Numerical Techniques for Astrodynamics: Application to Very Large Satellite Constellations

Abstract

Efficient numerical methods are essential for astrodynamics simulation and analysis. The astrodynamics community often depends on legacy implementations that do not leverage modern programming paradigms. This work explores the adoption of contemporary systems-oriented programming languages to integrate advanced numerical methods into astrodynamics workflows, improving computational performance, accuracy, and maintainability. This thesis develops a pure Rust implementation of classical numerical integrators (DOPRI5, DOP853, RADAU5, and BDF) with algorithmic fidelity to original Fortran codes. Python bindings provide a SciPy-compatible interface while leveraging Rust's performance. Benchmarking demonstrates that Rust implementations match or exceed Fortran performance by 2-11% on representative problems. Python bindings achieve 2-6x speedups for non-stiff problems and 12-24x for stiff problems versus SciPy. The VLISA case study evaluates three Sun-Earth constellation concepts for a very-long-baseline gravitational-wave observatory. The L4-L5-AEP configuration is identified as the optimal architecture, whereas natural configurations serve as lower-propulsion alternatives. This work challenges longstanding assumptions about programming language performance in scientific computing and demonstrates that modern languages can provide superior performance and maintainability for high-fidelity astrodynamics simulations.