Gobekli Tepe's Pillars

A note on Precession of the Equinoxes

(now on YouTube https://www.youtube.com/watch?v=rAen0kZly78&t=39s)

A few people have contacted me about an error in my calculations for precession of the equinoxes using Stellarium. In each case, it appears they are making the same mistake I made when I set out on this journey, as described in Prehistory Decoded. So, in this post I want to explain how to use Stellarium to do these calculations.

But before I begin, I should also point out that Stellarium is perfectly capable of making these calculations without any significant inaccuracy over the timescales we are interested in, i.e. 40,000 years or so. Gobekli Tepe's archaeologists have claimed that Stellarium might not be suited to this task. But they are wrong. I certainly agree that I would not use Stellarium to back-calculate the position of the moon (for visualising ancient eclipses, for example) over this timescale. But this problem does not apply to calculation of precession of the equinoxes, or the positions of the main planets or even the stars.

This is all connected with the accumulation of error, and the accuracy with which orbits can be calculated over such long timescales. Because the moon orbits Earth quite frequently - every 28 days or so - errors in its orbital calculations will accumulate faster than, say, errors in Jupiter's orbital calculations. Also, because the moon is much smaller than Jupiter, it is subject to gravitational perturbations in a way that Jupiter simply isn't. Jupiter's orbit is very stable and accurately known.

Therefore, we need to be careful about projecting the moon's position backwards over such long timescales, especially if we want to calculate the time of an eclipse, which requires precision on the timescale of minutes. So, I wouldn't use Stellarium to do this.

Like Jupiter,  Earth's orbit and the small oscillations in it's orbital parameters are accurately known. Moreover, the timescale for precession of the equinoxes is 26,000 years. This means we would only expect calculations of precession of the equinoxes to lose some precision after many hundreds or thousands of this time period, i.e. millions of years. So we are quite safe in making calculations backwards to 40,000 years, which corresponds to less than two full precessional cycles. Furthermore, because we only need an accuracy for our precessional calculations to within 100 years, say, we are completely safe. There is no problem at all with using Stellarium for this.

Right, having cleared that up, I'll now explain how to make accurate calculations of solstices and equinoxes with Stellarium. As I explain in Prehistory Decoded, the key to doing this properly is to realise that the summer solstice did not always fall on the 21st June. The date of the summer solstice can shift very slowly over thousands of years - which is exactly why this effect is known as precession of the equinoxes. In fact, it all depends on what calendar system you use.

But, rather than trying to explain the intricacies of different calendar systems, which I don't fully understand, I'll simply point out that Stellarium uses two different calendar systems, as far as I know. For dates after about 3,000 BC, Stellarium uses a 'tropical' calendar system which ensures the dates of the equinoxes and solstices are fixed to their current dates. That is, going back to 3,000 BC, Stellarium ensures the summer solstice always falls on, or very near, June 21st. In effect, it defines one year to be slightly shorter (by about 20 minutes) than exactly one complete orbit of the sun.

However, for dates before 3,000 BC, Stellarium uses a different calendar - one that allows the summer solstice date to drift. Actually, for before 3,000 BC it uses a 'sidereal' calendar that defines one year as exactly one complete orbit of the sun, i.e. 20 minutes longer than a tropical year. Therefore, to find the solstices and equinoxes before 3,000 BC you must use an astronomical method - you can't simply find them by locating the 21st June.

Actually, the best way to locate the solstice and equinoxes is to always use an astronomical method, as this will always be correct, regardless of which calendar system is used. This is how I do it.

First, you'll need to ensure the 'equator of date' is turned on, the 'atmosphere' is turned off and the constellations are turned on, so that you can see the sun against the backdrop of the constellations. You'll now see the equatorial line in the sky - a projection of Earth's equator onto the sky. To locate the spring and autumn equinoxes, simply find the dates in the year when the sun crosses this equatorial line. Roughly 3 months between these dates are the summer and winter solstices. To locate the solstices precisely you'll need to click on the sun and watch how its apparent altitude changes. Summer solstice is the day in the year when the sun reaches its highest altitude. Winter solstice is the day in the year when the sun's maximum altitude on any given day is lowest.

Good luck with your own decoding of ancient animal symbols using precession of the equinoxes - I think you'll find there is a lot more to do.