Last reviewed 16 Sept 2026 · 9 min read
Purpose of field astronomy
Field (practical) astronomy determines the absolute positions and directions on the earth from observations of celestial bodies (sun and stars):
- Azimuth (true bearing) of survey lines — orientation of traverses and triangulation networks, checking magnetic declination.
- Latitude and longitude of stations.
- Local time.
Today GNSS and gyro-theodolites provide much of this information, but the principles remain important for geodesy, verification and examinations.
The celestial sphere
The celestial sphere is an imaginary sphere of infinite radius with the observer (or earth's centre) at its centre, on which all celestial bodies appear projected.
| Term | Meaning |
|---|---|
| Zenith (Z) | Point on the celestial sphere vertically above the observer |
| Nadir | Point vertically below the observer |
| Celestial poles (P, P′) | Points where the earth's axis produced meets the celestial sphere |
| Celestial equator | Great circle where the plane of the earth's equator cuts the celestial sphere |
| Celestial horizon | Great circle perpendicular to the zenith–nadir line |
| Observer's meridian | Great circle through the zenith and the celestial poles |
| Prime vertical | Vertical circle through the zenith perpendicular to the meridian (through east and west points) |
| Vertical circle | Great circle through zenith and nadir |
| Hour circle (declination circle) | Great circle through the celestial poles |
| Ecliptic | Great circle traced by the sun's apparent annual path, inclined about 23°27′ to the celestial equator (obliquity of the ecliptic) |
| Equinoxes | Intersections of ecliptic and celestial equator — vernal equinox (first point of Aries, ♈) around 21 March and autumnal equinox (first point of Libra) around 23 September; day and night nearly equal |
| Solstices | Points of the ecliptic farthest from the equator — summer solstice around 21 June (sun's declination ≈ +23°27′) and winter solstice around 22 December (≈ −23°27′) |
Celestial coordinate systems
| System | Reference plane | Coordinates |
|---|---|---|
| Horizon system | Horizon | Altitude (α) — angle above the horizon (zenith distance ); Azimuth (A) — angle measured along the horizon from the meridian (north or south) |
| Independent equatorial system | Celestial equator | Declination (δ) — angle north or south of the celestial equator; Right ascension (RA) — angle measured eastward along the equator from the first point of Aries (independent of observer and time) |
| Dependent equatorial system | Celestial equator | Declination (δ); Hour angle (H) — angle measured westward along the equator from the observer's meridian (changes with time) |
| Ecliptic system | Ecliptic | Celestial latitude and celestial longitude |
Astronomical triangle (PZS triangle)
The spherical triangle formed by the celestial pole P, the zenith Z and the celestial body S.
| Side | Value |
|---|---|
| PZ | Co-latitude |
| PS | Co-declination (polar distance) |
| ZS | Co-altitude (zenith distance) |
| Angle | Value |
|---|---|
| At P | Hour angle |
| At Z | Azimuth |
| At S | Parallactic angle |
FormulaRelations in the astronomical triangle
Cosine rule:
Sine rule:
If any three of the six elements are known, the triangle can be solved.
Important relations
- Altitude of the celestial pole = latitude of the observer ().
- Culmination (transit) — a star crosses the observer's meridian twice a day: upper culmination (highest altitude) and lower culmination (lowest).
- Star culminating south of the zenith: (zenith distance at upper culmination).
- Star culminating north of the zenith: .
- Circumpolar stars — never set (always above the horizon) when (for northern latitudes); Polaris (declination close to 90°) is circumpolar in the northern hemisphere.
- Elongation — the position of a circumpolar star at its maximum azimuth east or west of the meridian; at elongation the parallactic angle is 90° and:
- Prime vertical transit — star crosses the prime vertical when .