# The Existence of Natural Satellites in Geostationary Orbits

While browsing through Physics SE, I noticed a question about satellites in geostationary orbit (unrelated to the one I'm asking here), and for a moment I interpreted it as referring to natural satellites (e.g. a moon). So I wondered: Could a natural satellite exist in geostationary orbit?

Then I stopped and thought. For large gas giants, such as Jupiter, having moons too close to the planet can be fatal (for the moon). If it ventures inside the planet's Roche limit, it's toast. But there is good news: the Roche limit depends on both the masses and densities of the primary body and the satellite. So perhaps this reason is non-applicable, as a high-mass natural satellite might be able to survive. So the question changes:

Could a sufficiently high-mass, high-density natural satellite occupy geostationary orbit over its primary body?

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I wonder if there are few inaccuracies in the question. Roach limits does not depend both on density and mass of the bodies in concern. Rather, it depends on density/mass of both bodies and radius of one body. See en.wikipedia.org/wiki/Roche_limit#Rigid-satellite_calculation – Krumia Sep 13 '14 at 20:19
Other thing is, for a satellite to be safe from tidal forces, it does not have to be low-mass and low-density. Rather, the satellite has to be high-mass and high-density. Bigger (thus heavier) satellites like Pluto's Charon will tend to stay. because the Roche limit is lower for heavier/denser satellites. – Krumia Sep 13 '14 at 20:22
Thanks, @Krumia I can't believe I messed that up. I checked the formulas a couple times before I posted it, but I must have mixed up the primary and satellite. – HDE 226868 Sep 13 '14 at 20:56
@Krumia Ah, now I know what I was thinking. A more massive satellite means more gravitational force between the two, meaning the two would be closer together, possibly negating the effects of having a smaller Roche limit. I might un-do my edit. – HDE 226868 Sep 13 '14 at 21:04

## 5 Answers

Of course, a natural satellite (moon) could have an orbital period equal to the spin period of its host (provided such an orbit would be accessible). However, the tidal friction that may generate such a locking is quite weak, so this would have to be a rare chance. Moreover, perturbations to the orbit from other moons or their host star may put the moon out of such an orbit.

On the other hand, what is rather common is that a moon's orbital period equals their own (rather than their host's) spin period. This is exactly the case for the Earth Moon (you may say that Earth is on a "selenostationary" orbit) and naturally occurs form the tidal interaction of the planet with its moon.

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Yes. Charon is in Pluto synchronous orbit. Pluto and Charon are mutually tide locked.

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Interesting. I hadn't considered Pluto and Charon. That's a pretty good example. I would note that this is a special case (i.e. Charon would not always have to present the same face to Pluto). – HDE 226868 Aug 24 '14 at 13:35

It would require a very precise trajectory for an asteroid to end up in geostationary orbit. It doesn't happen by chance. Space flight providing companies have to make a real effort to put their customers' communication satellites there. And geostationary isn't a very stable kind of orbit. The varying gravity of the Moon pulls satellites out of their geostationary orbits as the satellites move closer to and further away from it daily as the Earth rotates. GEO is about a tenth of the distance to the Moon. Satellites need their small rocket engines to do recurring station keeping maneuvers in order to stay there. The Earth has no lasting natural satellite in any orbit, except for the Moon.

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This does not answer the question. The OP didn't ask whether it would be easy or not, but if it would be possible. I can't see any reason why a planet couldn't have a moon in a stationary orbit (I don't want to use the term GEOstationary, as this refers to the Earth only). Actually, Pluto's moon Charon is in a synchronous orbit around Pluto (they are mutually tidally locked). A stationary orbit wouldn't be too far off! Moreoer, the perturbations you mention on geo sats could or not affect a massive moon – Etienne Pellegrini Aug 22 '14 at 19:55
@Etienne Pellegrini If they are tidally locked, they have a stationary relationship. The Earth doesn't move across the sky as seen from the Moon. And a satellite cannot stay for ever in a stationary orbit. The Sun, the eccentricity of the satellite's orbit, tidal forces will change its orbit over time. – LocalFluff Aug 22 '14 at 22:46
Well, I agree, the orbit would change over time. But the changes might be slow enough that you can consider the orbit to be stationary for some range of time (which might be fairly long, the Moon's orbit around Earth does not vary that quickly...). Saying that a stationary orbit is not possible because of the perturbations is like saying that a circular orbit is never possible. I guess it all depends on the timescale considered – Etienne Pellegrini Aug 22 '14 at 22:49
I would, unfortunately, agree with @EtiennePellegrini that this doesn't answer my question, although it is food for thought. For example, it could be possible, in the future, to move a small (read: very small) asteroid into geostationary orbit (see your interesting question astronomy.stackexchange.com/questions/6182/…). – HDE 226868 Aug 24 '14 at 13:22
I was thinking about natural satellites captured by Earth. Your question is broader. I don't know much about it. It's a good point by HopDavid here that double planets like Pluto-Charon tend to get synchronous orbits. Tidal forces help synchronize the rotation of the planet and moon, not only the orbit in itself. – LocalFluff Aug 24 '14 at 13:34

Charon and Pluto are bad examples. They have comparable mass: Pluto only 9 times heavier that Charon (Earth is 81 times more massive than Moon), so center of mass in that system lies outside main body (about 1000 km from the Pluto surface).

Main problem for satellites is Roche limit. For the Eath-Moon system Roche radius is about 15500 km from center to center (7400 km from surface to surface). Geostationary orbit for Earth is 42 164 from the Earth center or 35 786 from geoid surface (sea level). It works only in Equatorial plain (Moon is tilted 18,3-28,6 to Earth equator). So, Earth-size planet can have Moon-sized satellite in geostationary orbit. In distant past our Moon was much closer – possibly about 50 000 km (about 60 000 from center to center).

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charon and pluto are tidally locked, as is the moon to the earth. so you could say that earth is in a geostationary orbit with the moon. in fact, the earth rotation has been and will continue to be slowed by the moon until the moon is in a geostationary orbit with earth.

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tidal locking isn't the same as being in GEO. In GEO the moon would always be in the same point in the sky, which it isn't. – jwenting Sep 3 '14 at 8:53
However in the the case of Pluto and Charon, they are mutually locked, so Charon remains at a fixed point above Pluto, and Pluto is at a fixed point above Charon. This position has arisen because the two objects have similar sizes. – James K Sep 6 '14 at 10:42