← All parts of this equation

Equation 7 · Part 17 · How We Know What Is Inside a Planet

Ending index or upper bound: infty

U(r,θ)=GMr[1−∑n=2∞Jn(Rr)nPn(cos⁡θ)]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]
∞\infty

What this part means

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

Its job in the formula

infty appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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,θ)=GMr[1−∑n=2∞Jn(Rr)nPn(cos⁡θ)]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 →

Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

Open the illustrated sums and products: repeat an operation over an index guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.