system
Given the following post, respond as if you're commenting on Reddit:
human
Is it possible for a planet to have a perpetual solar eclipse if a satellite orbits at the same speed as the planets rotation?
gpt
Kind of, but it's not very stable.

In this arrangement, the satellite is at the "L1 Lagrange point". This is where the gravity from the planet, the gravity from the star, and the effective centrifugal force from movement of the planet and the moon all cancel out, and the moon is at an equilibrium point in-between the planet and the star.

However, this is not a *stable* equilibrium. Although all the forces add up to zero (in a rotating frame), if you give the moon a tiny push, then it will drift away further and further and faster and faster until it's not near the L1 point anymore.

This means that you don't get moons naturally hanging out at the L1 point. But you can put an artificial satellite there. You do need to constantly give little boosts to correct the orbit to keep it there, but they only need to be small boosts.