system
Given the following post, respond as if you're commenting on Reddit:
human
If Earth had a second moon hidden exactly behind the Moon, how would we know?

Assume that the second moon would be small or distant enough to be entirely eclipsed by our current moon. In addition, its orbit speed matches up with the moon's orbit in such a way so that it always stays exactly behind it from Earth's point of reference at all times.

What would we be able to detect in order to realize this body existed, short of sending probes far enough from earth to find it? Additionally, what effects might this second moon have on Earth, if any?
gpt
The hidden moon would not be able to orbit with the same angular velocity as our regular moon. In a stable orbit, there's a simple relation between the radius of the orbit and its period: the ratio between the orbital radius cubed and the square of the period is constant, given a fixed central body (in this case: Earth). (for simple circular orbits, which is a good enough approximation here, but similar laws hold for elliptic orbits)

This means that if the second moon orbits at a larger distance form Earth, it will necessarily have a longer orbital period, that is, it'll take more than 28 days to complete a full orbit. And therefore it won't be able to stay hidden. The same mechanism is behind the reason why all geostationary satellites orbit at the same distance from Earth.

The only way to get around this limitation is if the hidden moon is actually a spaceship with engines that continuously correct its orbit.