I'd say 'jerf is correct here: https://news.ycombinator.com/item?id=43078998 https://news.ycombinator.com/item?id=43078998 The equation we use to describe the

I'd say 'jerf is correct here: https://news.ycombinator.com/item?id=43078998 https://news.ycombinator.com/item?id=43078998 The equation we use to describe the motion does not contain a term for the ground being there. That assumption exists outside of the model described by the equation, and you use that assumption after the fact to reject a solution that would otherwise be valid, and describe the movement of the ball that's pulled down by gravity. In this form, it doesn't really describe a proper orbit, just a trajectory of being pulled down by a constant force. I believe this would correspond to an infinitely-ish heavy object located infinitely far below. The proper equation that gives you an orbital curve has the force of gravity proportional to inverse-square distance and point at the center of the body, which is what makes it possible to describe a circular or elliptical motion this way. Parabolic orbits exist too, but they're interpreted as failed orbital capture - "object is moving so fast that it'll curve around and fly away to infinity before turning around and coming back". And in all cases, the solutions make physical sense (+/- infinity), on the assumption the trajectory doesn't cross the ground, as there's no term for it there :). If you want, you can describe the ground as another equation (or inequality), and solve the resulting system - it'll then be clear what exactly is it that rejects some of the solutions.