[math-fun] Philae landing: equation of motion

What is the equation of motion of the PHILAE lander, relative to the '2km sphere' comet 67P, assuming: - it is released with a velocity vertically downwards of v1 m/s about the comet at time t(0), x(0) km above the surface - acceleration at the surface is 10-^3 m/s/s If x = k.t^(2/3), then d2x/dt2 = -(2/9)k^3/x^2 ... which may have something to do with it. Incidentally, it sounds like ESA are going to release the Philae lander at a much greater height than originally planned. Maybe this is because they cannot predict and deliver ROSETTA's position as accurately as they expected. Thanks. G