Task 098: 3D Orbital Analysis

Status: DONE (2026-02-24)

Motivation

Human directive: 2次元的な計算である程度の分析ができてきたら、3次元的な詳細な分析も行い、軌道傾斜角や土星の輪との位置関係などについても分析すること。

Scope

1. Extend orbit propagation to 3D (add orbital inclination, RAAN, argument of periapsis)
2. Analyze Saturn ring plane crossing — does Kestrel's trajectory intersect the rings?
3. Consider out-of-plane components for:

- Transfer orbits between planets with different inclinations

- Gravity assists (hyperbolic plane vs ecliptic)

- Enceladus orbit relative to Saturn ring plane

1. Add 3D visualization or projection views to reports

Completed Work

Rust Core (solar-line-core)

• Vec3: Added cross_raw(), cross_raw_with() (mixed types), normalize() methods
• ephemeris.rs: Extended PlanetPosition with z, latitude, inclination fields. Updated planet_position() from simplified coplanar λ=ω+ν+Ω to proper 3D rotation matrix (Ω, i, ω)
• orbits.rs: Added elements_to_state_vector() (Keplerian → Cartesian via perifocal rotation) and plane_change_dv() function
• orbital_3d.rs (NEW): Module for 3D orbital analysis:

- Saturn ring system constants and ring plane normal (IAU J2000 pole)

- Uranus system constants and spin axis computation

- saturn_ring_crossing(): analyzes trajectory intersections with Saturn's ring plane

- uranus_approach_analysis(): analyzes approach geometry relative to Uranus's extreme tilt

- ecliptic_z_height(), max_ecliptic_z_height(), out_of_plane_distance()

- transfer_inclination_penalty(): computes inclination-change ΔV for each transfer

- 17 tests in orbital_3d, 7 tests in orbits.rs (elements_to_state_vector, plane_change_dv)

• comms.rs: Updated distance_between_positions() to 3D, fixed test PlanetPosition construction

WASM Bridge (solar-line-wasm)

• Updated planet_position() binding to return z, latitude, inclination
• Added 9 new WASM bindings: ecliptic_z_height, max_ecliptic_z_height, out_of_plane_distance, plane_change_dv, transfer_inclination_penalty, saturn_ring_plane_normal, uranus_spin_axis_ecliptic, saturn_ring_crossing, uranus_approach_analysis, elements_to_state_vector

TypeScript

• ephemeris.ts: Updated PlanetPosition interface with z, latitude, inclination. Updated planetPosition() to use 3D rotation matrix
• orbital-3d-analysis.ts (NEW): 3D analysis script computing:

- Per-transfer ecliptic z-heights and out-of-plane distances

- Inclination change ΔV penalties per episode

- Saturn ring plane crossing analysis (EP02)

- Uranus axial tilt approach geometry (EP03/EP04)

• ephemeris.test.ts: Updated consistency test for 3D coordinates
• Output: reports/data/calculations/3d_orbital_analysis.json

Key Findings

• Coplanar approximation mostly valid: Plane change ΔV < 1% of transfer ΔV for EP01 (0.47%) and EP04 (0.71%). Slightly > 1% for EP02 (1.06%) and EP03 (1.51%)
• Saturn ring approach: 26.8° angle to ring plane from Jupiter approach. Enceladus orbits at 238,042 km, safely outside rings (140,180 km)
• Uranus approach: From Saturn at ~60° to equatorial, toward Earth at ~69° — nearly polar, consistent with Uranus's 97.77° obliquity
• Out-of-plane distances: Up to 0.22 AU for Saturn→Uranus transfer

Remaining Work (future tasks)

• 3D visualization/projection views in reports
• Ring crossing animation in orbital diagrams
• Extend to gravity assist out-of-plane analysis