That wasn't my point really. Oh well! I though most people would pick a parabola, which is a decent approximation for short throws but not the real shape.
It's an ellipse, but it is so elongated that it is extremely close to a parabola. If the entire mass of the moon was concentrated in a single point at its centre, and the projectile could pass through the moon, then the projectile would follow a parabola-like path and go down below the moon's surface, until it started curving around the other side of the centre and back up to its starting point. It's only when you look at the uninterrupted path that the difference between the parabola approximation and the ellipse becomes apparent.
The parabola results from assuming that the force due to gravity on the object is constant (which is a decent approximation over short vertical and horizontal distances). In fact it will change magnitude and direction as the projectile moves.
The curvature of the surface of the moon doesn't matter, but the fact that the rock is orbiting the center of the moon just like a satellite would is the insight that Newton needed a smack on the head to get :)
Would I be wrong if I said that the deviation between the parabola and the elliptical orbit trajectories is probably much smaller than the tidal effect of the earth and the sun, solar wind and other external forces on such short trajectories? And as such the elliptical model is "as wrong" as the parabolic one?
After all, a model is only as good as the precision of the results it produces...
It's not numerical approximations I'm worried about. It's the fact that if you don't understand what's going on underneath, you're not going to have good "intuition" when someone asks a question like: what happens when you don't ignore air resistance.
