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Equation 2 · Part 5 · Cosmological Natural Selection: A Theory That Named Its Own Killer

=

ΔS(ϕ)=−2r ln⁡ ⁣[1−ssin⁡ϕ]\Delta_S(\phi) = -2r\,\ln\!\left[1 - s\sin\phi\right]
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

The way you weigh a neutron star from a radio telescope, with no direct access to the star at all, is to time its pulses with enough precision to catch general relativity bending them. In a binary system seen close to edge-on, radio pulses from the neutron star are delayed by a few extra microseconds each orbit as they pass close to the companion star, because the companion’s gravity curves the spacetime the pulse crosses. The delay as a function of orbital phase ϕ\phi is standardly written ΔS(ϕ)=−2r ln⁡ ⁣[1−ssin⁡ϕ]\Delta_S(\phi) = -2r\,\ln\!\left[1 - s\sin\phi\right]. where the “range” parameter r is set directly by the companion’s mass and the “shape” parameter s by the orbit’s inclination. Because r and s are measured independently of the pulsar’s…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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