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If the Earth had a constant density ρ, the mass would be M(r) = (4/3)πρr 3 and the dependence of gravity on depth would be =. The gravity g′ at depth d is given by g′ = g(1 − d/R) where g is acceleration due to gravity on the surface of the Earth, d is depth and R is the radius of the Earth.
The best estimate of Earth's mass is obtained by dividing the product GM as determined from the analysis of spacecraft orbit with a value for the gravitational constant G, determined to a lower relative accuracy using other physical methods.
where R is the ideal gas constant, T is temperature, M is average molecular weight, and g 0 is the gravitational acceleration at the planet's surface. Using the values T=273 K and M=29 g/mol as characteristic of the Earth's atmosphere, H = RT/Mg = (8.315*273)/(29*9.8) = 7.99, or about 8 km, which coincidentally is approximate height of Mt. Everest.
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: [2] = = 9.80665 m/s 2 (32.1740 ft/s 2)
The gravity gradient (variation with height) above Earth's surface is about 3.1 μGal per centimeter of height (3.1 × 10 −6 s −2), resulting in a maximal difference of about 2 Gal (0.02 m/s 2) from the top of Mount Everest to sea level.
For geophysical applications, gravity is distinguished from gravitation. Gravity is defined as the resultant force of gravitation and the centrifugal force caused by the Earth's rotation. Likewise, the respective scalar potentials can be added to form an effective potential called the geopotential, .
GeographicLib provides a utility GeoidEval (with source code) to evaluate the geoid height for the EGM84, EGM96, and EGM2008 Earth gravity models. Here is an online version of GeoidEval . The Tracker Component Library from the United States Naval Research Laboratory is a free Matlab library with a number of gravitational synthesis routines.
Geopotential height differs from geometric height (as given by a tape measure) because Earth's gravity is not constant, varying markedly with altitude and latitude; thus, a 1-m geopotential height difference implies a different vertical distance in physical space: "the unit-mass must be lifted higher at the equator than at the pole, if the same ...