If the two bodies are in a central potential why does the potential U only depend on the distance r between the two bodies? Shouldn't the individual distances between particle and origin of the central potential also be considered? I would think that the total potential is U = U_12(r) + U(r_1) + U(r_2) with U_12 being the potential due to the two mass particles and U being the central potential.
The potential represents an interaction between the two bodies, not between each body and the origin. In this problem, there is no object at the origin, nor is there any source of a potential there. The term "central" in "central potential" refers to the fact that the interaction between the bodies depends only on their separation (and not on the angular variables).
If the two bodies are in a central potential why does the potential U only depend on the distance r between the two bodies? Shouldn't the individual distances between particle and origin of the central potential also be considered?
I would think that the total potential is U = U_12(r) + U(r_1) + U(r_2)
with U_12 being the potential due to the two mass particles and U being the central potential.
The potential represents an interaction between the two bodies, not between each body and the origin. In this problem, there is no object at the origin, nor is there any source of a potential there. The term "central" in "central potential" refers to the fact that the interaction between the bodies depends only on their separation (and not on the angular variables).
thank you! I understand now