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Subject: Re: Sextant Positions versus Map Datums?
From: dkruger (dkruger@XXX.XXX)
Date: Fri Jan 18 2002 - 12:06:24 EST
The astronomical positions of VSOP87, and all the derived variants are
computed first in Heliocentric coordinates, thus the shape of the
earth is irrelevant to that part of the computation.
Then, it is converted to geocentric coordinates based on the position
of the center of the earth. I don't remember seeing anything about
the ellipsoid here, but Hal if you have a page reference in Meeus, I'd
like to see it. What is much more relevant is nutation, because as
the Earth "nods" up and down due to the gravitational effects of the
moon on the equatorial bulge, the axis changes, and that changes the
entire coordinate system. So the accurate conversion to geocentric
coordinates takes into effect nutation, and for distant bodies (beyond
Mars) the time it takes light to arrive. Those are the only
corrections I have seen at this stage, and I believe Hal is wrong
about the ellipse.
You can read all this in Meeus, and there is a program out there
called Astrolabe which though not the best code, uses VSOP and is
therefore one of the simplest to read. By contrast, Steve Moshier has
some code out there that is supposedly even better (more accurate,
using the currently most accurate model, DE404) but it is nearly
impenetrable, filled with lots of different conflicting models, dead
code left in, and just a more complex algorithm (I think!). If you
are an astronomer, you care about accuracy to the arcsecond so you can
point your telescope. If you are interested as a navigator, you can
live with any of these models, they are more than accurate enough,
particularly this century. All this so far has nothing to do with the
ellipsoid or datums, except to contradict any claim that the position
of bodies in the almanac is somehow corrected for any of that. It
can't be -- the position is calculated based on the center of the
Earth, and a wild and crazy equation for Heliocentric position of the
other body based on the julian century T. The apparent position is
then corrected for lightspeed and nutation.
What you can measure is altitude, and as Trevor corrected me and
explained to everyone, if there were to be a correction for the
ellipsoid, you would do it as you convert between GP/AP and altitude
and azimuth. If you are using the standard equations, it's obviously
not happening. It could be in the 229, but if you look at the notes
about how the tables are generated, clearly no such correction has
been done. The equation they use is spherical, and the only note they
make is that for angles that would result in bad roundoff error they
use a different form that is analytically equivalent. That is an
issue of computation, not changing the shape of the sphere.
So perhaps Meeus merely mentions somewhere that when they record an
observation, astronomers convert the other way to determine the
position of the body? I assume that would have more to do with
parallax. Anyway, I would also like to see the reference.
>According to Jean Meeus, Astronomical Algorithms, 2nd edition,
>astronomical observations (which are the basis for the Nautical
>Almanac) use the IAU 1976 ellipsoid (International Astronomical Union
>1976). Those values are
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