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Sun-synchronous orbits are popular around Earth, and the Mars Reconnaisance Orbiter uses one as well (so I think Wikipedias definition as a geocentric orbit is wrong). Considering that probably any rotating body has some oblateness, is a sun-synchronous orbit always possible, or are there some fundamental limitations that make sun-synchronous orbits impossible around certain planets, minor planets, moons, or other bodies in the solar system?

(A heliocentric orbit is of course a special case)

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No. First, the matter of oblateness which introduces the necessary precession. In some cases it will force the sun-synchronous orbit altitude below the body's surface (obviously impossible). In other cases other bodies will disturb the orbital motion too strongly, destabilizing the orbit.

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    $\begingroup$ There is never a perfect sun-synchronous orbit. One around the Earth will be disturbed by the Moon, too, although much less. $\endgroup$ – s-m-e Aug 1 '13 at 11:58
  • $\begingroup$ @ernestopheles: Agreed, but one around Venus will only be affected by other planets and possibly stray meteors and the likes. $\endgroup$ – SF. Aug 1 '13 at 12:02
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    $\begingroup$ I kind of agree, but for the fun of this argument, even Venus has an inhomogeneous gravity field. Besides, just like Earth, it is not a sphere :-) $\endgroup$ – s-m-e Aug 1 '13 at 12:21
  • $\begingroup$ @ernestopheles There are no spheres. $\endgroup$ – gerrit May 17 '16 at 15:43
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    $\begingroup$ @MagicOctopusUrn: Depends on the type of system, take Alpha Centauri AB - Proxima Centauri style triple system, where A,B orbit each other very close to barycenter and C (Proxima) is 13,000 AU away. Is the planet's orbit around the barycenter, or around one of the constituents? In the former case, it could be only synchronous to barycenter. In the latter, the other star will be destabilizing but all single-star rules apply. Or you could go synchronous to a different star, there's not much problem with a Proxima's planet's satellite to be synchronous to Alpha AB. $\endgroup$ – SF. Aug 18 '18 at 10:11

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