I realize that I made an assumption in my first answer, that the moon is not rotating. A rotation may cause you to move out of the orbital path of the bullet be

I realize that I made an assumption in my first answer, that the moon is not rotating. A rotation may cause you to move out of the orbital path of the bullet before it gets back to you. If you shot from the poles though, you would remain in the bullet's orbit. That said, in ideal conditions, even with rotation, the bullet will hit you eventually, but not for a long time on average, given the scale of the moon. In reality it's orbit would probably destabilise due to collisions with dust and perturbations from other gravitational bodies (the Earth, Sun, etc. create an n-body situation which slowly changes the orbit over time). > Does there always exist a velocity `v(theta)` that will make the bullet hit you in the back after one orbit? The velocity must be great enough to stay above the surface, and not high enough to escape. Additionally, you must shoot horizontally, like I mentioned before, and not rotate out of the orbit (e.g. by being at the poles, or at the rotational equator, shooting along the equator).