Profile of Upper-Atmosphere Air Density at the Height 180–212 km. derived from the Orbit of Sputnik III

Abstract

THE resistance of the air to a moving object like a satellite causes a steady decrease of the semi-major axis and eccentricity of the orbit. The motion of the satellite grows faster and the satellite itself submerges deeper and deeper into the atmosphere at every revolution. When the satellite has descended to a certain level, where the heating from impact of air molecules on the frontal surface becomes great enough, the satellite burns out. For the purposes of ephemerides and for the prediction of the life-time of the satellite, it is necessary to know how its orbital elements will be changed by the resistance of the air—supposing that we have some knowledge of the density of the air at the height where the satellite is moving, and of the drag coefficient of the satellite. Unfortunately, these data are not usually known with sufficient accuracy. But we can reverse this problem and search for a solution of how the air density could be determined from observed changes in size and shape of the orbit when the drag coefficient of the satellite is known. If we do not know this drag coefficient (which depends on the size, shape and mass of the satellite), we can still determine at least the gradient of the air-density. G. V. Groves published two valuable papers^1,2 last year, in which very accurate methods for such a determination have been developed. The only assumption made here, which could be accepted as a general approximation, is that air-density varies with height according to the relation: where ρ₀₀ is the density of the air at the height h ₀₀, H ₁ is the scale-height in the case of an isothermal atmosphere, and H ₂ enables us to take account of the variation of atmospheric temperature with height. From the data of six different satellites with perigees between 180 and 650 km., Groves has found that, for h ₀₀ = 200 km.: In the second paper, methods have been developed for the determination of H ₁ and H ₂ without any knowledge of the drag coefficient. In this case, of course, the determination of ρ is not possible.