First, if anyone wants to say that my previous post, or this one, contains “pseudoscience”, then I invite them to actually specify a statement in the post that is “pseudoscientific”, or demonstrably incorrect.
Here’s a recent graph, from astronomer Jaques Laskar, showing how the precession-rate has varied over the millennia.
In case the image doesn’t post, here’s a link to it:
http://mb-soft.com/public/preces01.gif
As I mentioned before, when Fairall told the equatorial co-ordinates (RA and declination) of the vernal equinox in 10,500 BC, the position that he gave was exactly what you’d get if you assumed that precession has always had its current rate.
Don’t take my word for that. Determine it for yourself.
In every regard, I interpreted Laskar’s graph in the way that’s least favourable to my claim.
Laskar shows several lines, graphing precession-rate as a function of time. The green line doesn’t have s low a minimum as the others, making it less favourable for my claim, and so it’s the one that I used.
The green line’s minimum around the time of interest is 49 arcseconds per Julian year.
The current rate is 50.28 arcseconds per Julian year.
I used the average of 49 and 50.28 arcseconds per Julian year. That implies approximating the curve with a straight line between now and 10,500 BC.
But, for one thing, the curve is upward-curving over that interval. That means that the straight-line approximation implies overly much precession during that interval. …something unfavourable to my claim that the equinox was farther east in 10,500 BC.
For another thing, as I mentioned before, the curve spends some time near its minimum of 49, something that isn’t reflected in my linear approximation of the rate.
Another way in which I interpreted Laskar’s graphs unfavorably for my claim is my use of the green curve. As I said, of the several curves in the figure, the green one is the only one with the higher minimum in that region. Additionally, the blue curve, with a lower minimum, is the one that only extends over a 20,000 year period, suggesting that it’s intended to be accuracy-optimized for that period, which covers the interval of interest.
The other thing that most planetarium software probably doesn’t consider is proper motion. The stars gradually move in the sky, with respect to eachother. Denebola, the east (left) apex of Leo’s right triangle, and the east boundary of “Leo Proper” (Leo’s sickle and right-triangle), is a fairly fast-moving star. During the past 12,500 years, Denebola has moved about 1.72 degrees, roughly westward.
Any accurate determination of which side of Denebola the vernal equinox was on in 10,500 BC must consider the varying precession-rate, and Denebola’s proper motion.
When those two things are considered, then you’ll find that, in 10,500 BC, the vernal equinox was about 2/3 of a degree west (rightward) of Denebola.
In other words, in 10,500 BC, the vernal equinox was about 2/3 degrees into Leo Proper.
In order for the vernal equinox to be to the east of Denebola, it would be necessary for my approximation of the precession during the interval, based on my linear approximation of the rate, to be too low. In fact it would have to be off by 42% as much as the constant 50.28 assumption is, over that interval.
I’ve told why my precession-estimate is high. But, in any case, looking at the graph, it’s obvious that the linear approximation can’t result in an integral 42% as far off as the one that results from the constant 50.28 assumption.
The precession over that interval is the time integral of the rate over that integral. You can do it by Simpson’s rule if you want to, but you’ll find that, as I said, my estimate for the accumulated precession over the interval is a high estimate…unfavourable to my claim. In other words, the equinox in 10,500 would actually have been a little farther west (farther into Leo Proper) than the 2/3 degree figure that I stated.
But a look at the graph shows that the constant 50.28 rate-assumption is humungously farther off than any error of my linear approximation could be.
Nitpicker:
You said:
See the following link (Stellarium bug report) for a good description of possible inaccuracies in precession calculations (especially going back as far as 10,500 BCE).
I didn’t use Stellarium.
You might have to make your case (rather than just state it) if you are going to convince anyone who cares
Sure, reporting what I determined doesn’t prove it.
But I hope you’re not asking for a complete demonstration of the determination here. If anyone is interested, then I invite them to determine it for themselves. If anyone isn’t interested enough to do the determination for themselves, then it remains, for them, my word vs someone else’s.
I’m merely stating what I determined, and telling the information that I used, and which two astronomers disregarded, when they concluded that the vernal equinox was within the boundaries of modern Virgo in 10,500.
If anyone would like to use software to make the determination, then I emphasize that it’s necessary to use software that accounts for the varying precession-rate, and for proper motion.
Also, here is a screenshot of how Stellarium simulates the Northward Equinox in 10,500 BCE (which is probably not exact).
It isn’t. It shows the vernal equinox as being east (left) in ecliptic longitude, with respect to Denebola. That’s because Stellarium disregards variation of the precession-rate, or proper-motion, or both.
I’m not criticizing Stellarium. I like its realistic beauty. But it just isn’t intended for accuracy at times that are 12,500 years in the past or future.
My opinion is there really isn't much meat to the argument, one way or another.
Yes, the vernal equinox was quite close to Denebola in 10,500 BC. Most likely that’s what made 10,500 BC a time of interest for Hancock and others before him. Most likely, at some point, someone asked an astronomer when the vernal equinox entered Leo, or the “Leo Proper” sickle-and-right-triangle asterism’s range of ecliptic longitudes. The astronomer, according to that assumption answered “Around 10,500 BC”. If so, he didn’t disregard variable precession-rate or proper motion.
I didn't even bother looking up Hancock and Bauval. Regardless, it seems like the Northward Equinox was near the boundary of Virgo and Leo (based on either the modern or vague, ancient definition), circa 10,500 BCE.
Yes, and I suggest that its nearness to entering Leo Proper at that time was the thing that made the year 10,500 BC of interest—after someone found that out by asking an astronomer.
Edit: Of course, this date is roughly 10,000 years before the Babylonians first divided the ecliptic evenly into the 12 zodiacal signs.
Of course. But Leo’s sickle-and-right-triangle suggests a lion in the upright-rest position.
At this time of year, Leo rises early in the morning, before sunrise, so check it out for yourself.
Chris:
You said:
The main issue here is that Hancock and Bauval are pseudoscientific frauds
I clarified at the outset that I don’t subscribe to Hancock’s prehistoric super-civilization, or his “Orion correlation”.
My topic wasn’t Hancock. I said that in my initial post, quite clearly. My topic was the matter of which side of Denebola the vernal equinox was on, in 10,500 BC. It was about 2/3 of a degree west (rightward) of Denebola.
…about 2/3 of a degree into Leo Proper.
Michael112914