Imagine the equivalent of a sun-synchronous Earth orbit, just substituting the Moon for Earth and Earth for Sun. Such an orbit would have to have the following properties:
- It would be a polar or near-polar orbit around the Moon
- Its orbital plane would precess with the same rate as the Moon orbits around Earth so the angle between the Earth-Moon line and the orbital plane would be constant.
For example, if the orbital plane was (nearly) perpendicular to the Earth-Moon line, a satellite in this hypothetical orbit would be permanently visible from the Earth.
Can such an orbit exist?