Looking for a formula concerning artificial satellite eclipses

From: alain.figer@club-internet.fr
Date: Wed Nov 16 2011 - 13:06:14 UTC

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    Hi all, 
    
    Where may I find (who can provide me with) a ready-to-use formula giving :
     . for any terrestrial site and at any time, 
    . the altitude of the Earth shadow as a function of a satellite position in the sky (height, azimuth ; or else, R.A. declination) ?
    If possible, accounting also for penumbra-umbra would help.
     
    Thanks in advance
    Alain Figer
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