TABLE OF CONTENTS KEY FEATURES
For motion in general central force fields, the key results are the radial motion equation and the path equation. For motion in the inverse square force field, the key formulae are the E-formula, the L-formula and the period formula.
The theory of orbits has a special place in classical mechanics for it was the desire to understand why the planets move as they do which provided the major stimulus in the development of mechanics as a scientific discipline. Early in the seventeenth century, Johannes Kepler [*] published his laws of planetary motion , which he deduced by analysing the accurate experimental observations made by the astronomer Tycho Brahe. [ ]
First law Each of the planets moves on an elliptical path with the Sun at one focus of the ellipse.
Second law For each of the planets, the straight line connecting the planet to the Sun sweeps out equal areas in equal times.
Third law The squares of the periods of the planets are proportional to the cubes of the major axes of their orbits.
The problem of determining the law of force that causes the motions described by Kepler (and proving that it does so) was the most important scientific problem of the seventeenth century. In what must be the finest achievement in the whole history of science, Newton s publication of Principia in 1687 not only proved...
