Geopotential spherical harmonic model

In <a href="/facts/Geophysics/ywVQ1sAQ">geophysics</a> and <a href="/facts/Physical_geodesy/muDSdFLC">physical geodesy</a>, a geopotential model is the theoretical analysis of measuring and calculating the effects of <a href="/facts/Earth/HLLmDfj0">Earth</a>'s <a href="/facts/Gravitational_field/K1uTmJFy">gravitational field</a> (the <a href="/facts/Geopotential/5LFGRzhT">geopotential</a>).
The Earth is not exactly spherical, mainly because of its rotation around the polar axis that makes its shape slightly oblate. 
However, a <a href="/facts/Spherical_harmonics/bn98Gv2L">spherical harmonics</a> <a href="/facts/Series_expansion/ElmJVK7Q">series expansion</a> captures the actual field with increasing fidelity.
If <a href="/facts/Earth%27s_shape/z1LvpVgd">Earth's shape</a> were perfectly known together with the exact mass density ρ = ρ(x, y, z), it could be <a href="/facts/Numerical_integration/MwJnvcDV">integrated numerically</a> (when combined with a <a href="/facts/Gravitational_potential/x4ITT4gY">reciprocal distance kernel</a>) to find an accurate model for Earth's gravitational field. However, the situation is in fact the opposite: by observing the orbits of spacecraft and the Moon, Earth's gravitational field can be determined quite accurately. The best estimate of <a href="/facts/Earth%27s_mass/G74DaKFv">Earth's mass</a> is obtained by dividing the product GM as determined from the analysis of spacecraft orbit with a value for the <a href="/facts/Gravitational_constant/GdQ8tcBD">gravitational constant</a> G, determined to a lower relative accuracy using other physical methods.

Geopotential spherical harmonic model open-in-new

Geopotential spherical harmonic model