Orbit Computation: How? (Was "99099A elements")

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In a message dated 6/18/99 9:24:04 PM Eastern Daylight Time, molczan@home.com 
writes:

<< Pierre Neirinck has produced the following elements, based on 22 points 
from
 observations by himself, David Brierley and Peter Wakelin, from 10 Jun
 through 16 June: >> (ELEMENTS OMITTED)

The answer to this question may be over my head, but how does one 'produce' 
elements based on precision observations.  What is the procedure/math behind 
it?  Is there software to aid in this (formidable?) task?  

Quinn McCleery
Raleigh, NC

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