Geopotential model

In geophysics, a geopotential model is the theoretical analysis of measuring and calculating the effects of Earth's gravitational field.

Newton's law of universal gravitation states that the gravitational force F acting between two point masses m₁ and m₂ with centre of mass separation r is given by

where G is the gravitational constant and r̂ is the radial unit vector. For an object of continuous mass distribution, each mass element dm can be treated as a point mass, so the volume integral over the extent of the object gives:

${\displaystyle \mathbf {\bar {F}} =-G\int \limits _{V}{\frac {\rho }{r^{2}}}\mathbf {\hat {r}} \,dx\,dy\,dz}$

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