Task 181: Validate episode transfers with adaptive integrators

Status: DONE

The adaptive integrators (RK45 Dormand-Prince, Störmer-Verlet) are implemented in solar-line-core

but have only been validated with unit tests. Run the full episode transfer calculations through

the adaptive integrators and compare results against the existing RK4 fixed-step results.

This serves dual purposes:

Cross-validate the existing analysis results
Identify if any transfers benefit from adaptive stepping (e.g., near-body passages, thrust transitions)

Add integration tests that run each episode's key transfers through both RK4 and RK45
Compare ΔV, travel time, and arrival position accuracy
Check energy conservation metrics for ballistic phases (Störmer-Verlet vs RK4)
Document any meaningful differences in reports/data/calculations/
If adaptive results are significantly more accurate, update episode analyses

12 integration tests added in tests/episode_integrator_comparison.rs:

Test	Episode	Result
EP01 brachistochrone 72h	1	pos_diff 85k km (0.015% rel), speed_diff 0.66 km/s
EP01 flip point	1	Speed agrees to 0.015% (4272.1 vs 4272.7 km/s)
EP02 ballistic RK4 vs RK45	2	Machine precision agreement (~3e-15 relative)
EP02 ballistic RK4 vs Störmer-Verlet	2	Sub-km agreement; SV energy drift 2.5e-9 (bounded)
EP02 all integrators reach Saturn	2	All three agree to rounding: 0.877× Saturn orbit
EP03 brachistochrone 143h	3	pos_diff 112k km (0.008% rel)
EP03 nav crisis midpoint	3	Integrator diff ~0 km vs 14.36M km error budget
EP04 Uranus departure	4	~0 km, ~0 km/s (low thrust, short burn)
EP05 Uranus escape	5	Machine precision agreement
EP05 decel burn 35h	5	pos_diff 12.6k km (0.007% rel)
EP05 LEO insertion	5	pos_diff 1.28 km, speed_diff 0.004 km/s
Computation cost	1	RK45 uses 15× fewer derivative evaluations

Conclusion: RK4 and RK45 agree to high precision. No episode analyses need updating.

RK45 is 7-15× more efficient. Störmer-Verlet shows proper bounded energy oscillation.