The mathematical problems arising from modern celestial mechanics, which originated with Isaac Newton's Principia in 1687, have led to many mathematical theories. Poincaré (1854-1912) discovered that a system of several celestial bodies moving under Newton's gravitational law shows chaotic dynamics. Earlier, Euler (1707-83) and Lagrange (1736-1813) found instances of stable motion. For example a spacecraft in the gravitational fields of the sun, earth, and the moon provides an interesting system which can experience stable as well as chaotic motion.