Possible behaviour of one of three moons?

Question

Is it possible for a habitable earth-like planet [364 day cycle, circumference 25,200 miles], to have three moons, the largest with 13 full moons a year, the next in size with 4 full moons a year, and the smallest and closest being nearly tidally lock and not visible to a third of the planet for 7,500 years at a time, due to that moon nearly having orbital synchronicity with the planet's 24 hour long full axial rotation?

All information with the exception of that relating to to the third moon comes from source material not produced by me so that it is put that way to be accurate - I saw some questions. Where I have not provided information you feel you need just assume the planet is otherwise pretty much identical to Earth except its axial tilt is currently 30 degrees not 23 degrees and continental land-masses will have different distribution. The planet is hollow but can be assumed to have same gravity as Earth.

To give context the world is a published setting that is meant to have a third moon although the published setting history produced for it relating to one segment of the planet going back more than 6,000 years omits making any mention of this. The only explanation for this I can see is it has never been seen by a sizable chunk of the inhabitants, in order to be recorded yet. Ironically most of that population has done its slow colonisation of the planet moving in the same direction the moon would be moving without any maintenance of records from where they originally came in the west

My question really is get at whether or not this omission of the third moon from the material can be accounted for by lunar behaviour capable of eluding detection by recorded memory for that time span assuming the moon reaches the zenith over any point on the planet once every 25,200 years. The moon is essentially moving slightly faster than the planetary rotation so it sits constantly in the sky but travels West to East over time but not noticeably so. It is close to reaching zenith at a point roughly 7,000 miles East from the periphery of the area for where the published setting history is documented.

Answer 1

Yes ... I think.

Four full moons a year means a period of approximately 91 days. We know that Kepler's Third Law states T^2 / R^3 = constant for any given system, so we can calculate approximately the orbital radius of the moonlet by knowing that the Moon, orbiting with R=380,000 km in the same Earth system, has T=28 days.

This gives us that R^3 = (91/28)^2 * 380,000^3 and R = 380,000 * cube root of 10 = about 2,2 times the orbital radius of the Moon.

The problem might lie with the geostationary moonlet. The geostationary orbit will have stable equilibrium points due to planetary asymmetries; a moonlet drifting near one of these points with very low relative velocity (which would have, given the 7500 years required) would be captured, its extra kinetic energy diverting it into a sort of Lissajous curve around the equilibrium. Maybe (sorry, not an astronomer) the moonlet could bounce between two equilibrium points irregularly, whenever some external influence disturbs it.

Being "tidally locked" simply means that the moonlet always shows the planet the same face, after a period in which it appears (as seen from the planet) to rotate to and fro. It doesn't influence the period, not directly.

Answer 2

Yes, but:

• At our tech level they'd notice the earths orbit was off centre, the mass pulling the earth down would be noticeable to physicists.
• GPS would be more wrong by several hundred meters. Diving into the relativity maths alone could discover the extra moon.
• Some Geosyncronous, non geostationary satellites would mysteriously vanish. Theyd hit it or be redirected.
• Tides would be lower for 7500 years too. Thered be evidence of a high waterline everywhere that was never hit.
• over this timeframe the advancement would slow down, as nearly tidally locked moons tend to tidally lock. Our moon subtlety interacts with our day length even now, so much so that if we stopped spinning tommorow, the moon would slowly start us up again.