Latitude and longitude for the sky
Equatorial coordinates extend the Earth's latitude and longitude onto the sky. The reference plane is the celestial equator, the projection of the Earth's equator. Declination (δ) is the angle north or south of it, from +90° at the north celestial pole to −90° at the south pole. Right ascension (α) is measured eastward along the equator from the vernal equinox, the point where the Sun crosses the equator in March.
Right ascension is usually given in hours, minutes and seconds rather than degrees: 24h make a full circle, so 1h = 15° and 1m = 15′. This unit is not arbitrary. The sky turns by 1h of right ascension in about one hour of time, so the right ascension of a star tells you when it crosses your meridian.
Coordinates of some bright stars
| Star | Right ascension (J2000) | Declination (J2000) |
|---|---|---|
| Polaris | 02h 31m 49s | +89° 16′ |
| Capella | 05h 16m 41s | +46° 00′ |
| Betelgeuse | 05h 55m 10s | +07° 24′ |
| Sirius | 06h 45m 09s | −16° 43′ |
| Antares | 16h 29m 24s | −26° 26′ |
| Vega | 18h 36m 56s | +38° 47′ |
The hour angle and your local sky
Right ascension and declination do not change as the Earth turns: they are attached to the stars. To know where a star is in your sky, you also need the hour angle H, the angle between your meridian and the star, measured westward. It is simply the local sidereal time minus the right ascension:
H = LST − αH = 0h the star is on the meridian (transit)H = +3h the star crossed the meridian three hours agomaximum altitude = 90° − |φ − δ| (φ = observer's latitude)Vega (δ = +38.8°) seen from Paris (φ = +48.9°) culminates 79.9° high, almost overhead. A star is circumpolar, and never sets, when its declination is greater than 90° − φ: from Paris that means δ > +41.1°. Capella is circumpolar there, but Vega is not.
Epochs: J2000 and "of date"
The celestial equator and the equinox slowly move because of precession, so equatorial coordinates always refer to a date. Star catalogues use a standard epoch, today J2000.0 (1 January 2000, 12h TT). Since then Vega's right ascension has increased by about 54 s because of precession alone.
Astronomers distinguish mean coordinates, which include only precession, from true coordinates, which also include nutation, and apparent coordinates, which add aberration and are what you would really measure. Modern catalogues are referred to the International Celestial Reference System (ICRS), whose axes stay within a few hundredths of an arcsecond of the J2000 equator and equinox.
Converting to ecliptic coordinates
The equator and the ecliptic are inclined by the obliquity ε, about 23.44°. A rotation around the line of equinoxes converts one system into the other:
tan λ = (sin α cos ε + tan δ sin ε) / cos αsin β = sin δ cos ε − cos δ sin ε sin αMeeus' example uses Pollux (α = 7h 45m 18.946s, δ = +28° 01′ 34.26″, ε = 23.4392911°). The result is λ = 113.215630° and β = +6.684170°. Use the two-argument arctangent (atan2) to get λ in the right quadrant.
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Frequently asked questions
Why is right ascension measured in hours?
Because the sky turns by 360° in about 24 hours, so 1 hour of right ascension equals 15°. A star with a right ascension one hour greater than another crosses the meridian about one hour later.
Do the coordinates of a star change?
Slowly. Precession shifts right ascension and declination by up to about 20″ per year, and nearby stars have their own proper motion. This is why catalogues give coordinates for a stated epoch such as J2000.0.
Which stars never set from my location?
Those whose declination is greater than 90° minus your latitude, in the northern hemisphere. From latitude 49°N, every star north of declination +41° is circumpolar.
