The Kepler problem

The Kepler problem involves understanding how two objects, like a planet and a star, move under their mutual gravitational attraction. It predicts that the planet's orbit will be an ellipse, with the star at one focus, and describes how their positions change over time. Kepler's laws, derived from this problem, explain planetary motion, such as orbits, orbital periods, and the shape of paths. It’s fundamental in celestial mechanics, helping us understand the movements of objects in space, from planets to satellites, based on the principles of gravity and the laws of motion.