For example, if Jupiter were nearer to the sun, would that move their mutual barycenter slightly farther from the sun? Or if Pluto and Charon were orbiting closer together, would their barycenter be at a different location?
Found answers online but they talked about multiple bodies, so they weren’t clear about if two isolated bodies were orbiting at different distances from each other if that would affect the barycenter position.
Comments
The answer should be obvious if you think about it – you are basically asking whether the position of two bodies affects the position of their centre of mass.
What doesn’t change is the relative position of the centre of mass – that depends only on the mass ratio. So for example if two bodies have equal mass then the centre of mass will always be equidistant between them, whereas if they have a 10:1 mass ratio then the centre of mass will be ten times closer to the heavier body than the lighter one.
Yes and no.
Let’s assume an initial case where two objects are 1 AU away from each other. If they were the same mass, then the barycenter would be halfway between the two objects. That relative position would be the same regardless as to whether the two were 1 AU or 5,000 AU. But the actual position would change.