An Introduction to the Mathematics and Methods of Astrodynamics, Revised Edition

This article appeared in the New York Times on the eve of the Apollo 8 mission. It was reprinted in a special Look magazine issue titled: Apollo 8 Voyage to the Moon.
The Apollo voyage to the moon represents a new and exciting plateau in the ancient art of navigation.
By applying principles as old as the planetary theories of Kepler and technologies as new as the high-speed electronic digital computer, an astronaut can determine the position and course of his craft in the vastness of outer space with an accuracy that Columbus or Prince Henry the Navigator would have deemed impossible in their time.
Ever since man first went to sea, the need to navigate accurately has been a constant challenge. For many centuries only the brave or foolhardy dared to venture out of sight of land except for short distances. Progress in navigation was extremely slow, and not until just 200 years ago could a ship's location at sea be determined with anything approaching precision.
The ability to determine latitude the distance north or south of the Equator by observing the angle that the North Star makes with the horizon was known in early times. The instrument used for this purpose, the astrolabe, was invented by the Greeks more than 2,000 years ago and well may be the oldest scientific instrument in the world.
The mariner's compass was introduced much later, in the 12 th or 13 th century. With it, a seaman could set a course...