Suppose an object is moving toward the Earth(with a direction perpendicular to the Earth's surface) at an initial speed v0, starting from a distance r0. The object also experiences gravitational acceleration. Is it possible to obtain an expression of r as a function of t? In other words, whats the distance from the Earth at a time t? I tried solving this second order differential equation: d2r/dt2 = GM/r2 I ended up with a mess of stuff. And it seems impossible to make r the subject of the equation.