When we have two bodies and a central force acting towards the center of each other, we could treat the whole problem as a one body problem by introducing the relative coordinate. My question is, when you were to calculate the relative coordinate, you are working out the acceleration of a fictitious particle, which does not exist.
However, if you work out the coupled differential equations, you would get exact acceleration of both particles.
Therefore I think reduced mass is not a reliable method , but I was told that the reduced mass method can get the exact solution as the coupled differential equation. Therefore I think I am wrong, could anyone shed the light on this please?