Two masses mi and m move under their mutual gravitational attraction in a uniform external gravita- tional field whose acceleration is g. choose as coordinates the cartesian coordinates x, y, z of the cen- ter ofmass vector r (taking z in the direction ofg) and the spherical coordinates r, θ and φ that define the relative vector r from mi and m2 (see hw problem set 1 for the definition of r). write down the lagrangian in terms of these 6 coordinates. calculate all 6 generalized momenta. which of these 6 momenta is conserved? write down the 6 euler-lagrange equations of motion.