Long-Term Precession, HORIZONS & Stellarium

Ask questions, find resources, browse the virtual shelves.
User avatar
alter-ego
Serendipitous Sleuthhound
Posts: 717
Joined: Mon Apr 21, 2008 4:51 am
Location: Redmond, WA

Long-Term Precession, HORIZONS & Stellarium

Postby alter-ego » Mon Jan 12, 2015 4:03 am

The topic of Earth's axial precession occasionally arises and for long-term precession (> ± several hundred years) I've typically wanted to know more. Specifically, the familiar plots showing north celestial pole (NCP) precession are incomplete at best. Also, the "real" precession period length and ephemerides accuracy errors are common questions. So for a 56,000-year period (~2 precession cycles), I've generated an NCP precession plot that should answer many of these questions "at a glance". The position plot is overlaid on the correct (static) J2000 star field and centered on the J2000 ecliptic pole.

Below left is the NCP position plot over 56,000 years. Unlike other similar plots I've seen, this graphic includes the varying precession rate and the varying obliquity. The plot also includes Stellarium's simple constant obliquity / constant precession model, and note the "S" and "H" symbols designating Stellarium's and JPL HORIZONS NCP position at -10,000 years. The spiral-like precession curve and non-linear time increments are separately consistent with other graphics I've seen, but this is the first I've seen that has all the information in one graphic. To the right, plotted are Stellarium's NCP position errors (log scale) bounded within time range windows.

Long Term Precession - NCP Position per Owen, 1990 - Horizons & Stellarium_2.JPG




HORIZONS long-term precession (limited to a ±9999-year range, it is applied before Jan 1799 and after Jan 2202) is based on a model from a dissertation by William Owen, 1990. Owen's model spans 1million years and uses thousands of coefficients. I chose to use this model over much smaller 56,000yr range requiring 140 coefficients. Also, Owen proposed this model for more "easily" characterizing precession wrt a more natural reference plane - the solar system's invariable plane. I used only the components necessary to describe precession wrt the J2000 ecliptic. To check myself, I compared Owen's obliquity and precession to Lasker et al. (1993) results over the same 56,000-yr span. Very nicely, the two sources agreed. Owen's accumulated (or cumulative) precession, pA, error did not exceed 20 arcseconds over 20,000 years (or 0.001%), and obliquity results differed from Lasker's by < 0.02 arcseconds. For the purposes here, these errors are of no concern.

With regard to Stellarium (which I use a lot), I verified both obliquity and precession rate are held constant (rates are also annotated on the graph). As mentioned, the circle precession curve is also plotted. The utility does permit an input of ±100,000 years, so one must be careful with expected accuracy when going to calendar dates more than a few hundred years away from the J2000 epoch. Fortunately, most applications involve times within this shorter range.


Below is a copy of Owen's thesis plot showing the 1Myr NCP precession curve wrt the solar system's invariable plane. (Precession over this long a time scale reminds of scribbling to get a pen to work :-D)




Additional Links
HORIZONS documentation
Tropical Events: The Solstices and Equinoxes (Overview and interpretation of Jacques Lasker's work)
New Precession Expressions, Valid for Long Time Intervals, J. Vondrák (2011)
You do not have the required permissions to view the files attached to this post.
A pessimist is nothing more than an experienced optimist

User avatar
MargaritaMc
Look to the Evenstar
Posts: 1717
Joined: Wed Jan 09, 2013 10:14 pm
Location: 28°16'7"N 16°36'20"W

Re: Long-Term Precession, HORIZONS & Stellarium

Postby MargaritaMc » Mon Jan 12, 2015 8:43 pm

Thanks so much for this, alterego.

But, my eyes aren't what they used to be and I'm having difficulty with seeing the details and text in this, embiggen it as I may:
Image

Is it possible to have access to a version in higher definition?

And, yes, the 1Myr NCP precession plot does look exactly like getting a Biro to work! :lol2:

Margarita
"In those rare moments of total quiet with a dark sky, I again feel the awe that struck me as a child. The feeling is utterly overwhelming as my mind races out across the stars. I feel peaceful and serene."
— Dr Debra M. Elmegreen, Fellow of the AAAS

User avatar
Nitpicker
Inverse Square
Posts: 2397
Joined: Fri Sep 20, 2013 2:39 am
Location: S27 E153

Re: Long-Term Precession, HORIZONS & Stellarium

Postby Nitpicker » Mon Jan 12, 2015 11:42 pm

Love your work alter-ego, but the variable speed of the NCP's motion is a little difficult to detect with "graticules" spaced at 4000 years.

User avatar
alter-ego
Serendipitous Sleuthhound
Posts: 717
Joined: Mon Apr 21, 2008 4:51 am
Location: Redmond, WA

Re: Long-Term Precession, HORIZONS & Stellarium

Postby alter-ego » Tue Jan 13, 2015 3:33 am

MargaritaMc wrote:Thanks so much for this, alterego.

But, my eyes aren't what they used to be and I'm having difficulty with seeing the details and text in this, embiggen it as I may:
Image

Is it possible to have access to a version in higher definition?

And, yes, the 1Myr NCP precession plot does look exactly like getting a Biro to work! :lol2:

Margarita


Hi Margarita,
Did you click twice?
I made a 50% larger image below to help. See if that is better - so click once to open the image, then click again to get the full size version.
Long Term Precession - NCP Position per Owen, 1990 - Horizons & Stellarium_Large.jpg
You do not have the required permissions to view the files attached to this post.
A pessimist is nothing more than an experienced optimist

User avatar
alter-ego
Serendipitous Sleuthhound
Posts: 717
Joined: Mon Apr 21, 2008 4:51 am
Location: Redmond, WA

Re: Long-Term Precession, HORIZONS & Stellarium

Postby alter-ego » Tue Jan 13, 2015 6:44 am

Nitpicker wrote:Love your work alter-ego, but the variable speed of the NCP's motion is a little difficult to detect with "graticules" spaced at 4000 years.

Thanks Nit, I'm glad you liked it.

Yeah, I struggled a bit with tic marks. I wanted to customize the locations of the polar plot's dashed azimuth (radial) indicators but I couldn't. I finally decided to locate "o" symbols as the azimuth angle indicators. And thanks to you, I discovered my tic marks were off. I mixed up "Year 2000 + Interval" with Year 0 + Interval" ending up with some nonsense, although maybe a bit subtle. You are right too that the nonlinearity is not obvious (especially now :)). The difference between the largest and smallest 4000-yr interval is ~8%. Not very much, but it is visible. Anyway, I redid the tic marks and am posting the correction here:

Long Term Precession - NCP Position per Owen, 1990 - Horizons & Stellarium_Large.jpg


Thanks for your comments. The correction only affects tic mark location, nothing else.
Hopefully any further errors now are at a level we can ignore.
You do not have the required permissions to view the files attached to this post.
A pessimist is nothing more than an experienced optimist

User avatar
MargaritaMc
Look to the Evenstar
Posts: 1717
Joined: Wed Jan 09, 2013 10:14 pm
Location: 28°16'7"N 16°36'20"W

Re: Long-Term Precession, HORIZONS & Stellarium

Postby MargaritaMc » Tue Jan 13, 2015 5:39 pm

Thank you, that's a lot easier to read!
M
"In those rare moments of total quiet with a dark sky, I again feel the awe that struck me as a child. The feeling is utterly overwhelming as my mind races out across the stars. I feel peaceful and serene."
— Dr Debra M. Elmegreen, Fellow of the AAAS


Return to “The Library: Information Desk and Educational Resources”

Who is online

Users browsing this forum: CommonCrawl [Bot] and 1 guest