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Concept
Theoretical gravity
Summary
In geodesy and geophysics, theoretical gravity or normal gravity is an approximation of the true gravity on Earth's surface by means of a mathematical model representing Earth. The most common model of a smoothed Earth is a rotating Earth ellipsoid of revolution (i.e., a spheroid). The type of gravity model used for the Earth depends upon the degree of fidelity required for a given problem. For many problems such as aircraft simulation, it may be sufficient to consider gravity to be a constant, defined as: based upon data from World Geodetic System 1984 (WGS-84), where is understood to be pointing 'down' in the local frame of reference. If it is desirable to model an object's weight on Earth as a function of latitude, one could use the following: where
=
= latitude, between −90° and +90° Neither of these accounts for changes in gravity with changes in altitude, but the model with the cosine function does take into account the centrifugal relief that is produced by the rotation of the Earth. For the mass attraction effect by itself, the gravitational acceleration at the equator is about 0.18% less than that at the poles due to being located farther from the mass center. When the rotational component is included (as above), the gravity at the equator is about 0.53% less than that at the poles, with gravity at the poles being unaffected by the rotation. So the rotational component of change due to latitude (0.35%) is about twice as significant as the mass attraction change due to latitude (0.18%), but both reduce strength of gravity at the equator as compared to gravity at the poles. Note that for satellites, orbits are decoupled from the rotation of the Earth so the orbital period is not necessarily one day, but also that errors can accumulate over multiple orbits so that accuracy is important. For such problems, the rotation of the Earth would be immaterial unless variations with longitude are modeled. Also, the variation in gravity with altitude becomes important, especially for highly elliptical orbits.Official source
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