"the 4D Moon wouldn't be orbiting the 4D Earth in a simple circle or an ellipse" Actually, I'm pretty sure the Moon would remain in the 2-dimensional subspace determined by its initial position relative to the Earth and its initial velocity. What you say could apply to the rotation of a rigid body in 4 dimensions, but that's plenty complicated in 3D already. – Rahul Feb 12 at 13:35