This study aims to enhance Low Earth Orbit (LEO) satellite orbit prediction accuracy. We propose the Precise Orbit Determination with Optimized Perturbations (PODOP) method, considering Earth’s non-spherical gravity, atmospheric drag, etc., and a Long Short-Term Memory (LSTM)-based approach for orbital element time series. Validation shows that PODOP’s 10-day median error is 8.1 km (19% larger than Simplified General Perturbations (SGP4)’s 10.1 km) and LSTM’s 10-day median error is 5.3 km, outperforming SGP4 (48.5 km) and PODOP and improving constellation management and collision prevention.