The Kepler problem - new symmetries of an old system
Gil Bor(CIMAT, Guanajuato, Mexico)
207 (Bat 1R2)
The Kepler problem, introduced by Newton in 1687, is a system of second order differential equations describing the motion of a planet around the sun. The orbits of the motion form a 3-parameter family of plane curves, consisting of all conics (ellipses, parabolas and hyperbolas) sharing a focus at a fixed point (the sun). A rich structure emerges, with a 7-dimensional group of symmetries for the full family, the maximum dimension possible for a 3-parameter family of plane curves, a 3-dimensional group for the 2-parameter family of orbit of fixed energy, and an 8-dimensional group for Kepler parabolas or orbits of fixed non-zero angular momentum. Underlying these symmetries is a duality between Kepler’s plane and Minkowski’s 3-space parametrizing the space of Kepler orbits.