Astronomy & Celestial Mechanics
the sky, computed
Concept

Celestial coordinates — where it appears

Systems of angles that locate objects on the sky, such as right ascension and declination measured from the celestial equator. Each is tied to a reference frame, and converting between frames is part of every precise position.

Named by 2 essays across one field — 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 The whole sky leans towards the east point. The direction and relative size of the diurnal aberration at points across the sky for an observer at latitude 52°, drawn against azimuth and altitude with the arrows enlarged several hundred thousand times. Every star is moved along the great circle towards the east point of the horizon, by 0.197 arcseconds times the sine of its distance from that point: most on the meridian and at the zenith, not at all at the east and west points themselves.

A third of an arcsecond set by where the telescope stands

The ground under a telescope carries it east at up to 465 metres a second, and every star is displaced towards the east point of the horizon by up to a third of an arcsecond. It is the smallest aberration that changes, the only one that differs between two observatories looking at the same star at the same moment, and it makes a star near the pole cross the meridian a second late. In orbit the same effect is sixteen times larger and reverses every forty-six minutes.

sky · Aberration

Named alongside it

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

AberrationAstrometryReference frameSpeed of lightDoppler effectEclipticParallaxProper motionSolar apexStellar aberration

All concepts