Calculate the normal gravity on an ellipsoid or sphere using geocentric coordinates.
Usage
value = NormalGravity (geocentriclat, gm, omega, a, b)
Returns
- value : float, ndarray
- The normal gravity in SI units.
Parameters
- geocentriclat: float, array_like
- Geocentric latitude in degrees.
- gm : float
- The gravitational constant multiplied by the mass of the planet.
- omega : float
- The angular rotation rate of the planet.
- a : float
- The semi-major axis of the flattened ellipsoid on which the normal gravity is computed.
- b : float
- The semi-minor axis of the flattened 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.
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