Calculate the normal gravity on an ellipsoid or sphere using geocentric coordinates.
Usage
value = NormalGravity (geocentriclat, gm, omega, a, b)
Parameters
value: output, real(dp)- The normal gravity in SI units.
geocentriclat: input, real(dp)- Geocentric latitude in degrees.
gm: input, real(dp)- The gravitational constant multiplied by the mass of the planet.
omega: input, real(dp)- The angular rotation rate of the planet.
a: input, real(dp)- The semi-major axis of the ellipsoid on which the normal gravity is computed.
b: input, real(dp)- The semi-minor axis of the ellipsoid on which the normal gravity is computed.
Description
NormalGravity will compute the magnitude of the total gravity (gravitation and centrifugal) on the surface of a rotating ellipsoid (in m/s^2). The latitude is input in geocentric coordinates in degrees.
For a rotating ellipsoid, the surface corresponds to a constant potential, and the gravity vector is normal to the surface. The normal gravity is computed using Somigliana’s formula, as taken from Physical Geodesy (Hofmann-Wellenhof and Moritz, 2nd ed., sections 2.7 and 2.8). In this routine, the geodetic latitude is computed internally from the input geocentric latitude.
For the case of a sphere (a is equal to b), the normal gravity is defined as the magnitude of the sum of the normal gravitation (GM/r^2) and the centrifugal gravity. For a rotating sphere, the surface does not correspond to a constant potential and the gravity vector is not normal to the surface.
References
Hofmann-Wellenhof B, and H. Moritz, “Physical Geodesy,” second edition, Springer, Wien, 403 pp., 2006.