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The Great Year is nearly halfway through

by Simon at 17:45 06/10/08 (Blogs::Simon)

Notes to self for future reference...

As a result of precession of the equinoxes, the altitude reached by a south-transiting star at its daily culmination due South of an northern hemisphere observer varies over very long time periods.

For a particular star and location, the start of a Great Year (being the length of time for one precessional cycle to complete, roughly 25920 years) can be taken to be the year in which the star has its lowest altitude at culmination.

For the next 12,960 years the star's altitude at culmination increases until a maximum is reached. After that, the altitude decreases until it returns to its minimum again.

Choosing Betegeuse (α Orionis) as the star, and my back garden as the location, to a first approximation the midpoint of the current Great Year will therefore occur in 2080 AD.

At 00:04:47 (UT) on winter solstice 2080 Betegeuse will reach an altitude of 45° 34.374' at culmination (winter solstice is chosen because the Sun is diametrically opposite Orion in the sky at that time of year).

12,960 years ago, at the winter solstice (where then the Sun was directly above Orion in the sky, being 'half a cycle' back from where we are today), Betelgeuse did not rise at this location - it grazed below the southern horizon by roughly 2° at culmination.

This is because the diameter of the precessional circle traced by the north celestial pole is 2 * 23.5° (approx) = 47° which is greater than Betelgeuse's maximum culmination altitude.

So I am going to date the start of the current precessional cycle to 10880 BC (give or take).

At that time, the vernal equinox point was in the constellation Virgo and Vega was the "bright star of evening" closest to the north celestial pole.

--
simon

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The Great Year is nearly halfway through	Simon - 17:45 06/10/08
Re: The Great Year is nearly halfway through	Simon - 16:03 09/10/08
Further notes: When determining the maximum culmination that a star has in a cycle that correlates with a Summer Solstice, the star must have the same Right Ascension as the summer solstitial point - ie 6h 0m 0s in that epoch. By definition, in any epoch, the summer solstice RA is 6h, winter solstice 18h and the vernal and autumnal equinoxes are 0h and 12h respectively. The 2080AD date arises directly from having chosen Betelgeuse as the star whose maximum altitude at the summer solstice we are seeking. Had Rigel been chosen, a different date would be found instead (2938AD) As to which star to choose, that is where the argument as to determining the exact date of the halfway point starts. Splitting the difference, and using Alnilam (the middle star of Orion's belt stars) as the reference gives a date for the Great Year midpoint of 2468AD. There may be some justification in picking Alnilam over Betelgeuse in that it has a supposed association with the Giza equinotial marker pyramid (Khafre) and monument (Sphinx). Summer Solstice 2468AD also happens to be the day of new moon, but that is not an unreasonable coincidence given that a new moon on any particular date repeats every 19(ish) years. -- simon
Re: The Great Year is nearly halfway through	Simon - 11:31 23/01/09
Clarification note: In any particular year any given star will have a maximum altitude above the horizon when it's due south, ie on the observer's meridian (northern hemisphere). Where I've referred to summer/winter solstice and Orion/Betelgeuse it's because Orion transits the meridian around midnight at the winter solstice and midday at summer solstice in our era. In winter I rise at sunset In summer I rise at dawn In autumn I rise at midnight In spring I rise at noon 2080AD falls out when we seek the year that Betelgeuse transits the meridian at noon on summer solstice at its maximum possible altitude in this precessional cycle, because that's when Orion is 'crowned' by the Sun at the height of each of their respective powers. If we choose a slightly different methodology, that of "in which year does Betelgeuse have a RA of 6h 0 0s" (implying it shares the same meridian as the summer solstice colure - by definition 6h), then we end up with a date of 2089AD instead. 9 years in 25920 isn't a very large error bar, and I'm working within the limitations of the software I have to hand which certainly isn't sophisticated enough to account for all the variables that govern precessional movements, so I'm comfortable with picking 2080AD as the turning point. The cardinal points of the sky (solstices and equinoxes) are - as of Summer Solstice 2008 - now within one degree of where they will be at Orion's turning point, and every full moon from then until 2080 takes them a shade more than 4" of arc closer. Tick, tick, tick, ~1" a week, and exactly 883 lunations to go as of 28th Jan 2009. -- simon