# Geostationary moon

My planet is very Earth-like with a day length of 26.87h. The moon has a radius of about 1550km, a mass of $5.2\times10^{22}$ kg and orbit 45500 km from the center of planet.

My scenario is that the formation of this moon is the same as our Moon (i.e. from a collision) but that the planet was spinning slower so they would be both totally locked to each other, thus the moon wouldn't slow down and move away, staying in a geostationary orbit.

Is this realistic? Would it have an effect on plate tectonics, and what other effect on the shape of my planet would it have?

Note: I'm not asking for climate, only the things above

• You might want to look into tidal locking. – Joe Bloggs Sep 5 '18 at 20:37
• This would be similar to Pluto and Charon. – Alexander Sep 5 '18 at 20:39
• It would probably have an effect on plate tectonics, but they're pretty poorly understood as it is, so no one will really be able to give you any specifics. – Ryan_L Sep 5 '18 at 20:43
• I know what is tidal locking, the two main things I want to know are if it is stable over geologic times and if it would affect the plate tectonics – Jean-Abdel Sep 5 '18 at 20:51
• Some related questions. Is it possible? And full disclosure, the next one is one of my questions which may be of interest, on moon phases. – EveryBitHelps Sep 6 '18 at 4:26

It is possible.

First, you did the math correctly, a center-to-center distance of 45500 km would result in geosynchronous orbit assume mass = 1 earth.This is well beyond the Roche Limit, so you bodies are stable.

Whether this could happen is entirely dependent upon how fast the rotations were at the initial conditions. For our Earth and moon, the initial conditions result in a mutual tidal lock in about another 50 billion years -- though the expected red-giant phase of the sun may make this a moot point.

Certainly Venus is spinning much slower than Earth even though the planets are very similar in other ways. So there is clearly great variety in initial conditions and/and events history to get us to this point in time. Your system is certainly within the realm of the possible.

Since your planet is mutually locked with your moon, there is actually less tidal stress since the moon is always in the same place in the sky. Your planet would be stretched a little more in the moon direction because the planet would have time to fully adjust -- but this does not mean more strain. Earth's bulge due to this rotation is many times larger than a tidal bulge, but the important factor is not how non-spherical it is, but how strain is induced because of this regular orbital cycle.

Your planet's tidal strain would be only that of the sun, which presumably would be similar to Earth. On Earth, solar tidal force is about 46% of the lunar tidal force. So, still some tidal strain, but only about one-third as much as on Earth (tidal forces are additive).

The difference in Planetary shape due to tidal locking is negligible on Earth (only about 1 meter in the deep ocean). However, since the tidal force in your case is based on a moon 0.71 times the moons mass, but 8.4 times closer you should expect a permanent tidal bulge of about 428 meters in deep ocean but less over land (rock is heavier than water). That may sound like a lot, but you would never notice it without good instrumentation.

If you want tidal strain, it is easily accomplished. Just make the moon's orbit eccentric. Because your moon is so close, the tidal effects are magnified considerably. Our moon varies from 363,104 to 405,696 km., a bit over 10% variation. Because tides are proportional to distance cubed, a 10% variation results in a 33.1% variation in tidal force. This would result in very significant tidal stress, large ocean tides, etc. The local residents would definitely notice these tides and would be able to correlate them to apparent changes in the moon diameter.

• Wouldn't tidal stress slow down the moon, thus making it move away? – Jean-Abdel Sep 6 '18 at 16:03
• @Jean-Abdel Our moon moves to a higher orbit because there is a net torque because the tidal bulge of the Earth does not point directly to the moon. This would not be the case when mutual tidal lock exists. I do not know what the net effect would be under these conditions. – Gary Walker Sep 6 '18 at 16:22
• Huge tides look cool but it will mess even more the computation for how much solar energy each place of the planet will get – Jean-Abdel Sep 6 '18 at 16:43