Consider two celestial bodies of masses m₁ and m2. The bodies only interact gravitationally and can be considered pointlike for the purpose of this problem. (a) List the conserved quantities of the system. (b) For each conserved quantity, state the Noether symmetry responsible for its conservation.

Consider two celestial bodies of masses m₁ and m2. The bodies only interact gravitationally and can be considered pointlike for the purpose of this problem. (a) List the conserved quantities of the system. (b) For each conserved quantity, state the Noether symmetry responsible for its conservation.