Hi everybody, I am trying to find an analytical solution of the equation of a falling particle of mass M in a gravitational field (described by constant K) when the gravity depends on distance, as in Newton classical theory(I simplified in one dimension). The equation could be M*d2 X(t)/ dt2 = -K * 1/x(t)**2. Initial condition X(t0)= X0 and initial speed V0. I tried to find a solution and a range of existance of this solution with tecniques of second order non linear differential equation with separation of variables, but I lost myself on the road. Could somebody help me. Thank you very much.