  The Simplified General Perturbations 4 (SGP4) orbital propagation method is
widely used for predicting the positions and velocities of Earth-orbiting
objects rapidly and reliably. Despite continuous refinement, SGP models still
lack the precision of numerical propagators, which offer significantly smaller
errors. This study presents dSGP4, a novel differentiable version of SGP4
implemented using PyTorch. By making SGP4 differentiable, dSGP4 facilitates
various space-related applications, including spacecraft orbit determination,
state conversion, covariance transformation, state transition matrix
computation, and covariance propagation. Additionally, dSGP4's PyTorch
implementation allows for embarrassingly parallel orbital propagation across
batches of Two-Line Element Sets (TLEs), leveraging the computational power of
CPUs, GPUs, and advanced hardware for distributed prediction of satellite
positions at future times. Furthermore, dSGP4's differentiability enables
integration with modern machine learning techniques. Thus, we propose a novel
orbital propagation paradigm, ML-dSGP4, where neural networks are integrated
into the orbital propagator. Through stochastic gradient descent, this combined
model's inputs, outputs, and parameters can be iteratively refined, surpassing
SGP4's precision. Neural networks act as identity operators by default,
adhering to SGP4's behavior. However, dSGP4's differentiability allows
fine-tuning with ephemeris data, enhancing precision while maintaining
computational speed. This empowers satellite operators and researchers to train
the model using specific ephemeris or high-precision numerical propagation
data, significantly advancing orbital prediction capabilities.
