Using Sidereal Time and Geocentric Coordinates

My recent interest in calculating LMST (Local Mean Sidereal Time) came
about from a paper some 30 years old in which the author produce "The
rectangular geocentric systems of coordinates is given by:

X = (R+h)*cos(phi')*cos(LMST)
Y = (R+h)*cos(phi')*sin(LMST)
Z = (R+h)*cos(phi')
where phi' is the geocentric latitude.

I have not found these equations on the web, and am beginning to think
they have been replaced over the decades. Comments?

W. eWatson wrote:
My recent interest in calculating LMST (Local Mean Sidereal Time) came
about from a paper some 30 years old in which the author produce "The
rectangular geocentric systems of coordinates is given by:

X = (R+h)*cos(phi')*cos(LMST)
Y = (R+h)*cos(phi')*sin(LMST)
Z = (R+h)*cos(phi')
where phi' is the geocentric latitude.

I have not found these equations on the web, and am beginning to think
they have been replaced over the decades. Comments?

Looks like a conversion from a topocentric coordinate
to a rectangular, Earth-centered coordinate system (SEZ ?)
with its fundamental plane coincident with the equatorial
plane and the x-axis pointing to the vernal equinox.

Presumably R is the Earth radius, and h the height above
the surface. Did the paper use this to place the
location of an observatory in the SEZ coordinate system?

This coordinate system is used in the reduction of
topocentric observations of satellites and such to the
SEZ coordinates for orbit tracking.

The book Fundamentals of Astrodynamics by Bate, Mueller,
and White (a real bargain at under $12 at Amazon) covers
this.

Google Books seems to have it online. Check out chapter
two.

On 6/25/2010 8:31 AM, Greg Neill wrote:
W. eWatson wrote:
My recent interest in calculating LMST (Local Mean Sidereal Time) came
about from a paper some 30 years old in which the author produce "The
rectangular geocentric systems of coordinates is given by:

X = (R+h)*cos(phi')*cos(LMST)
Y = (R+h)*cos(phi')*sin(LMST)
Z = (R+h)*cos(phi')
where phi' is the geocentric latitude.

I have not found these equations on the web, and am beginning to think
they have been replaced over the decades. Comments?

Looks like a conversion from a topocentric coordinate
to a rectangular, Earth-centered coordinate system (SEZ ?)
with its fundamental plane coincident with the equatorial
plane and the x-axis pointing to the vernal equinox.

Presumably R is the Earth radius, and h the height above
the surface. Did the paper use this to place the
location of an observatory in the SEZ coordinate system?

This coordinate system is used in the reduction of
topocentric observations of satellites and such to the
SEZ coordinates for orbit tracking.

The book Fundamentals of Astrodynamics by Bate, Mueller,
and White (a real bargain at under $12 at Amazon) covers
this.

Google Books seems to have it online. Check out chapter
two.



I did some browsing on the web before posting this, and found his use of
coordinate systems a bit baffling or maybe peculiar to Europe, Czech,
where he lived. I found a web page where it's pretty well spelled out.
Well, actually it's a pdf from the Intl. Meteor Org. The methodology I'm
working is for meteor obs. The pdf probably can be found by Googling
"Definition of Terminology Used in Meteor Orbit Determination". One
author is Koschny. See figures 2 and 3 on page 5.

I'll take a look for the book. I'll mention The Foundations of Celestial
Mechanics by George Collins. It may have something about these matters.
It's a freebie on the web, courtesy of the author. I've only printed and
downloaded the first few chapter.

This is kind of amusing. The book you mentioned, I used to own. As soon
as I saw the cover, I recognized it. I think I gave it to a local
college library about 10 years ago. Unfortunately, Chap. 2 is not
displayable. It was a good book. I may order it up, or try for an
interlibrary loan.

Well, I finally found a web article that goes into considerable detail
with the three equations. It took two other articles to get there. About
22 pages of reading. Interesting stuff. What I found that was more
interesting though was those three equations must be solve by iterating
over two other ones.

I think I mentioned my interest started with a 1978 professionally
published paper that included the three. There was no mention of the
extra two equations. I guess the publication expected everyone to know
about them. The author only hints at what's going on by saying the three
must be solved. Ho, ho. Here's the link for the first, change the last 3
to 1 and 2 to get the first two. http://celestrak.com/columns/v02n03/