Say you have a gravitational acceleration between a spherical object of mass M and inner radius R and a much smaller spherical object of mass m (essentially point-like) and distance ro away (M >> m) with an acceleration on mass m at any point r given by a = GM/r2Knowing that the acceleration with respect to the distance between the two objects is not constant, how would you calculate the amount of time it would take for the object to hit the surface of the larger sphere (also assuming the larger sphere moves negligibly)? The smaller object moves from a distance ro away from the center of mass of the larger object (r = 0) to a distance R away from this center. Solving this as a differential equation has gotten hairy. My other approach was to take the average force with respect to the distance from the center given by (the definite integral from ro to R of Fdr)/(R - ro) where F is the standard gravitational force. This comes from the equation for the average of any function. Once this average force is calculated, the acceleration is constant, so can it be inserted into the regular kinematic constant-acceleration equations to find the amount of time it would take to transverse the distance? I am not a physicist (yet), so be merciful. Thanks!