Elliptical Orbits and their Precession
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Chapter 5 discusses the motion of an object that is propelled in an elliptical orbit by a gravitational force. The distance, speed, and direction of the motion of the object (relative to the attracting body) are determined as functions of the elapsed time from periapsis (the point of nearest approach to the attracting body). This study proceeds via the calculus of trigonometric functions and relies on Kepler’s equation and its solution. Several concluding sections apply power series in the solution of relevant definite integrals. One of them computes the length of a planet’s elliptical orbit and another provides an analysis of the precession of the orbit’s perihelion.