ON THE REPRESENTATION OF AIR DENSITY IN SATELLITE DECELERATION EQUATIONS BY POWER FUNCTIONS WITH INTEGRAL EXPONENTS

Abstract

The scale height in height-bands between 150 and 400 km is assumed to vary linearly with height. Integration of the hydrostatic equation for an ideal gas above a spherical earth then leads to a power function representation of the air density over the band. With integral exponents such power laws give better fits to several proposed model atmospheres over altitude ranges of several hundred kilometers than those provided by the usual exponential representation of air density. The representation of air density in satellite deceleration equations by power functions with integral exponents reduces them to elementary forms. It was possible with such density distributions to obtain simplified formulas which may be useful for (a) computing atmospheric densities from satellite accelerations, (b) comparing proposed model atmospheres with observations, and (c) developing the theory of satellite orbits in the presence of air drag. As is possible with the exponential form, these power functions may be modified to take account of the effect of an oblate, rotating atmosphere. Their use may, therefore, permit the development of a simplified, accurate orbit theory for satellites with perigee heights below 300 km. Certain preliminary results are discussed and compared with previous theory and observations.