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In April, Antoine Couëtte mentioned inaccurate coordinates from the 
IMCCE online ephemeris. The error is not significant for navigation. 
However, it may be noticeable to programmers using the IMCCE site to 
check their software, so I think it would be proper to say a few words 
on this matter.

April message from Antoine:
http://www.fer3.com/arc/m2.aspx/Talking-Official-Authorities-Cou%C3%ABtte-apr-2012-g18950

IMCCE online ephemeris:
http://www.imcce.fr/en/ephemerides/formulaire/form_ephepos.php


Antoine noticed the ecliptic latitude of the Sun fails to remain within 
a few 0.1" of zero throughout the year -95. This is happens because the 
IMCCE uses the IAU (International Astronomical Union) 1976 precession 
model. At such a remote epoch, it's significantly less accurate than the 
current (2006) IAU model. Nevertheless, it should be satisfactory for 
analysis of historic almanacs, and definitely for navigation. My tests 
show that even as far back as the year 1600, IAU 1976 precession is 
within 0.1" of the 2006 model.

Another error in the IMCCE output is independent of time. It's
about 0.02" for bodies near the ecliptic, and is due to the
difference between two coordinate reference systems: the older J2000 
dynamical system (based on the mean equator and equinox at 2000 Jan 1 
Greenwich noon), and the ICRS (International Celestial Reference System).

The ICRS was defined as close as practical to the J2000 system, but the 
difference, called "frame bias," is significant in precise work. Frame 
bias correction is explained in Section B in any recent edition of The 
Astronomical Almanac.

Regrettably, the IMCCE online calculator ignores all that. It 
incorrectly assumes the output of the IMPOPxx or DExxx ephemeris (you 
can select the desired one) is in the J2000 system. So, when you select 
"Equator" as the reference plane and select the "astrometric J2000" 
button, it computes astrometric place in the ICRS, not the J2000 system.

The "apparent (true equator ; équinox of the date)" button gives a
result 0.022" from the correct result with the IAU 1976 precession /
nutation model, because frame bias isn't applied.

Likewise, "Mean of the date" computes geometric place with respect to
the mean equator / equinox of date, but off by 0.022".

"Mean J2000" computes geometric place with respect to the ICRS, not the
J2000 system.

On May 5 I emailed a couple people at IMCCE about these problems. They
have not replied, and when I tested the calculator 4 days ago it had not 
been fixed. Earlier, Antoine had contacted one of their astronomers 
regarding the Sun latitude problem, with equally negative result. He 
suggested that an email with my findings might get some action out of 
these people. I said it probably wouldn't do any good. Unfortunately, I 
was right!

The Astronomical Almanac always has a fully worked example of the 
correct computation of geocentric apparent place. In this year's 
edition, the planetary example is Venus at 2012 Dec 3 12 h UT1. Delta T 
is assumed to be exactly 67 s, so TT = 12:01:07. The ephemeris is the 
JPL DE405. (Formally, the DE405 time scale is TDB, but the difference 
from TT is insignificant at the precision of this example.)

The first step is to compute the geocentric astrometric place of Venus: 
where the planet was, when it emitted the light that a geocentric 
observer sees at the given time. The result, as a unit vector (i.e., 
length = 1) is

(-.718 994 379, -.648 418 711, -.250 200 434)

in the ICRS. After applying aberration and relativistic light deflection
by the Sun's gravity (the latter = .006"), the vector becomes

(-.719 056 198, -.648 359 500, -.250 176 224)

Finally, transformed to the true equator and equinox system via the IAU 
2006 / 2000A precession / nutation model:

(-.716 819 148, -.650 484 409, -.251 078 360)

or RA = 14h 48m 53.3935s, dec. = -14° 32' 28.799".

If we substitute the IAU 1976/81 precession nutation model, the correct 
result is

14h 48m 53.3957s  -14° 32' 28.811"

which is .035" different from the Almanac, and .022" different from the 
IMCCE online calculator. The latter discrepancy is the effect of 
ignoring frame bias.

Although it's insignificant for navigation, .022" is way too large if 
you're using the IMCCE calculator to validate almanac software. With the 
same ephemeris, same precession / nutation model, and the correct 
algorithms, you should never be that far off. For example, my free 
little almanac program for Windows duplicates the Almanac coordinates 
with an accuracy of plus or minus 1 in the last digit.

That's not to say a program with less accuracy is necessarily a bad one. 
If output precision is 0.1', a rigorous computation is a waste of time. 
But the IMCCE's calculator displays coordinates to 0.0001". The last two 
digits are meaningless. I expect better from an organization of such 
prestige.

-- 

   

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