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I'm wondering if it is possible for a planet to be impossible to orbit stably over a significant length of time. The shorter the length of time the planet can be orbited for, the better. It should be possible to land on the planet, just not to maintain an orbit around it without the requirement for near-constant fuel expenditure for stationkeeping purposes.

What mechanism could cause the planet to be almost impossible to orbit for more than a few orbital periods?

Gryphon
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  • Orbit at any altitude? – Alexander Jan 15 '19 at 22:23
  • At any altitude or any inclination, ideally. – Gryphon Jan 15 '19 at 22:24
  • I would imagine a rogue planet that's spinning randomly without an axis could be a candidate for an "unorbitable" planet due to it's unstable/inconsistent gravity. Though since there's a hard-science tag, I don't really have the proof or numbers to prove this. – Basher Jan 15 '19 at 22:44

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The simplest answer that comes to my mind is that the planet is surrounded by a cloud of debris (micrometeorites).
These are usually quite small, so can be detected only some minutes before the impact and follow very different orbits, with different inclinations compared to one anothe. So a ship in orbit should continuously maneuver to keep itself safe from impacts, while a landing ship could easily find a free window to cross safely the cloud and land.
The cloud of debris should be recent: in the long run, such a cloud would probably gradually fall onto the surface of the planet because of kinetic energy loss for high atmosphere friction or impacts among the micrometeorites.
Consider also that it is not necessary to have the orbits of the planet "covered" by these micrometeorites: I think that just some tens of thousands of these object, with enough random trajectories, could make orbiting around the planet a risky choice.
Of course the danger would be high only near the planet: probably it would be still possible to orbit it, even from very far.

EDIT

As Fay pointed, a similar scenario is called Kessler syndrome. In such case, the lower orbits would be safer for a ship to orbit (but it would still need to periodically burn its engines in order to correct its orbit because of air drag)

McTroopers
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  • Psst, since you've started down this particular line: https://en.wikipedia.org/wiki/Kessler_syndrome You know you can edit your answer to improve it if you want right? – Escaped dental patient. Jan 15 '19 at 22:59
  • I think this idea has two problems, one, as Fay said, if only stops you from some orbits and second, it would prevent you from landing on the planet. – Etaila Jan 15 '19 at 23:10
  • @Fay Suggers: Thank you for the suggestion, I've updated the answer – McTroopers Jan 15 '19 at 23:17
  • @Etaila: I think that a landing ship could cross the cloud fast enough to minimize the chances of a collision (the debris would be in any case sparse enough that crossing it would present a far lower danger than staying in orbit for an undefined period of time) – McTroopers Jan 15 '19 at 23:21
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    Better than Kessler syndrome, I think, would be a moon that had ventured within its Roche limit and was being torn apart. More debris, in a wider variety of locations, and the moon itself will perturb other bodies' orbits as it passes by making the whole system more chaotic. – Cadence Jan 15 '19 at 23:23
  • @McTroopers The problem of this is, that the speeds of orbiting objects are so extreme, that even dust sized particles have the force of bullets, you need some serious armor, to take punches from small particles, which makes you bigger and more heavy. And then you need to detect, the particles that are too big for your armor, meaning that you need detection equipment and a strong computer that can simulate the path of all those particles. Or in other words, some serious science fiction. While on the other side, you only need a more massive planet and more particles to outdo your defenses. – Etaila Jan 19 '19 at 04:04
  • @ Cadence That would be a ring like the ones of saturn. Those are actually relatively harmless, the problem with Kesslers syndrome is, that the debris is flying chaotic, in millions of different directions, if you match your speed to one debris particle, you cross the path of another, while debris of a shattered moon fly's pretty monotone. You could replace moon with a lot of comets or maybe a multi moon system where a view moons collided, but I don't know how that would turn out. – Etaila Jan 19 '19 at 04:11
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Have it orbit very close to a massive body

What you want is a very small Hill sphere, which is the region of space where a particular body's gravitational influence dominates. On the other hand, the celestial body probably will have to become a moon.

If the mass of the smaller body (e.g. Earth) is ${\displaystyle}$ m, and it orbits a heavier body (e.g. Sun) of mass ${\displaystyle M}$ with a semi-major axis ${\displaystyle a}$ and an eccentricity of ${\displaystyle e}$, then the radius ${\displaystyle r_{\mathrm {H} }} $ of the Hill sphere of the smaller body (e.g. Earth) calculated at pericenter is, approximately

${\displaystyle r_{\mathrm {H} }\approx a(1-e){\sqrt[{3}]{\frac {m}{3M}}}.} $

The above equation means if a satellite orbits a more massive body, it will have a smaller Hill sphere even if the satellite orbit stays the same. There is a limit on how close bodies can orbit each other however. Its called the Roche limit, and objects closer than this limit gets ripped apart by tidal forces.

The Roche limit for a rigid spherical satellite is the distance, ${\displaystyle d}$, from the primary at which the gravitational force on a test mass at the surface of the object is exactly equal to the tidal force pulling the mass away from the object:

...

${\displaystyle d=R_{m}\left(2{\frac {M}{m}}\right)^{\frac {1}{3}}}$

where ${\displaystyle R_{m}}$ is the radius of the secondary, ${\displaystyle M}$ is the mass of the primary, and ${\displaystyle m}$ is the mass of the secondary.

(edited for formatting clarity)

So put your planet-like moon close to the parent body and make the parent body big. That might cause a host of other problems though depending on your story such as massive amounts of radiation, high delta-v cost to get to and from the planet, etc, depending on the details.

Community
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To orbit a planet the main factor for orbiting a Planet is Mass (gravity of an object) and Speed. The best way would be a multi planet solar system, where the planets orbits are getting close enough to interfere with each others gravity, so orbiting would only be possible for a short time. However I don't know how the planets themselves could stay in their orbits and not change orbits themselves.

Etaila
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