Converting RA/Dec to earth centered coordinates?

On Mon, 02 May 2011 18:48:38 -0700, "W. eWatson"
wrote:

On 5/2/2011 2:28 PM, Steve Willner wrote:
In ,
"W. writes:
My xy plane is in the plane of the equator, and its projection into the
sky represents the celestial equator. Declination is measured +/- from
the celestial equator to each pole along great circle lines that pass
through each pole.

Somewhere on the celestial equator is point from where RA is measured.

To go from RA/Dec to an x,y,z unit vector is just simple trignometry:

x = cos(dec)*cos(RA)
y = cos(dec)*sin(RA)
z = sin (dec)

Make sure to convert RA/dec to degrees or radians (whatever units
your calculator or program uses). It's easy to forget to multiply
hours by 15 to get degrees.

The zero point of RA is the place where the ecliptic and celestial
equator intersect with the equinox heading north. Both this zero
point and the location of the celestial poles changes with respect to
the stars because of precession. If you want a _current_ x,y,z unit
vector, you need to start from current RA/Dec coordinates rather than
coordinates at a standard "ecliptic and equinox" (B1950 or J2000).
The Meeus book will tell you how to do that calculation.

Ah, the obliquity of the ecliptic (e) is what I need.

Don't see why you need that. Did you mean ecliptic coordinates
rather than celestial?

Whoops, I posed the question backwards. I have the x,y,z coordinates of
a vector and I want to convert them to ra/dec. In a unit sphere I think
of z as pointing through the north pole, x pointing south through 1,0,0,
and y pointing east through 0,1,0.

In my case, precession does not enter into matters. I'm constructing a
simulation that is mostly grounded in az/el and lat/lng. I wrote a
program that produces the path of a fake meteor moving in a straight
line. Time is not yet useful as a consideration yet.

The direction of the line points to the radiant point in the sky.
Meteors lie on a great circle, hence pass their plane passes through the
earth's center (spherical earth). My program has not yet needed ra/dec,
which is usually the measure of the radiant point in the sky and is
given in ra/dec. However,I have the data from a similar program, and
they provide the radiant as ra/dec. internally, my program seems sound
when I sort of run it backwards. I get agreeable results. I want to see
if the independent source and I agree.
See if this explanation regarding nomenclature will help clarify
things and perhaps bring an end to the random and inexplicable
outbursts of vituperation.
You have written a program that simply calculates the path of a meteor
in XYZ coordinates whose origin is in the equatorial plane. From the
XYZ coordinates you want to calculate the pitch and yaw or elevation
and azimuth as measured on an equatorial mount that would point at the
meteor.
You apparently raised the hackles of purists by using the terms right
ascension and declination which have specific astronomical meaning and
are measured from the point of Aries if I recall correctly, and
therefore has no place in your problem.
I think you will find that the equations I gave you will give you the
correct result.
John Polasek