Because position is relative, is it possible to see a star orbiting a planet?

Question

Position is relative, as it depends on the reference frame. We usually visualize the sun at the center of the solar system. BUT, we can also visualize the Earth at the center of the solar system, with the sun orbiting around it and the planets orbiting around the sun. Therefore, shouldn't we be theoretically be able to see a star orbiting around a planet? (given that the planet happens to be stationary relative to the Earth)?

Answer 1

2 objects will orbit about their common centre, that is to say they will be accelerating towards this centre. Something that is stationary/at constant velocity is not accelerating.