Generation of Orbital Elements for the TELSTAR Communications Satellites

The calculation of elements for orbits similar to those of recent nearearth satellites such as the first and second TELSTAR communication satellites, Echo I and II, the Tiros series and the Syncom satellites is accomplished in this analysis by considering the secular effects of the earth's gravitational potential upon the satellite's orbit. Here, the earth is taken as an oblate spheroid whose field is independent of longitude and is symmetrical about the equatorial plane. In the analysis, the gravitational effects of all bodies other than the earth arc ignored, as are atmospheric drag effects and solar light pressure.1 For orbits at distances in the thousand-mile range, luni-solar attraction can change the satellite height by no more than a few hundred feet. This can alter ground station pointing angles by less than 0.01°, which is below the resolution and tracking accuracy of the horn antenna* at Andover, Maine which supplies the bulk of the basic pointing data for Bell Telephone Laboratories use. The principal planetary perturbation is from Venus, which peaks at 3 to 4 orders of magnitude less than the luni-solar effects. Air drag effects at 1,000 miles are at least an order of magnitude below the solar gravity perturbations. In the technique to be described, modified orbital elements (osculating elements plus explicit secular perturbations) are derived essentially from three sets of observations of the satellite. If only angle information is available, a modified form of Gauss' method is used to ascertain the range, f If some range information is available, this is added to the analy* This antenna lias a tracking jitter of about 0.005°.