Definition
Heliocentric coordinates give the position of a body as seen from the centre of the Sun. The usual form is ecliptic: heliocentric longitude l, measured along the ecliptic from the vernal equinox; heliocentric latitude b, measured north or south of the ecliptic; and the radius vector r, the distance from the Sun in astronomical units. They can also be expressed as rectangular coordinates x, y, z.
This is the natural frame for the planets: in it, each planet follows a nearly fixed ellipse with the Sun at one focus. Seen from the Earth, the same motion includes the Earth's own orbit, and produces the loops and stations of retrograde motion.
Computing them: VSOP87
Astronomical Algorithms computes heliocentric coordinates of the planets with VSOP87 (Variations Séculaires des Orbites Planétaires), the theory published by Pierre Bretagnon and Gérard Francou at the Bureau des Longitudes in Paris in 1988. Each coordinate is a sum of periodic terms multiplied by powers of time:
τ = (JDE − 2451545.0) / 365250 (Julian millennia from J2000.0)L = L0 + L1 τ + L2 τ² + L3 τ³ + L4 τ⁴ + L5 τ⁵Li = Σ A cos(B + C τ)The full theory has thousands of terms per planet. Meeus publishes a truncated set, accurate to a few arc seconds in the current era, enough to compute positions far beyond what the eye can distinguish. The heliocentric view and the other views on this site are built on these same periodic terms.
Heliocentric positions of the planets
| Planet | Radius vector range | Daily motion in longitude |
|---|---|---|
| Mercury | 0.307 – 0.467 AU | 2.8° to 6.3° |
| Venus | 0.718 – 0.728 AU | 1.6° |
| Earth | 0.983 – 1.017 AU | 0.95° to 1.02° |
| Mars | 1.381 – 1.666 AU | 0.44° to 0.64° |
| Jupiter | 4.95 – 5.46 AU | about 0.083° |
| Saturn | 9.0 – 10.1 AU | about 0.033° |
Heliocentric latitudes stay small, at most equal to each orbit's inclination: up to ±7° for Mercury, ±3.4° for Venus, under ±2.5° for the others.
The Earth seen from the Sun
The Earth's heliocentric longitude is exactly opposite the Sun's geocentric longitude: L(Earth) = λ(Sun) − 180°. At the March equinox the Sun is at λ = 0° as seen from the Earth, so the Earth is at heliocentric longitude 180°. To compute the Sun's position, Meeus therefore computes the Earth's heliocentric coordinates with VSOP87 and simply turns them around.
The same Earth coordinates are subtracted from a planet's heliocentric coordinates to obtain its geocentric position.
Heliocentric or barycentric?
Strictly speaking the planets orbit the barycentre of the solar system, the centre of mass of the Sun and all the planets. Because of Jupiter and Saturn, the Sun itself moves around this point, by up to about two solar radii, in a looping path with a period close to Jupiter's. Modern ephemerides such as the JPL DE series are barycentric; heliocentric coordinates remain the natural choice for describing an individual orbit.
Heliocentric Julian Date
Observers of variable stars, exoplanet transits and pulsars correct the times of their observations to the Sun's centre. Depending on the Earth's position on its orbit, light from a star reaches the Earth up to about 8.3 minutes before or after it reaches the Sun. The heliocentric Julian Date (HJD) removes this effect, so that timings made at different seasons can be compared. Precise work now uses the barycentric version, BJD.
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Frequently asked questions
What are heliocentric coordinates?
Coordinates measured from the centre of the Sun: usually heliocentric ecliptic longitude, latitude and distance (the radius vector). They describe the planets' orbits directly.
What is VSOP87?
A planetary theory published by Bretagnon and Francou in 1988, giving the heliocentric coordinates of the planets as sums of periodic terms. Meeus uses a truncated version of it in Astronomical Algorithms.
Do planets orbit the Sun or the barycentre?
The barycentre, the centre of mass of the solar system. The Sun itself moves around it by up to about two solar radii, mostly because of Jupiter. For describing a single orbit, heliocentric coordinates are close enough and simpler.
