Generator

The two-body-barycentre generator

Two bodies at a mass ratio of 3 to 1

Both bodies orbit their common centre of mass, on similar ellipses whose sizes are in inverse proportion to the masses — here 3 to 1, so the heavier body's path is 3 times smaller.

3 essays call two-body-barycentre. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Every figure listed here is the same construction drawn at different numbers, so a correction to one is a correction to all of them.

Gravitation

Neither body is still, and the wobble is how planets are found

A planet does not orbit its star. Both orbit a point between them, and the star's share of that motion is small, measurable, and the reason thousands of planets are known.

One measured number, and every pair of masses that produces it. The plane of the two component masses of an inspiralling binary, with three curves of constant chirp mass across it. The middle one is GW150914's value of 28.7 solar masses, and the chirp mass recovered from the coordinates of the drawn curve varies along its whole length by 7.4e-14 per cent — which is the point: every binary on that line radiates the same frequency sweep at leading order, so the early inspiral cannot tell them apart. Two of them are marked. An equal pair of 33.0 and 33.0 solar masses and a lopsided pair of 63.6 and 18.4 sit on the same contour, and their total masses differ by a factor of 1.24. What separates them is the mass ratio, which enters the phasing only at the first post-Newtonian order, suppressed by the square of the orbital speed in units of the speed of light — small through the hundreds of cycles that carry most of the signal, and appreciable only in the last few, where that speed approaches a third of c. So the chirp mass is a measurement and the individual masses are an inference from the end of the signal, which is exactly the part a detector's high-frequency noise eats first.

Gravitation

One number where two masses were

The hundreds of orbits an inspiralling binary completes inside a detector's band depend on its two masses only through one combination of them. Every pair on that contour radiates an identical sweep, so the early signal — which carries nearly all the signal-to-noise — cannot say which pair it was.

Two bodies at a mass ratio of 2.6 to 1. Both bodies orbit their common centre of mass, on similar ellipses whose sizes are in inverse proportion to the masses — here 2.6 to 1, so the heavier body's path is 2.6 times smaller.

Stars

The companion survives, and it is moving

When one star of a close pair explodes, the other is left holding an orbital velocity and no orbit. Whether the pair stays bound turns on a single question — did more than half the total mass leave? — and the stars that answer no are running across the Galaxy at a hundred kilometres a second with nothing visible behind them.

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