Atmospheric Contribution to the Time-Dependent Geopotential

Abstract

Integral expressions for the geopotential of the earth plus atmosphere are derived from the solution of Poisson's equation. The series of integrals involves position-weighted density integrated over all space exterior to the earth. From this, the acceleration due to gravity can be derived by a routine gradient operation. The time-dependent geopotential is calculated first in terms of the time rate of change of atmospheric density and then converted, via the equation of continuity, to integrals over density and wind velocity. The results could, for example, be related to perturbations of close satellite orbits due to atmospheric mass shifts, and to planetary atmospheres such as those of Venus and Jupiter.