Love the blog, thanks for your work here! I have a fantasy world with 4 moons. A is the largest, then B C and D being the smallest. A is Geosynchronous, over an ocean, and D orbits around A. While B and C have "regular" moon orbits around the planet. Would A and D be possible? And besides complex tides, how else could this set up affect the planet?
D is plausible within certain parameters, but wouldn’t be very likely. Moon A would have to be fairly big, and moon D would have to be very very small and orbit around A at a very very close distance,
Moon D would have to orbit around moon A closer than its Hill Sphere, and higher that it’s Roche Limit. These distances would depend on the mass of the planet, the mass of moon A, and the mass of moon D. Without knowing specifics, I’d have to say that both A and D would have to be fairly small (at least compared to out Earth’s Moon) assuming your planet is fairly much Earth sized.
So, lets assume that your planet P is the same size and mass as Earth. We’ll set moon A as the equivalent of the asteroid Ceres. That’s about 475 km across - a nice size moon without being obnoxious. Moon D would have to orbit around A less than about 1300 km or it would be pulled out of orbit by your planet’s gravity. Moon D would also have to orbit around A higher that about 1150 km, or the gravity of moon A would tear moon D apart.Moon D is threading the needle between being pulled away and being pulled in and being destroyed.
So, yeah, it’s possible, but that situation is going to be very unstable, and after a few hundred thousand years, Moon D will either be pulled into an orbit around your planet or be pulled into Moon A and break up into a ring around moon A.
