The type of trajectory of a body subject to the gravity of a central body depends on its total energy: an ellipse if bound, a parabola at the limit of escape, a hyperbola if it escapes with excess energy. This section classifies orbits, shows how conservation of angular momentum gives Kepler’s second law, sets up the classic problem of maximum and minimum distance, and lists the three laws of Kepler as derived by Newton.

Try it — interactive simulation

A light body orbits a large mass. Change the initial speed with the slider, or drag on the canvas to launch from anywhere: the orbit goes from ellipse to circle to escape. The dashed line is the predicted conic, with periapsis and apoapsis marked.