Hi everyone,
I would like to know if the energy of each body of a two body gravitationnal problem is separately conserved. I know that the individual angular momentum are separately conserved and that the TOTAL energy of the two bodies is conserved. However, I don't know if there could be energy transfer between the two bodies or if it's forbidden by symmetry considerations.
In my mechanics textbook, the two-body central force problem is only treated as a one-dimensional problem of the motion of a reduced mass in an effective potential, where only the energy of a reduced mass orbiting around the center of mass is considered. This confuses me when I try to think of the energy of ONE of the two bodies. Is the energy of ONE of the two bodies conserved? Is there a way to see this?
Thank you a lot for considering my request. Best regards,
Kami
I would like to know if the energy of each body of a two body gravitationnal problem is separately conserved. I know that the individual angular momentum are separately conserved and that the TOTAL energy of the two bodies is conserved. However, I don't know if there could be energy transfer between the two bodies or if it's forbidden by symmetry considerations.
In my mechanics textbook, the two-body central force problem is only treated as a one-dimensional problem of the motion of a reduced mass in an effective potential, where only the energy of a reduced mass orbiting around the center of mass is considered. This confuses me when I try to think of the energy of ONE of the two bodies. Is the energy of ONE of the two bodies conserved? Is there a way to see this?
Thank you a lot for considering my request. Best regards,
Kami