Calculation of the Life-time of a Satellite

Abstract

THREE recent discussions of the effect of friction on a satellite^1–3 have been based on the assumptions (1) that the atmosphere is spherically symmetrical, (2) that SC _D is constant, where C _D is the drag coefficient and S the cross-sectional area perpendicular to the direction of motion, and (3) that the density of the atmosphere is exponential over the heights within which the perigee lies. The convenience of the third assumption is that the actual values of the density and the scale-height are not required, the mere constancy of the scale-height being sufficient. On the other hand, an elaboration of (3) requires a knowledge of the density distribution and is likely to lead to less rather than greater accuracy. The failure of (2) will presumably be a consequence of rotation of the satellite and will introduce periodic rather than progressive variations in the orbit. It seems that greater accuracy should be sought in correction for the lack of spherical symmetry of the atmosphere; this can be done with only a minor modification of the analysis of Scott².