Right Ascension

Definition

Right ascension, written α or RA, is one of the two equatorial coordinates that locate a star on the celestial sphere. It is the angle measured eastward along the celestial equator, from the vernal equinox to the hour circle through the object, the great circle running from pole to pole through it. Together with declination, the angle north or south of the equator, it plays the role that longitude and latitude play on Earth.

Unlike altitude and azimuth, right ascension does not depend on where you are or what time it is. The stars keep the same right ascension night after night, while the whole sky turns overhead. This is what makes it the standard coordinate of star catalogues, ephemerides and telescope mounts.

Why right ascension is measured in hours

Right ascension runs from 0h to 24h rather than from 0° to 360°, because the sky turns once a day. The conversion is fixed:

24h = 360°      1h = 15°1m = 15′         1s = 15″α(°) = 15 × α(h)

Example: Sirius is at α = 6h 45m 09s, that is 6 + 45/60 + 9/3600 = 6.7525 h, or 101.2875°. Note that the minutes and seconds of right ascension (m, s) are units of time, larger than the arcminutes and arcseconds (′, ″) of declination by a factor of 15.

The name is historical. For an observer on the Earth's equator, where the celestial equator stands at right angles to the horizon (the sphaera recta of medieval astronomers), right ascension measured the time it took a point of the sky to rise.

Hour angle and sidereal time

Measuring in hours links right ascension directly to the clock. The local sidereal time is the right ascension currently crossing your meridian, the north–south line through the zenith. The hour angle H of a star, the time since it crossed the meridian, follows by simple subtraction:

H = θ − αθ = local sidereal time

A star culminates, reaching its highest point in the south for northern observers, when the local sidereal time equals its right ascension. Local sidereal time at midnight is about 0h around 22 September and gains about 2 hours per month. So Sirius, at 6h 45m, culminates at midnight around 1 January and is a winter star, while Vega, at 18h 37m, culminates at midnight in early July.

This is how an equatorial telescope mount is used: set the hour angle on its axis, and a motor turning at the sidereal rate keeps the star in the field.

Computing right ascension

Planetary theories such as VSOP87 give positions in ecliptic coordinates, longitude λ and latitude β. Meeus converts them to right ascension with the obliquity of the ecliptic ε:

tan α = (sin λ × cos ε − tan β × sin ε) / cos λ

The quadrant of α must be taken from the signs of the numerator and the denominator, for example with the atan2 function, otherwise the result can be 180° off. Right ascension is never exactly the same as ecliptic longitude for points on the ecliptic at 0h, 6h, 12h and 18h: midway between an equinox and a solstice the two differ by about 2.5°.

Right ascension changes slowly: precession

The vernal equinox, the zero point of right ascension, slides westward along the ecliptic by about 50″ per year because of precession. Every star's right ascension therefore changes slowly, by about 3 seconds of time per year for stars near the equator, more near the poles. Catalogues give coordinates for a stated epoch, nowadays J2000.0, aligned with the International Celestial Reference System. To point at a star today, its position must be precessed to the current date, and for accuracy corrected for nutation and aberration as well.

Δα ≈ m + n × sin α × tan δ       (per year)m = 3.075 s     n = 1.336 s

Coordinates of some bright stars

Explore it on AstroAlgos

• Equatorial coordinates — the full system
• Sidereal time — the right ascension on your meridian
• All-sky disk — the stars above you now
• Precession — why right ascensions drift