Long-Term Precession, HORIZONS & Stellarium
Posted: 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.
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
)
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)
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.
- NCP Position Over ± 28,000 Years - Note Stellarium's 3.2° position error at -10,000 years
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
)
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)
). 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: