# How many constants of motion are there in a 2D two body problem?

A system consists of two masses interacting with gravitational force, rotating around their centre of mass. If we only consider the $$xy$$ plane where the masses rotate, the system has 8 degrees of freedom ($$xy$$ position and velocity for each mass). How many independent constants of motion are there?

I know: (1) energy, (2, 3) momentum in $$x$$ and $$y$$, (4) angular momentum. So it probably has 4 or more constants of motion. Do I miss the others?

• Apr 17 at 3:42