This page last modified 1998 July 21

Positional Astronomy

Positions on Earth

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We measure positions on Earth's surface by Latitude and Longitude. Latitude is referred to a reference plane, an imaginary plane which passes through Earth at the Equator. Longitude is referred to a reference direction, the meridian which passes through Greenwich.

Positions on the Celestial Sphere

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We imagine that astronomical objects are projected onto a celestial sphere, centred upon Earth. Earth's North and South poles are projected to the North Celestial Pole (NCP) and South Celestial Pole (SCP) respectively. Earth's equatorial plane passes through the Celestial Equator, which forms our reference plane. (The determination of the reference direction will be covered later)


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An observer on Earth sees part of the curve of Earth's surface as the horizon.

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This horizon can also be projected onto the celestial sphere as the Celestial Horizon. The point directly above the observer is the Zenith; the point directly below is the Nadir. The observer's compass directions, N, E, S, W, can also be projected onto this plane. A great circle on the which passes through N, S and the Zenith is called the Meridian. The meridian also passes through the NCP and the SCP. The altitude of an object is measured with respect to the Celestial Horizon; i.e. its reference plane is the horizontal plane. (Zenith Distance = 90° - altitude) Azimuth is measured through east from North; i.e. its reference direction is the North point on the horizon.

Altitude of Celestial Pole

The altitude of the NCP is equal to the latitude of the observer. The highest altitude of the celestial equator (i.e. due S) is the complement of the latitude.


Equatorial Co-ordinates

Equatorial Co-ordinates are referred to the Celestial Equator as the reference plane and to the First Point of Aries (FPA) as the reference direction. The FPA is the position of the Vernal Equinox; it is where the Ecliptic crosses the Celestial Equator. Owing to the Precession of the Equinoxes, the FPA moves around the equator with a period of about 26,000 years. Equatorial positions must therefore be referred to a date or Epoch. The epoch currently used is AD2000.0

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The Declination (Dec) of an object is its position measured northwards from the equatorial plane. It is measured in degrees. Objects south of the equator have negative declinations. Dec is analogous to Latitude.

The Right Ascension (RA) of an object is it's position, measured eastwards around the equator, from the FPA. By convention, the equator is not divided into 360°, but into 24 hours (and minutes and seconds. (The reason for this will become apparent in the section on Sidereal Time.) RA is analogous to Longitude.

The Hour Angle (HA) of an object is its position, measured around the celestial equator, westward from the observer's meridian.

Co-ordinate conversions

Users of altazimuthally mounted instruments often find it useful to be able to convert equatorial co-ordinates to horizon (altitude and azimuth) ones.

r = right ascension
LST = local sidereal time
d = declination
A = azimuth
a = altitude
l = latitude

sin(a) = sin(d) × sin(l) + cos(d) × cos(l) × cos(LST-r)

cos(A) = (sin(d) - sin(l) × sin(a)) / (cos(l) × cos(a))


Among the best is Chris Kitchin's excellent Telescopes and Techniques, which is thorough and explains it in clear language.

For detailed accounts of co-ordinate transformations, see Gerald North's chapter in The Modern Amateur Astronomer gives a simple introduction which expands upon the notes given above.