Fine, using astrometry I was able to derive the following coordinate sets from each image for each of the following timepoints previously listed:
7:12:15.769 20h 27m 14s 32 degrees 17' 57"
7:12:45.632 20h 27m 53s 32 degrees 00' 01"
7:13:45.359 20h 29m 09s 31 degrees 23' 17"
7:14:15.322 20h 29m 48s 31 degrees 04' 34"
7:15:40.707 20h 31m 39s 30 degrees 09' 24"
7:16:14.908 20h 32m 24s 29 degrees 46' 34"
7:26:08.535 20h 46m 08s 21 degrees 55' 38"
7:26:38.432 20h 46m 52s 21 degrees 27' 21"
7:31:16.043 20h 53m 59s 16 degrees 35' 32"
7:34:19.693 20h 59m 01s 12 degrees 49' 19"
An initial orbital determination was made using the first, last, and a middle astrometric determination (the 7:26:08.535 observation), then refined with the other 7 measurements to determine the following orbital elements relative to earth (indeed, it was an earth-orbiting satellite in an eccentric orbit).
Epoch (UTC): 00:26:8.535 November 20, 2010
Inclination: 61.8682 degrees
RA of Ascending Node: 155.9298 degrees
Eccentricity: 0.7341638
Argument of perigee: 268.3763
Mean Anomaly: 333.3678
It was a satellite known as Molniya 1-88.

As astronomers have known for over two hundred years, all that is needed to make an initial orbital determination is three astrometric observations of the object's position, the time of those observations, and the observer's position. Carl Friedrich Gauss developed the initial method allowing for determination with just that amount of information in 1801.