Geopotential model in spherical harmonics

Summary

A geopotential model expands the gravitational potential of the Earth in spherical harmonics. Outside the Earth the potential is a harmonic function that tends to $0$ at infinity. So it is a series of terms $r^{-n-1}$ times surface spherical harmonics of degree $n$. The model is a table of coefficients $\bar C_{nm}, \bar S_{nm}$, estimated from satellite orbits and gravity data. The largest term after the central one is $J_2$, which describes the Earth's flattening.