Future Artificial Satellite Theories

Hoots Felix R.

GRC International

Since the time of Newton the focus of astrodynamics has been largely concentrated on the analytical solution of orbital problems. This focus was driven by the theoretical desire to obtain an understanding of the nature 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. As computers became more readily available and more powerful, it became more routine to address orbital problems using numerical integration rather than an analytical solution method.

Today numerical integration is used exclusively by control centers which only need to deal with maintainig the orbits for a small number of satellites. An example of such a system is the Global Positioning System (GPS) which has a constellation of 24 satellites. However, for a large system such as the US Space Surveillance System which must deal with over 8000 satellites, the majority of all satellites are predicted using an analytical orbit model and less than 50 satellites are maintained with a numerical integration method.

When we consider the rate at which computer capabilities have improved in the last decade, it is easy to project a time in the future when it will be practical to maintain the entire space inventory with numerical integration. Current experiments are exploring the practicality of parallel processing to address such a job. However, currently we are in a transition period which is being driven by the unprecedented increase in computational power. This paper explores this transition and how it will affect the future of analytical, semi-analytical and numerical artificial satellite theories.

In addition to the main problem of maintaining the orbital elements at the central site, we must also consider the users of this data. Although the central site may have the capacity to maintain the orbits using numerical integration, the user may not have such a capacity or may need results in a more timely manner. Thus, in the transition period, there will remain a need for the user to be able to obtain quick running and accurate predictions of satellite ephemeris. One way to provide for this transition need is through the use some series representation of the satellite ephemeris. This paper will present some results of the use of a mixed series of power and polynomial terms for the approximation of a satellite ephemeris.