Symbol P_n

The passage around this formula

A spacecraft in orbit is a gravimeter. Its along-track velocity is perturbed by mass anomalies beneath it, and Doppler tracking of the radio link records those perturbations. Expanded outside the body, the potential from a rotationally symmetric mass distribution takes the form $U(r,\theta) = \frac{GM}{r}\left[1 - \sum_{n=2}^{\infty} J_{n}\left(\frac{R}{r}\right)^{n} P_{n}(\cos\theta)\right]$. and the factor (R/r)^{n} is the whole epistemology of gravity-based interior work. Each successive degree n decays faster with altitude, so high-degree terms are measurable only from low orbit and are dominated by shallow structure. Low-degree terms reach deep but are few. A gravity field is therefore a filter that attenuates depth information in a known, unavoidable way.

Read this part in the article →