercury is in a 3:2 spin-orbit resonance --- so it completes 3 rotations every 2 orbits. The spin periods of Earth and Mars, however are almost identical despite different masses and semi-major axes. Finally, Uranus has a shorter rotational period than earth --- but is tilted almost 90degrees relative to the orbital plane.

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  • $\begingroup$ Thanks. But isn't there any relation with distance, mass, density or any other factors? $\endgroup$ – Omur Nov 4 '15 at 16:54
  • $\begingroup$ @Omur There are no such known relations, again --- because the systems evolve chaotically. I've tried to add some examples to help clarify. $\endgroup$ – DilithiumMatrix Nov 4 '15 at 16:56
  • $\begingroup$ Thanks again. Just to be sure I got the answer one last question: If there were no atmosphere around earth, will the day length be same? BTW, can you suggest some edits to the question to increase clarity?? $\endgroup$ – Omur Nov 4 '15 at 17:05
  • $\begingroup$ @Omur that seems like a completely unrelated question. But yes, it would be the same. The atmosphere has negligible dynamic influence on Earth's rotation. $\endgroup$ – DilithiumMatrix Nov 4 '15 at 17:06
  • $\begingroup$ DilithiumMatrix is spot on. Small points to add but close to the sun tends to have a slow orbital speed due to stronger solar tides (Mercury/Venus). Also, as objects grow more dense and lose size, they rotate faster - that's due to concervation of angular momentum. Jupiter may have shrunk a bit as it cooled and added mass. Jupiter (maybe) shrinking and coalescing could partially explain why it rotates quickly. White dwarfs and Neutron stars can rotate at very fast for this reason. Earth used to rotate very fast as a result of the giant impact. There's no neat and tidy formula. $\endgroup$ – userLTK Nov 4 '15 at 17:07
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About the only relationship worth considering is whether the planet orbits close enough to its parent star so that tidal forces lock the rotation period to the orbital period. Even this is fraught with problems because we currently don't know the exact "tidal friction" coefficients for exoplanets. This will depend greatly on the structure of these planets (e.g. rocky cores, average density, size of envelope) and how long they have spent close to their parent star (since planets migrate) and on the mass and size of the parent star.

It is generally expected that most hot Jupiter's with orbital periods less than a few days will probably be tidally locked.

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