The study of artificial satellites is today a subject of topical interest and naturally much work has been completed in the field of satellite orbits. Many aspects of this work involve the use of differential equations. Unfortunately very few of these may be solved by ordinary analytic techniques. One possibility is to define a new function to be the solution of the given equation, for example the logarithmic function. Nowadays we use computers. Nevertheless it is highly satisfying to produce an analytic solution to a problem in applied mathematics for in a sense we have succeeded in displaying a pattern in the physical world.