I'm sure this has become a tedious question, but wasn't able to ween out an exact answer through searching. A ship orbits an asteroid using retro rockets to maintain an orbit. The gravity is insignificant and can be ignored. A clock on the ship will tick more slowly than a clock on the asteroid. Even though the ship feels acceleration due to the retro rockets, time dilation in this case is not due to acceleration by virtue of the Clock Hypothesis so I'm guessing we can ignore the forces felt on the ship as having anything to do with the time dilation. The ship is experiencing time dilation strictly because of its velocity relative to the asteroid. Now if we switch our observation from the asteroid to the ship then an observer on the ship would instead see the asteroid orbiting the ship at the same relative velocity. This appears to be a symmetric situation with the exception of the retro rockets. So is this situation the same as just two ships passing each other (each seeing the others clock move more slowly) or is this an asymmetric situation (similar to the twin paradox or a curved timeline in a world line diagram) where the ship has to be considered accelerating while the asteroid is not.