Polygon Closure Initial Orbit Determination for Low Earth Orbit Space Debris: J2-Corrected Lambert in an Over-Determined Framework

Space debris in low Earth orbit represents an escalating risk to operational satellites. The current standard for optical-only orbit determination produces inclination errors of 5-15 degrees from a single telescope pass, insufficient for reliable conjunction analysis. This work adapts the Polygon Closure IOD framework (PC-IOD M=4) to the LEO debris problem, replacing heliocentric Keplerian Lambert with a J2-corrected geocentric numerical propagator. Using four anchor observations within a single 8-minuteoptical pass, the over-determined constraint system yields sub-0.005-degree inclination accuracy without radar — a 3,700 to 7,400-fold improvement over Gauss IOD. We quantify the J2 perturbation significance during an 8-minute pass and establish that J2-corrected propagation is mandatory for multi-pass conjunction prediction, where Keplerian drift reaches 1,108 km per day. The complete Python implementation is provided under PolyForm Noncommercial 1.0.0.