In geodesy and geophysics, theoretical gravity or normal gravity is an exact solution for gravity for an idealized model of the Earth. In this model all the mass in contained within an ellipsoid of revolution which rotates about its polar axis. The mass distribution is such that gravity is normal to the surface of the ellipsoid; i.e., gravity potential is constant on the ellipoidal — it is a level ellipsoid. Theoretical gravity is the underlying model for more accurate models of the Earth's gravity.
In this article, the term gravity refers to the sum of gravitational attraction and the centrifugal force. The exposition below is taken from
The theoretical gravity model is specified by 4 parameters
The solution of the for potential was found by Somigliana (1929) and is expressed in ellipsoidal coordinates, u, β, λ. These are related to Cartesian coordinates, X, Y, Z, by
where
The level ellipsoid is given by u = b; on the ellipsoid β is the parametric latitude; λ is the longitude.
The normal potential exterior to the ellipsoid is given by
where
The acceleration due to gravity is given by
A more recent theoretical formula for gravity as a function of latitude is the International Gravity Formula 1980 (IGF80), also based on the WGS80 ellipsoid but now using the Somigliana equation:
where, [1]
providing,
A later refinement, based on the WGS84 ellipsoid, is the WGS ( World Geodetic System) 1984 Ellipsoidal Gravity Formula: [1]
(where = 9.8321849378 ms−2)
The difference with IGF80 is insignificant when used for geophysical purposes, [2] but may be significant for other uses.
In geodesy and geophysics, theoretical gravity or normal gravity is an exact solution for gravity for an idealized model of the Earth. In this model all the mass in contained within an ellipsoid of revolution which rotates about its polar axis. The mass distribution is such that gravity is normal to the surface of the ellipsoid; i.e., gravity potential is constant on the ellipoidal — it is a level ellipsoid. Theoretical gravity is the underlying model for more accurate models of the Earth's gravity.
In this article, the term gravity refers to the sum of gravitational attraction and the centrifugal force. The exposition below is taken from
The theoretical gravity model is specified by 4 parameters
The solution of the for potential was found by Somigliana (1929) and is expressed in ellipsoidal coordinates, u, β, λ. These are related to Cartesian coordinates, X, Y, Z, by
where
The level ellipsoid is given by u = b; on the ellipsoid β is the parametric latitude; λ is the longitude.
The normal potential exterior to the ellipsoid is given by
where
The acceleration due to gravity is given by
A more recent theoretical formula for gravity as a function of latitude is the International Gravity Formula 1980 (IGF80), also based on the WGS80 ellipsoid but now using the Somigliana equation:
where, [1]
providing,
A later refinement, based on the WGS84 ellipsoid, is the WGS ( World Geodetic System) 1984 Ellipsoidal Gravity Formula: [1]
(where = 9.8321849378 ms−2)
The difference with IGF80 is insignificant when used for geophysical purposes, [2] but may be significant for other uses.