Since the time of Newton, astrodynamics has focused on the analytical solution of orbital problems. This was driven by the desire to obtain a theoretical understanding of the motion and the practical desire to be able to produce a computational result. Only with the advent of the computer did numerical integration become a practical consideration for solving dynamical problems. Although computer technology is not yet to the point of being able to provide numerical integration support for all satellite orbits, we are in a transition period which is being driven by the unprecedented increase in computational power. This transition will affect the future of analytical, semi-analytical and numerical artificial satellite theories in a dramatic way. In fact, the role for semi-analytical theories may disappear. During the time of transition, a central site may have the capacity to maintain the orbits using numerical integration, but the user may not have such a capacity or may need results in a more timely manner. One way to provide for this transition need is through the use of some type of satellite ephemeris compression. Through the combined use of a power series and a Fourier series, good quality ephemeris compression has been achieved for 7 day periods. The ephemeris compression requires less than 40 terms and is valid for all eccentricities and inclinations.