Is Earth Longitude Aligned Correctly in 1.6.0?

[VikingTechJPL]

While working on a script regarding the Equation of Time, I found that the Earth Longitude over which Celestia draws the Sun does not match exactly the theoretical values of computational astronomer Jean Meeus in his book ASTRONOMICAL ALGORITHMS. The difference is somewhat small (only a few miles if projected to the Equator) but this seems significant enough to take a look.

Example 1: At 12:00:00 UTC on 2000 Nov 2, Celestia 1.6.0 shows the Sun over Earth Longitude -4.05703?. At 4 minutes (of time) per degree, this means that Celestia shows that is the Sun is "running fast" by 16 minutes 13.7 seconds. In other words, it arrived early by that amount over the Prime Meridian since it has passed it by 12:00:00. According to the text of ASTRONOMICAL ALGORITHMS, chapter 27, the Sun should "run fast" by 16 min 25 sec for that date, though if you do his math for the date according to the method of Example 27.b, you get 16 min 28.1 sec. With 4 minutes (240 seconds) of time per degree, even in the former of ASTRONOMICAL ALGORITHMS' two figures this means that Celestia is plotting Earth's subsolar point 11.3 sec / 240 sec / degree = 0.047083? too far to the east on this date. This equates to roughly 3 miles.

Example 2: If you set Celestia 00:00:00 UTC on 1992 October 13 (as in the ASTRONOMICAL ALGORITHMS, example 27.b), Celestia shows the Sun above Earth Longitude 176.65265?. Subtract this from 180? and you get 3.34735?. Multiply it by 4 min/degree and you get that the Sun is running early by 13.3894 minutes or 13 min 23.4 sec. But the Meeus prediction in Example 27.b states that the amount should be 13 min 42.7 sec. (And I did verify his math.) This equates to Earth's subsolar point being shown about 5 miles east of where it should be.

Meeus's algorithms are supposed to be based on VSOP87, as are Celestia's, so I'd be glad if someone else took a look at this and checked my math. If Meeus is right, then it suggests that Celestia's alignment of Earth's Longitude or speed of Earth's rotation may be off by a bit. This would affect times of eclipses viewed at Earth's surface, sunrise and sunset times etc. Could such a significant difference be caused by round-off or by Celestia's truncation of VSOP87?

Many thanks to anyone who can help clarify this discrepency or show me where my math went wrong.

Regards,
VikingTechJPL

P.S. I just checked the same in 1.4.1, and discrepencies occur there too—but in the opposite direction! So it goes.

[selden]

I don't have the expertise to comment on issues with its implementation, but one of the changes in v1.6.0 was to use IAU rotational elements for most solar system bodies, including the Earth, so that their longitudinal orientations would be more accurate than in previous versions. (This is mentioned in changelog.txt in the Celestia distribution kit.)

It's implemented in celephem/customrotation.cpp, which can be seen at
http://celestia.svn.sourceforge.net/vie ... p?view=log

[chris]

Nutation isn't included in the Earth rotation model in Celestia 1.6.0, but I'm pretty sure that omitting this isn't enough to cause the observed discrepancy. Celestia also doesn't include the effects of aberration.

The two principle nutation terms have magnitudes of 17 and 9 seconds. These are fractions of a degree--not fractions of an hour--so it's not going to add up to a 13 second time difference. I haven't investigated the error caused by omitting aberration.

--Chris

[VikingTechJPL]

Selden,

Thanks for the input. I'll take a look at customrotation.cpp when I have some time.

Chris,

Yes, I was surprised a little by the magnitude also—especially since seconds of time are 15 times larger than arcseconds. And the fact that (even using Meeus's theoretical max) it was an 11.3-second difference in the year 2000 was a surprise too. In distant years maybe, but not in 2000. I don't know how the IAU indexes its rotational elements. Do they use an epoch also? I'll try to find out.

A friend contributed that, if the subsolar point is only displaced by a few miles, then the Coast Guard looking for the folks on LOST would find the island! GROAN! But finding a cave ON the island with that tolerance would be difficult.

Nutation-wise, all we're really concerned about is the nutation in longitude, and the Nov 2 or 3rd dates are very near a cusp (the westward maximum) for the function. Plus, abberration never exceeds 20 arcseconds, does it? And isn't it always fairly constant for the Sun since Earth essentially travels perpendicular to its received light? So it would seem that nutation PLUS aberration could only be part of the problem.

I HAVE checked the Sun's geocentric RA and Dec relative to the J2000 epoch, and they appear correct. They also appear correct when I transform to an Equinox of Date for 1993 and 1994 and check them against USNO Astronomical tables for those years. Just a few fractions of an arcsecond off. So it doesn't appear that the Sun's position relative to Earth's center or to other bodies or to the Equinox is the issue.

Am interested to hear what you find.

--Gary