The zero gravity curve and surface and radii for geostationary and geosynchronous satellite orbits

Abstract

A geosynchronous satellite orbits the Earth along a constant longitude. A special case is the geostationary satellite that is located at a constant position above the equator. The ideal position of a geostationary satellite is at the level of zero gravity, i.e. at the geocentric radius where the gravitational force of the Earth equals the centrifugal force. These forces must be compensated for several perturbing forces, in particular for the lunisolar tides. Considering that the gravity field of the Earth varies not only radially but also laterally, this study focuses on the variations of zero gravity not only on the equator (for geostationary satellites) but also for various latitudes. It is found that the radius of a geostationary satellite deviates from its mean value of 42164.2 km only within ±2 m, mainly due to the spherical harmonic coefficient J 22 , which is related with the equatorial flattening of the Earth. Away from the equator the zero gravity surface deviates from the ideal radius of a geosynchronous satellite, and more so for higher latitudes. While the radius of the former surface increases towards infinity towards the poles, the latter decreases about 520 m from the equator to the pole. Tidal effects vary these radii within ±2.3 km.

Ellipsoidal Spacetimes and the Kerr Metric

“…In geodesy, to describe the gravitational field of a compact object, such as the Earth, from the point of view of Newtonian gravity, a specific shape of the object is usually assumed. A particularly interesting case is represented by a level ellipsoid for which a detailed description exists that is known as the Somigliana-Pizzetti gravity field (Ardalan and Grafarend, 2001;Pizzetti, 1894;Sjöberg et al, 2017;Somigliana, 1930). This field can be represented in different manners, but a particular useful representation is given in terms of the Jacobi spheroidal coordinates (l, f, u), which are related to the Cartesian coordinates by means of the transformation…”