This question has been bugging me for quite some time and i'm not too sure if i'm missing out some important factor in the understanding of this scenario:
Given two objects of equal mass and size both orbiting around a central axis x where ObjectA is distance n away from x and ObjectB is distance 2n away from x.
Now lets assume some force f is being applied to ObjectA and force 2f being applied to ObjectB such that it takes the exact same time for ObjectA and ObjectB to do one full orbit around x.
Logically, there will have to be a greater force being applied to ObjectB to make it travel faster, as it has a greater circumference around x, in order for it to complete the orbit at the same time ObjectA completes its orbit.
However, if we were to join ObjectA to ObjectB via a long pipe for example and only apply a single force f on the pipe such that both objects will orbit around x at the same time.
How is it now that both objects will complete the orbit at the same time using one single force but yet ObjectB still has a larger circumference which means it has a greater distance to travel in order to complete the orbit?
P.S. Clearly i'm no physics expert and lack the knowledge for the proper terminology for the concepts I described above.