An atmospheric model, and some remarks on the inference of density from the orbit of a close earth satellite
. The U. S. Air Force has extended the U. S. Standard Atmosphere to over 540,000 meters of altitude. The author has extended the Air Force model to still greater heights, and suggests the employment of the resulting model for inferring the air density from observations of the orbit of a close earth satellite. Convenient equations, involving easy numerical quadratures in the eccentric anomaly, are derived accurately and fundamentally for the time-derivatives of the perigee and apogee distances of a close earth satellite moving through an atmosphere.If the extended Air Force atmos- pheric model is nearly correct, then a 50-centimeter, io-kilogram, spherical earth satellite with a perigee height of about 200 miles and an apogee height of about 800 miles should be expected to have a life-time of about nine years. Calculations of only slide-rule accuracy enable rather accurate adjustments to be made to the density near perigee, from observations of the changing apogee distance. The density may not be determined from astronomical observations with much relative accuracy at heights much above the initial perigee. It is suggested that definitive adjustment of the atmospheric density be made by a least-squares solution in which the unknowns are the vertical gradients of the ratio of temperature to molecular weight in selected altitude zones. Equations are given for the differential changes in air density caused by differential changes in such gradients.