Solar-Pressure Three-Body Orbital Dispersion — STM Covariance & Monte Carlo

Task

Analyse initial-state uncertainty growth for a spacecraft in the circular restricted three-body problem (CR3BP) with solar radiation pressure (SRP) in the barycentric co-rotating frame. Extended model: lightness factor q1 (modifies only P1 monopole), zonal oblateness J2, and sectoral ellipticity C22 harmonics fixed in the co-rotating frame. Produce results for 12 independent scenarios.

Derivations (from first principles)

All closed forms derived independently — no expressions provided:

• Pseudo-potential Ω(x, y, z): centrifugal term + both point-mass attractions + SRP-modified P1 monopole + full J2 and C22 harmonic contributions with correct angular structure in the co-rotating frame
• Acceleration field: full gradient of Ω plus Coriolis terms (-2ω × v)
• 6×6 Jacobian A(t): every partial derivative of the acceleration field, including all harmonic gradient terms — no term negligible
• Jacobi constant C: 2Ω(x,y,z) − (vx² + vy² + vz²) using the full Ω

Computations

For each scenario:

1. Converted initial state from body-centred (P1 or P2) to barycentric co-rotating coordinates
2. Linear (STM) forecast: propagated the 6×6 STM alongside the state using the derived Jacobian A(t), mapped initial covariance to final covariance
3. Monte Carlo forecast: propagated an ensemble of n_samples perturbed initial states using fixed-step RK4 (dt, n_steps times), computed sample covariance

Scenarios varied in which harmonics were active (J2 only, C22 only, both, neither), SRP strength, mass ratio μ, and integration duration.

Key Techniques

CR3BP dynamics, spherical harmonic gravity (zonal + sectoral), STM propagation, RK4 numerical integration, Monte Carlo uncertainty quantification, coordinate frame transformations, numpy

Environment

Isolated Docker environment. Automated validation of JSON output files (one per scenario) against reference solutions with numerical tolerances.