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Equation 16 · Part 2 · A Neutron Star Is a Redshift Standard

Symbol c^2

Φs/c2\Phi_s/c^2
c2c^2

What this part means

The square of c: multiply c by itself.

Its job in the formula

c2c^2 is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

The passage around this formula

That test would not be a marginal addition to existing equivalence-principle work. The emitting atoms on a neutron-star surface sit in a gravitational potential Φs\Phi_s/c2c^2 of order 0.2 to 0.4 — a QCD-dominated binding environment seven to eight orders of magnitude deeper than anything a terrestrial free-fall experiment reaches. MICROSCOPE’s satellite test of the weak equivalence principle, the most precise ever flown, bounds a titanium-platinum pair’s differential free fall at η\eta=(-1.5±\pm2.3±\pm1.5)×\times10^{-15} [ 13 ] , but at a potential difference near 10^{-10} — many orders shallower than a neutron star’s surface. In the dilaton-coupling framework Thibault Damour and John Donoghue laid…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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