The spherical-harmonic expansion of the gravitational potential of the Earth in the external space and its convergence.
Abstract
It has sometimes been argued that the expansion in spherical harmonics of geopotential in space no longer converges as the test point approaches the earth surface. The present paper investigates the convergence of this series expansion and demonstrates that it does uniformly converge in space and on the earth surface.
- Publication:
-
Gerlands Beitraege zur Geophysik
- Pub Date:
- 1978
- Bibcode:
- 1978GBzG...87...81A
- Keywords:
-
- Earth (Planet);
- Earth Gravitation;
- Geopotential;
- Gravitational Fields;
- Spherical Harmonics;
- Convergence;
- Legendre Functions;
- Orbit Perturbation;
- Satellite Orbits;
- Series Expansion;
- Weierstrass Functions;
- Earth:Gravitation