# Is an earth-sized moon orbiting a super-earth feasible?

Is an earth-sized moon orbiting a super-earth feasible?

Or would tidal forces say 'no thanks'?

I'm making a system for the Kerbal Space Program Kopernicus mod and am trying to make it as realistic as possible.

This is an answer only to the second part of your question. If such an enormous moon somehow gets formed or captured, its tidal interaction with its host planet will follow the regular laws.

• If the moon is created or captured above the synchronous radius of the planet, it will be tidally receding from the planet (like our own moon). Owing to the angular-momentum conservation law, the rotation rate of the planet will be slowing down. Several billions years down the road, the two partners will become mutually synchronised, i.e. showing the same face to one another like Pluto and Charon. For this to happen, two conditions must be fulfilled, though. First, the time scale of mutual synchronisation must be shorter than the expected age of the stellar system. (E.g. at some point the star may expand and absorb both the planet and its moon.) Second, the mutual synchronisation can happen only if the receding moon stays within the Hill radius. (Rigorously speaking, I should have said "the reduced Hill radius", but we better keep things simple.) Otherwise, the gravitational pull of the star will "steal" the moon from the planet before the two reach the stable configuration.

• If the moon is created or formed below the planet's synchronous radius, it will start descending, like Phobos. Due to the angular-momentum conservation law, the planet's rotation rate will be increasing (for which reason its synchronous radius will be decreasing). If the moon's mass is much smaller than that of the planet, the moon will reach the planet's Roche lobe and disintegrate there. If the moon is sufficiently massive, then, in its tidal descent it may catch up with the decreasing synchronous radius of the planet. (This must happen above the Roche lobe, however, -- lest the moons gets destroyed before reaching the synchronous radius.) In this case, the moon will synchronise the planet. So the two will reach the Pluto-Charon-like configuration -- but will reach it not through tidal ascent but through tidal descent.

• If the moon is born or captured just a tiny bit below the planet's synchronous radius, and if it is spinning sufficiently swiftly -- then a weird situation will take place: the planet-raised tides in the moon will overpower the moon-raised tides in the planet, and the moon will cross the synchronous radius, and will jump out! For this to happen, the angular momentum of rotation of the moon must exceed the needed difference in the orbital angular momentum. But this, again, can happen if the nascent moon is created only a little bit lower than the synchronous orbit. This scenario thus implies fine tuning, which reduces the chances for this scenario to be implemented. A very rare event it is.

This said, I am not aware how realistic could formation or capture of an Earth-size moon by a huge super-Earth be. While the emergence of such a couple is not prohibited in principle, its probability may be extremely low. An expert on SPH codes could be of help.

• What apparatus are designed to search for such exoplanets?
– ayr
Commented Nov 9, 2023 at 15:47
• Several projects are dedicated to the search for exoplanets, the most impressive effort being probably Kepler Commented Nov 9, 2023 at 17:24