Even Zonal Harmonics in the Earth's Gravitational Potential

Abstract

THE Earth's gravitational potential U at an exterior point distant r from the Earth's centre, and having geocentric latitude ϕ, may be written in a series of spherical harmonics as: where G is the gravitational constant, M the mass of the Earth, and R the Earth's equatorial radius. P_n(sin ϕ) is the Legendre polynomial of degree n and argument sin ϕ, and the J_n are constant coefficients. Equation (1) does not take into account the small variation of U with longitude, and represents an average over all longitudes.