Re: Optical sighting orbit determination method

From: Jim Scotti (
Date: Tue Feb 03 2004 - 16:17:21 EST

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    I have not used MathCAD, but have done some programming on orbit
    determination (I'm one of those "old" Fortran types...) and have looked at
    the Bate, Mueller & White book.  I like the unique way they approach the
    problem, reducing it to vectors is not something I'd seen before seeing it
    there.  The main trouble I had with that book is that they use canonical
    units, so converting from the real world into their equations is often
    difficult (they should at least leave the various constants in the equations,
    but they don't....).
    You mention that you have trouble if all three observations are at zero
    declination.  That is to be expected in such a case for the longitude of the
    ascending node and arguement of pericenter since they are undefined for an
    orbit that has a zero inclination (as such an orbit would have).  You have to
    simply choose a longitude of the ascending node (zero, for example) and then
    measure the direction of pericenter from there.  The other elements defining
    the shape and size of the orbit should work fine.
    There are some programs available on the internet, for example Orbfit which
    you should be able to google and find.  There are also some other books that
    describe the techniques and a few that even list programs, such as Boulet's
    "Methods of Orbit Determination for the Microcomputer".  That book is getting
    a bit old and I think uses Basic for its programs.  You can probably still
    order it from Willmann-Bell.  Danby's "Fundamentals of Celestial Mechanics"
    is a good book as well with some subroutines and programs and A.E. Roy's
    "Orbital Motion" has some useful approaches for the programmer.  Another
    great book for orbit determination is Escobal's "Methods of Orbit
    Good luck!
    On Tue, 3 Feb 2004, Fernandez Amiel wrote:
    > Hello all,
    > Has anyone out there ever implemented the Gaussian angles only orbit
    > determination method using f and g series in MathCAD?  I followed the method
    > described in Bate-Mueller-White's Fundamentals of Astrodynamics but do not
    > get reasonable answers on use of it.  In fact, even after checking my
    > nomenclature and implementation many times over I am still getting a trivial
    > answer if the declination of a satellite is zero for all three of the times
    > it is observed.
    > I have searched on the internet but can't find software that gives the
    > orbital elements from optical sightings - actually I do - but all of the
    > sites that I get to aren't functioning or the links are broken.  Any
    > recommendations on doing this either in MathCAD or with any other programs?
    > Thanks in Advance,
    > Amiel Fernandez
    > Senior Consultant
    > Booz Allen Hamilton
    > (703) 377-1681
    > -------------------------------------------------------------------------
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    Jim Scotti
    Lunar & Planetary Laboratory
    University of Arizona
    Tucson, AZ 85721 USA           
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