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

Polygon Closure Initial Orbit Determination for Low Earth Orbit Space Debris: J2-Corrected Lambert in an Over-Determined Framework This paper adapts the PC-IOD M=4 polygon closure framework to LEO space debris tracking, using four optical observations within a single 8-minute telescope pass to determine the debris orbit without radar. A J2-corrected Lambert solver (Newton-Raphson + RK4) enforces velocity continuity at interior polygon vertices. The result: inclination error 0.001° — 8,500× better than Gauss IOD, and robust where Systematic Ranging (Farnocchia et al. 2010) fails due to near-zenith degeneracy. Experimental comparison included. C++ implementation with ARM NEON vectorization achieves full orbit determination in 227 ms on ARM Snapdragon 8 Gen 2 (vs 97 s for Systematic Ranging in Python). Package includes Python validation code (MIT), C++ scalar and NEON implementations (PolyForm Noncommercial 1.0.0), and the systematic ranging comparison script.