Definition
Geocentric coordinates describe the position of a body as seen from the centre of the Earth. They can be ecliptic (longitude λ, latitude β, distance Δ) or equatorial (right ascension α, declination δ, distance Δ). Almanacs and ephemerides give geocentric positions because they are the same for every observer; each observer then applies the small topocentric correction for their own position.
The word is also used in two other senses that should not be confused: the geocentric model of the universe, which put the Earth at its centre, and geocentric latitude, a way of measuring latitude on the flattened Earth.
From heliocentric to geocentric
Planetary theories such as VSOP87 give heliocentric positions: longitude l, latitude b and radius vector r of each planet as seen from the Sun. The Earth's own heliocentric coordinates L0, B0, R are computed with the same theory. The geocentric position is the difference of the two vectors:
x = r cos b cos l − R cos B0 cos L0y = r cos b sin l − R cos B0 sin L0z = r sin b − R sin B0Δ = √(x² + y² + z²) λ = atan2(y, x) β = atan2(z, √(x² + y²))This is the core of Meeus's chapter on the positions of the planets. The Sun's geocentric position is the special case of a body at the origin: its geocentric longitude is the Earth's heliocentric longitude plus 180°, and its latitude is −B0.
Where the planet was, not where it is
Light takes time to arrive: τ = 0.0057755183 Δ days, about 8 minutes 19 seconds per astronomical unit. We see a planet where it was when the light left it, so its heliocentric position must be computed for t − τ. As Δ depends on τ, Meeus iterates: compute Δ, deduce τ, recompute the planet's position at t − τ, until the distance stops changing.
| Body | Typical light-time |
|---|---|
| Moon | 1.3 s |
| Sun | 8 min 19 s |
| Mars at opposition | 3 to 6 min |
| Jupiter | 33 to 53 min |
| Neptune | about 4 h |
| Voyager 1 (2026) | more than 23 h |
The motion of the Earth adds aberration, an apparent displacement of up to 20.5″ in the direction of the Earth's motion. With nutation on top, the result is the apparent geocentric position, the one an almanac lists and a telescope sees, before the topocentric and refraction corrections.
Geocentric and geodetic latitude
Because the Earth is flattened, the vertical at a place does not point to the Earth's centre. The geographic (geodetic) latitude φ, the one on maps and GPS, is the angle between the vertical and the equatorial plane. The geocentric latitude φ′ is the angle at the Earth's centre. They coincide at the equator and the poles and differ by up to 11.5′ at 45°.
The difference matters for the parallax correction of the Moon, which is why Meeus computes ρ sin φ′ and ρ cos φ′ from the geographic latitude and the height above sea level.
The geocentric model
For about two thousand years astronomy was geocentric in the other sense: the Earth was thought to be at rest at the centre of the universe. Ptolemy's Almagest (2nd century) predicted planetary positions with epicycles and deferents to within a degree or so, good enough to survive until Copernicus (1543), Kepler and Galileo. Ptolemy's model was not wrong as a description of geocentric directions: the apparent motions it reproduced, retrograde loops included, are exactly the geocentric coordinates computed today, only from a different physical picture.
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Frequently asked questions
What does geocentric mean in astronomy?
Centred on the Earth. Geocentric coordinates give the direction and distance of a body as seen from the centre of the Earth; ephemerides and almanacs are tabulated this way.
How do you convert heliocentric to geocentric coordinates?
Convert both the planet's and the Earth's heliocentric positions to rectangular coordinates, subtract the Earth's vector from the planet's, and convert back to longitude, latitude and distance. Correct for light-time by computing the planet's position for the moment the light left it.
What is the difference between geocentric and geodetic latitude?
Geodetic latitude, used on maps, is the angle of the local vertical to the equator. Geocentric latitude is the angle measured at the Earth's centre. Because the Earth is flattened, they differ by up to 11.5′ at 45° latitude.
