Can planets have orbits other than elliptical or circular orbits? All of the planets in our solar system have either a circular orbit or an elliptical orbit (perhaps like Pluto).

  • $\begingroup$ See, for example, the Sitnikov problem. $\endgroup$ – HDE 226868 Dec 21 '15 at 2:44
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    $\begingroup$ Actually, no planets have a circular or even an elliptical orbit. Planetary orbits are affected ("peturbed") by all other planets (and satellites and asteroids and comets and anything that has mass), so the actual paths they follow are fairly complicated. In theory, even distant stars affect planetary orbits, but only to a very small extent. I can't find it at the moment, but there's even a gravity simulator film that shows planetary orbits spelling out "LINUX ROCKS" or something similar. $\endgroup$ – user21 Dec 21 '15 at 4:12
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    $\begingroup$ Janus and Epimetheus, moons of Saturn, have a funny twist to their shared orbit. $\endgroup$ – LocalFluff Dec 21 '15 at 8:41
  • $\begingroup$ @LocalFluff : Woah, that was an interresting read. Thanks for sharing ! $\endgroup$ – Nico Dec 21 '15 at 12:49
  • $\begingroup$ @LocalFluff that was really quite interesting, and now I am wondering if it is possible to create such interactions using our satellites and if it could serve any practical purposes. $\endgroup$ – Astroynamicist Jan 23 '16 at 14:22

Orbits are conic sections therefore can be either circular, elliptical, parabolic or hyperbolic. Of these 4, only first two form a closed curve under 2 body hypothesis, while the later two extend to infinity.
If you talk about planet, by definition it has to orbit a star which would require it to have a closed orbit hence circular or elliptical, with respect to the star. For any other kind of orbit the body will just fly away to infinity never to return back. Infact comets are considered to be parabolic, but in theory they have highly elliptical orbits with their aphelion lying near the edge of the solar system.

But it is possible for a planet to have other kind of orbits if we consider their motion from a different reference frame such as with respect to another planet. So for an inertial frame of reference a planet will have a circular or elliptical orbit, even Pluto.

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But you'd have to think in Einsteinian, rather than Newtonian, terms. Inertial frames of reference and all.

If you view our planet as motionless, then the orbit of Venus, for instance, would resemble a telephone coil cord.

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