PrecessX for Macintosh OSX
Precession of the equinoxes, pole, and celestial sphere

PrecessX is a Macintosh OSX program which performs luni-solar-planetary precession of celestial coordinates according to the rotation matrices defined in Green's 'Spherical Astronomy' and the 'Astronomical Almanac'. Nutation is not performed. Celestial objects at coordinates for epoch J2000 can be precessed to any date. For example, here is the precessional path of the Vernal equinox from the years 2000 to 22500, during which this point makes one complete circuit about the celestial sphere:

Here is the precessional path of the Earth's north pole from the years 2000 to 23500, during which this point makes one complete circuit about the pole of the ecliptic:

Here is the precessional path of the star Thuban (Alpha Draconis) from the years 5000 BC to 2000 AD. The maximum declination of this star (89d 54m 10s) occurs at about 2800 BC, at which time it was the Earth's northern 'pole star':

It has been suggested that the Great Pyramid of Khufu was constructed to be aligned with this star when it was the pole star. See the following sites (or do a Google search on 'Thuban pyramid') for more info:

After making one revolution about the ecliptic pole, the Earth's pole appears to flip over several times, and then chaotically pass through every point in the celestial sphere. The following images show the path of polar orientation from 2000 to 23500, 30000, 40000, 50000, 100000, and 200000 years:

Whether or not this will actually happen (and therefore also happened in the past) is a matter of speculation, since there are no human astronomical records from the equivalent dates in the past. However, the extreme behavior of the pole is probably due to the underlying equations for the 3 precession angles zeta, z, and theta, which are third degree polynomials in Julian centuries, and thus go to infinity outside of a near-linear range in which they are accurate (about +/- 1 polar revolution):

Nevertheless, the planetary astronomer J. Kelly Beatty, in a talk given at Stanford University in the early 1990's, suggested that the Earth's pole undergoes exactly this chaotic motion, but on a much longer time scale. As a demonstration, he played with a gyroscope on the end of a string. While he held the string still, the gyroscope precessed in a regular periodic manner according to the torque exerted on it by gravity. However, when he moved his hand in a circular periodic path with a different period, the gyroscope began to pitch up and down --almost upside down-- in a very chaotic fashion. He suggested that the large size of the Earth's moon, and its orbital period, works to stabilize the Earth's polar precession so that it does not behave in this manner (and cause considerable climatic changes) during the period necessary for human life to evolve. It has also been suggested that Mars, due to the small sizes of its moons, is subjected to this chaotic motion, and this may be the reason why life did not evolve on that planet.

The PrecessX program can also show the positions of any number of stars at any time in past or future history. Here are the positions of some of the stars from the Yale Bright Star Catalog at 2000 AD and 2800 BC. The area of the circle used to display each star is based on its visual magnitude:

Here is detail of the night sky in the northern hemisphere at 2800 BC and 2000 AD, showing the polar shift from Thuban to Polaris (Alpha Ursa Minor). The 'big dipper' can be seen to the right of the pole at 2800 BC, and below the pole at 2000 AD:

© Sky Coyote 2004