The problem of motion of two bodies under the inuence of gravitational attraction was solved in PhIa when we looked at 'The Kepler Problem' P.S. He had many more problems during his life, but that 's the way it 's phrased in Physics books. The equation that deals with the radial motion ended up being (equation 17.25 of The Mechanical Universel): mvf + Ueo) = E, (3) L2 GMm U630.) 277172 T 3 (4) where m is the mass of the orbiting planet, vT is the radial component of the orbital speed (it is not the total orbital speed), L is the angular momentum of the orbiting planet, 0 is the universal gravitational constant, M is the mass of the 'large' body}, M >> m, and E is the constant total energy of the orbiting planet (E