A comprehensive textbook encompassing the analytical methods of classical celestial mechanics, the recent numerical experiments into the orbital evolution of gravitating masses, and the astrodynamics of artificial satellites and interplanetary probes. It requires little or no prior familiarity with astronomy or space science but assumes a knowledge of calculus and elementary vector analysis. Problems, with answers, are included as are appendices of relevant astronomical and mathematical data. This text is intended primarily for postgraduate and advanced undergraduate students but its discussion of orbital computation will be of interest to serious amateur astronomers. The third edition includes new data concerning various bodies in the Solar System, particularly in the systems of Jupiter and Saturn. New results from recent work on the stability of the Solar System and its sub-systems are included to update the text throughout.