Closed orbits in Kepler potentials can drive gravitational instabilities. Though the Kepler potential is common in astrophysics -- relevant for stars orbiting massive black holes, for planets orbiting stars, and for moons orbiting planets — few instabilities have been explored beyond the linear regime in this potential.
I will describe a new instability in Keplerian disks of massive particles on eccentric orbits. Gravitational torques drive exponential growth of their orbital inclination and clustering in their angles of pericenter. This instability dynamically produces the unusual distribution of orbits observed for minor planets beyond Neptune, suggesting that it has helped shape the outer Solar System. I will also discuss implications for extra-solar planets and for nuclear star clusters in the centers of galaxies.