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Equation 1 · Part 2 · The Atlas That Refuses to Close

Symbol a

RN=∑amara/∑ama\mathbf R_N = \sum_a m_a \mathbf r_a / \sum_a m_a
aa

What this part means

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

Its job in the formula

a 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

Start with the least controversial position anyone has ever assigned to an extended body: the Newtonian, mass-weighted centroid, RN\mathbf R_N = ∑a\sum_a mam_a ra\mathbf r_a / ∑a\sum_a mam_a , a sum over the body’s constituent mass elements mam_a at positions ra\mathbf r_a , evaluated at one common instant. That last clause is doing all the work relativity is about to object to. “One common instant” means one value of a time coordinate t shared by every term in the sum — the coordinate time…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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