A discussion on orbital analysis - Satellite accelerations and air densities at extreme altitudes

Abstract

Since 1962 observational studies on very high satellites have been made by means of the 24 in. reflecting telescope of the University of London Observatory. Analysis of the observations involves use of orbit elements specially provided by the Smithsonian Astrophysical Observatory (S.A.O.). Initially our attention was concentrated on the Midas type objects; these are Agena vehicles in nearly polar and nearly circular orbits, at heights of 3000 to 4000 km. It was hoped that precise observations might show small accelerations due to air drag, though it would be necessary to resolve P to better than 1 x 10~10 for this purpose. Observations are confined to the times when the orbit does not contain shadow; for the Midas orbits these periods last roughly 3 months. The acceleration due to solar radiation pressure when the orbit includes shadow is in principle calculable—and is indeed included in routine analyses for the higher satellites, by for example the S.A.O. It is important to realize, though, that for the very high satellites this acceleration due to solar radiation pressure (s.r.p.) may greatly exceed the acceleration due to air drag. For example, even in the case of Echo 2 at a height of about 1200 km, presently (1966) i r.p. may at times equal Pdrag. (see Cook & Scott 1966). In the case of the small balloon satellite 1963- 30D, with a mean altitude of about 3500 km and an orbital eccentricity of nearly 0.1 presently, Ps.r.p. may exceed pdrag by a factor of 100 on occasion. Consequently one cannot extract the air drag effect from the total observed acceleration; the value of Ps.r.p. is not known to an accuracy of 1 % for various reasons—neither the area/mass ratio for the satellite is known to this accuracy, nor is the reflexion coefficient. Therefore, one must confine the investigations of air drag effects to the all-in-sunlight phases (or, possibly, use very nearly circular orbits, for which Psrp is much reduced; but unfortunately the balloon satellites’ orbits rapidly depart from initially small eccentricities through s.r.p. perturbations).