Normal gravity

In geodesy and geophysics, theoretical gravity or normal gravity is an approximation of the true effective or apparent gravity on Earth's surface by means of a mathematical model representing (a physically smoothed) Earth. The most common model of a smoothed Earth is an Earth ellipsoid, or, more specifically, an Earth spheroid (i.e., an ellipsoid of revolution).

Various, successively more refined, formulas for computing the theoretical gravity are referred to as the International Gravity Formula, the first of which was proposed in 1930 by the International Association of Geodesy. The general shape of that formula is:

in which g(φ) is the gravity as a function of the geographic latitude φ of the position whose gravity is to be determined, ${\displaystyle g_{e}}$ denotes the gravity at the equator (as determined by measurement), and the coefficients A and B are parameters that must be selected to produce a good global fit to true gravity.

Using the values of the GRS80 reference system, a commonly used specific instantiation of the formula above is given by:

Using the appropriate double-angle formula in combination with the Pythagorean identity, this can be rewritten in the equivalent forms

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