A spinning top the size of a planet
Spin a top slightly tilted and its axis slowly sweeps a cone instead of staying fixed. The Earth does the same. Its axis, tilted 23.4° from the perpendicular to its orbit, traces a full circle in about 25,800 years. This motion is called axial precession, or the precession of the equinoxes.
The cause is the Earth's shape. Rotation makes the planet bulge at the equator, where the radius is about 21 km larger than at the poles. The Moon and the Sun pull on this bulge and try to bring it into the plane of their orbits. Because the Earth is spinning, it does not straighten up: its axis swings sideways instead, like the top. The Moon is responsible for about two thirds of the effect, the Sun for the rest.
A discovery from ancient star catalogues
Around 130 BC Hipparchus compared his own star positions with those recorded about 150 years earlier by Timocharis. The longitudes had all increased by the same amount, while the latitudes had not changed. He concluded that the equinox itself was moving westward along the ecliptic, by at least 1° per century. The modern value is 1° in 71.6 years, or about 1.4° per century.
What precession changes
- The equinoxes move. The vernal equinox, the zero point of right ascension and ecliptic longitude, slides westward along the ecliptic by about 50.3″ per year. Every star's ecliptic longitude increases by the same amount.
- The year is shorter than one orbit. Because the equinox moves to meet the Sun, the tropical year of the seasons (365.2422 days) is about 20 minutes shorter than the sidereal year (365.2564 days), the time the Earth takes to return to the same position among the stars.
- The pole star changes. The celestial pole moves among the stars, so Polaris is only a temporary pole star (see the table below).
- Star coordinates change. Right ascension and declination are measured from the equator and the equinox, which both move. A catalogue must therefore state its epoch, and modern catalogues use J2000.0 (1 January 2000, 12h TT).
Pole stars through the ages
| Star | Epoch as pole star | Note |
|---|---|---|
| Thuban (α Draconis) | around 2700 BC | Pole star when the Great Pyramid was built |
| Kochab (β Ursae Minoris) | around 1000 BC | Shared the role with Pherkad, but never very close to the pole |
| Polaris (α Ursae Minoris) | now, closest around AD 2100 | Will come within about 0.45° of the pole |
| Errai (γ Cephei) | around AD 4000 | |
| Deneb (α Cygni) | around AD 10,000 | About 7° from the pole |
| Vega (α Lyrae) | around AD 14,000 | Within a few degrees: a brilliant pole star |
Correcting star positions
Over a few years, the annual change in right ascension α and declination δ caused by precession can be estimated with a simple formula from Meeus:
Δα = m + n × sin α × tan δ (seconds of time per year)Δδ = n' × cos α (arcseconds per year)m = 3.075 s, n = 1.336 s, n' = 20.04″Worked example: Vega (α = 18h 36m 56s, δ = +38° 47′ at J2000.0). Here sin α = −0.987 and tan δ = 0.804, so Δα = 3.075 − 1.060 = 2.015 s per year and Δδ = 20.04″ × 0.160 = +3.2″ per year. Between J2000.0 and late 2026 Vega's right ascension has increased by about 54 s and its declination by about 1.4′. That is why the current right ascension of Vega is about 18h 37m 50s.
Over longer intervals, or for stars near the pole where tan δ becomes large, the simple formula breaks down. The rigorous method rotates the coordinates with three angles (ζ, z and θ) given as polynomials in time, and Meeus gives both approaches.
Planetary precession and nutation
The planets also tug on the Earth, and they slowly tilt the plane of the Earth's orbit, the ecliptic, by about 47″ per century. The combined motion of the equinox caused by the Moon, the Sun and the planets is called general precession, and it currently amounts to about 5029″ per century in longitude.
Precession is not perfectly smooth. The Moon's orbit is tilted and its nodes turn every 18.6 years, so the pull on the equatorial bulge varies, and the axis nods back and forth around its mean position by up to about 17″ in longitude and 9″ in obliquity. This nodding is called nutation. Precise positions include both precession and nutation.
Precession and the zodiac
In the time of Hipparchus the vernal equinox lay in the constellation Aries, and the sign of Aries was defined to start there. Precession has since carried the equinox about 30° westward, into Pisces, and it will reach Aquarius in several centuries. This is the origin of the "Age of Aquarius". The tropical zodiac used in Western astrology stays tied to the equinox, while the sidereal zodiac used in Indian astrology stays tied to the stars. The two systems currently differ by about 24°. The heliocentric view on AstroAlgos can display both sets of zodiac limits so you can see the shift.
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Frequently asked questions
How long is the precession cycle?
About 25,800 years for one full turn of the Earth's axis. The equinox moves westward along the ecliptic by about 50.3″ per year, or 1° every 71.6 years.
Will Polaris always be the pole star?
No. Polaris will come closest to the celestial pole around the year 2100, at about 0.45°, and then drift away. Errai will take over around AD 4000, and around AD 14,000 the brilliant Vega will lie within a few degrees of the pole.
Does precession affect the zodiac signs?
Yes. The signs of the tropical zodiac are tied to the equinox, which has moved about 24° against the stars since the zodiac was defined. So the Sun is usually in a different constellation from its tropical sign. For example, at the March equinox it is now in Pisces, not in Aries.