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Most of the planets that we know of have a sidereal day (rotational period) that is shorter or on the same order of magnitude as their sidereal year (orbital period), the latter being the case in tidal locked bodies.

Without invoking magic or super-advanced technology, is it possible for a planet to have a sidereal day that is significantly longer than its sidereal year?

What natural processes could explain such a situation?

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    $\begingroup$ Do you count being tidally locked? $\endgroup$ – Xavon_Wrentaile Apr 10 '16 at 0:55
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    $\begingroup$ @Xavon_Wrentaile Sure, if you can show how it satisfies the criteria in the question. Intuitively, a tidally locked body would seem to have a sidereal year length very close to its sidereal day length; isn't that pretty much the definition of tidally locked celestial bodies? (The smaller body always showing the same side to the larger body.) $\endgroup$ – a CVn Apr 10 '16 at 10:25
  • $\begingroup$ Yes, in a tidally locked system the sidereal day and the sidereal year are of equal length. $\endgroup$ – ApproachingDarknessFish Jun 20 '16 at 20:01
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The classic example here is Venus, with a sidereal day of 245 Earth days and a sidereal year of 224.7 Earth days - clearly less than its sidereal day. I wrote an answer related to this on Astronomy Stack Exchange that explains Venus's slow rotation (and why it has retrograde rotation). The sequence of events, according to Alemi & Steveson (2006), is as follows:

  1. A large body collides with Venus in a giant impact.
  2. The resulting debris coalesces into a disk and then eventually a moon, which moves away because of tidal acceleration.
  3. Venus is hit by another large body, which reverses its rotation.
  4. The moon moves inwards and collides with Venus.

Now, this merely produced a sidereal day that is only slightly longer than a sidereal year. It seems quite possible that the second giant impact could have resulted in a different scenario. The motion of the moon falling towards the planet will accelerate the planet's rotation a bit. All the second impact has to do is change the planet's angular velocity just enough prior to the collision with the moon.

I wish I could give you more specific information about the exact necessary velocity and angle of the impacting bodies. The problem is that the proposed giant impacts on Venus haven't been studied in nearly as much depth as the collision between Earth and Theia that gave rise to the Moon, and it's a much more complicated problem to deal with. In terms of strict feasibility, however, the giant impact $\to$ moon formation $\to$ second giant impact $\to$ collision with moon scenario can almost certainly work.

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    $\begingroup$ Good answer, this was the first thing I thought of also. Mercury also has a very interesting orbit. While its sidereal day is shorter than its sidereal year (57 days vs 88 days), an observer on the surface would experience a day that lasts twice as long as a year. They would see the sun rise, then reverse direction, touch the horizon, and rise again before setting. $\endgroup$ – ApproachingDarknessFish Jun 20 '16 at 20:10
  • $\begingroup$ Related to this answer: Why is the rotation rate of Venus so slow? on Space Exploration. $\endgroup$ – a CVn Nov 26 '16 at 18:46
  • $\begingroup$ @MichaelKjörling Interesting. We had an identical question on Astronomy Stack Exchange. $\endgroup$ – HDE 226868 Nov 27 '16 at 18:52

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