Such as here:
> If you calculate out the geodesics, no; all the parts of Earth down to its individual molecules and below "want" to travel on geodesics sourced by the system and do so unless the stronger three forces interfere with that "want" (and in bulk Beiglböck and Dixon show that the Earth has a coordinate-independent centre-of-mass that does travel on a timelike geodesic, and you arrive at it by considering the vector position of each particle).
This is a very dressed up non-response, because my initial comment was about geodesics braiding around that central one, and the resulting complexity of the paths, emissions caused by that finer level of path resolution, etc.
Responding that you can calculate paths entirely misses the point.