Astronomy & Celestial Mechanics
the sky, computed
Concept

Speed of light — where it appears

The speed at which light and every other electromagnetic signal travels in a vacuum, fixed by definition at 299,792,458 metres a second. It was first measured from the delays of Io's eclipses and the aberration of starlight, and now turns timing delays into distances.

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

The same ellipse at 955 times the size, and a quarter of a year out of step. The aberration ellipse (solid) and the parallax ellipse (dashed) for γ Draconis at four ecliptic latitudes, drawn to one scale. Aberration is v/c towards the Earth's own direction of travel, so its ellipse has semi-major axis 20.49551″ for every star in the sky; parallax is 1/d towards the Sun, so its semi-major axis is that star's own 0.02147″ — 955 times smaller, and drawn 955 times smaller here. At the ecliptic pole both are circles; on the ecliptic both collapse to lines; in between both are ellipses of semi-minor axis sin β times the major, and the ratio is identical at every latitude because both effects project the same way. The marks are the same four dates on each: they are a quarter of a year apart between the two, because the aberration displacement follows the Earth's velocity and the parallax displacement follows its position, and velocity leads position by 90° on a circular orbit. That quarter-year is the only thing distinguishing the two phenomena on the sky, and it is why Bradley, looking for the dashed ellipse in 1728, spent months unable to interpret the solid one he had found instead.

The other twenty arcseconds

Every star in the sky traces a small ellipse over a year, of the same shape as its parallax ellipse and 90° out of step with it — and the same size for all of them, near or far. Bradley found it in 1728 while hunting for parallax, and it proved the Earth moves a century before anything's distance was known.

sky · Aberration 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.

Doppler effectAberrationAstrometryBarycentreCelestial coordinatesEclipse timingEclipticEphemerisLight-travel timeParallaxProper motionPulsar timing

All concepts