Using Odyssey tools we can run continual conjunction analysis on the entire catalog using SGP-4 propagation. Schafer has a developmental analysis technique called Fast Geometric Conjunction Analysis (FastCon) which can determine the approximate location of all conjunctions with minimal orbit propagation. It uses the 3D orbit geometries described by NORAD two line element sets (TLEs). As shown in Figure 1 below, orbit inclination and longitude of the ascending node can be used to orient angular momentum. This can then be used in a special algorithm to locate potential orbital conjunctions. These can be sorted for range, and high fidelity orbit propagators can accurately predict the conjunction geometry for only those conjunctions that meet the minimum distance threshold criteria. The Odyssey algorithm extracts the geometry of each relative orbit pair from the Keplerian elements of the standard NORAD TLE. These elements consist mainly of angles that orient the orbit, and a few other parameters that size the orbit.
Odyssey calculates conjunctions for all objects, which means every object in the NORAD TLE catalog against all other objects. The number of tests that Odyssey calculates is thus n2/2-n. For the current NORAD space catalog (well over 14,000 objects), Odyssey tests for multiple conjunctions for approximately 100 million unique pairs. It reduces the number of tests significantly with an apogee-perigee filter. Any object with a perigee higher than the paired object’s apogee is skipped.