Astronomy & Celestial Mechanics
the sky, computed
Concept

Eclipse timing — where it appears

The measurement of when a binary star's eclipses occur, compared with a uniform schedule. Departures from that schedule reveal a third body, either by its pull on the pair or by the light-travel delay as the pair is carried round a wider orbit.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Three causes, three shapes, one residual. An eclipse-timing residual: the observed minus the computed time of each eclipse, against cycle number, in days. Three effects are superposed and each has its own functional form. A slow change in the orbital period — from mass transfer or from magnetic braking — integrates to a parabola. A third body in a wide orbit moves the whole binary towards and away from the observer, so its light-travel time adds a sinusoid at the third body's period. And an eccentric orbit whose apsides are precessing moves the two eclipses in opposite directions, which is a sinusoid that changes sign between primary and secondary minima. The last is why both eclipses have to be timed: a third body moves them together and apsidal motion moves them apart, and a series of primary minima alone cannot tell the two apart at all.

Three causes with three shapes in one curve

The times of eclipse in a binary star are a clock, and the clock runs late and early. Three completely different things make it do so — a third body, a changing period, and a slowly turning orbit — and they are separable only because each imposes a different shape on the residual.

stars · Binary stars Io's eclipses, early at opposition and late at conjunction. The delay in the timing of Io's eclipses by Jupiter's shadow caused by the changing distance between the Earth and Jupiter, against days from an opposition, for circular orbits at 1 and 5.2026 AU. At opposition the two planets are closest and the eclipses arrive 8.3 minutes early against the average; 199 days later, near conjunction, they are furthest apart and arrive 8.3 minutes late. The whole swing, 16.6 minutes, is the time light takes to cross the diameter of the Earth's orbit, and the pattern repeats every 399 days, the synodic period. This is transit timing done on a moon in 1676, with a clock that ran on Io's 42.5-hour orbit and a residual that had nothing to do with Io.

A transit late by the width of an orbit

A transiting planet's clock can run fast and slow for a reason that has nothing to do with gravity acting on the planet. If its star is itself in orbit about a distant companion, each transit's light has further or less far to travel, and the timing wanders by the light-travel time across the star's orbit. It is the measurement that first showed light has a speed, made again on a different kind of clock.

exoplanets · Transit-timing

Named alongside it

The objects these essays reach for when they reach for this one.

EphemerisLight-travel timeApsidal motionBarycentreDegeneracyDoppler effectMagnetic brakingMass transferO minus cPeriod changePulsar timingRadial velocity

All concepts