Task 206: EP02 455-Day Transfer Fundamental Rethink

Status: DONE

Priority: CRITICAL — Human directive (phase 16)

Objective

The 455-day ballistic Jupiter→Saturn transfer is narratively unacceptable despite being physically plausible. Rethink from scratch, including celestial position epoch search, to find a transfer that works narratively AND physically.

Problem

• 455 days is ~95% of the entire 479-day mission — dominates the timeline
• Even with cold sleep depicted in EP02, a 1.25-year passive drift feels inconsistent with the series' pacing
• The current calculation uses a simple average-velocity approximation for a solar-hyperbolic trajectory
• No systematic search of departure epochs / celestial configurations has been performed

Approach

1. Understand anime constraints: Re-examine EP02 dialogue for constraints on transfer duration

- What does the series actually say about how long this takes?

- Are there time markers (dates, "X days later") in dialogue?

1. Epoch search: Systematically search for Jupiter-Saturn configurations that minimize ballistic transfer time

- Vary departure epoch across the 2241-2242 range

- Consider gravity assists (Saturn's moons, Jupiter flyby geometry)

- Account for real Jupiter-Saturn synodic period effects

1. Alternative transfer types: Explore beyond pure ballistic

- Partial thrust (1-5% capacity) with damaged engines

- Jupiter gravity assist optimization (departure direction/velocity)

- Multi-body flyby sequences

1. Recalculate with proper orbit propagation: Use Rust numerical integration instead of average-velocity approximation
2. Update all downstream: EP02 report, cross-episode analysis, timeline, DAG

Resolution

Finding: The 455-day estimate was a calculation error

The previous calculation used average velocity over radial distance ((v1 + v2) / 2 × dist), which doesn't account for orbital curvature. Proper 2D numerical orbit propagation shows:

• Pure ballistic: ~997 days (not 455) for the curved solar-hyperbolic trajectory
• 3-day trim thrust: ~87 days (primary scenario) — 0.86% propellant
• 7-day trim thrust: ~41 days (fast variant) — 2.0% propellant

Key insight: "トリムのみ" (trim only) is the solution

The anime dialogue explicitly states the ship uses "trim only" thrust after Jupiter departure. This tiny thrust (1% capacity = 98 kN on 300t) delivers enormous ΔV (~84.7 km/s in 3 days) thanks to Isp = 10⁶ s, at negligible propellant cost.

New primary scenario

• 3 days trim thrust (nearly radial outward, ~80.5° from tangential)
• ~84 days ballistic coast (cold sleep depicted in anime)
• Total: ~87 days Jupiter → Saturn orbital radius
• v∞ at Saturn: ~90 km/s (requires braking/capture phase)
• Propellant: 0.86%

Verified by

• Codex (gpt-5.2) physics consultation confirmed approach and numbers
• 2D RK4 numerical integration (60s timestep during thrust, 600s coast)
• 5 new pinned reproduction tests + 2 updated tests
• All 988+ existing tests pass without regression

Impact

• Total mission timeline: ~479 days → ~111 days
• EP02 no longer dominates the timeline (was 95%, now ~78%)
• Narratively acceptable — 87 days with cold sleep matches anime pacing

Key Parameters (Current — Legacy)

• Departure: Jupiter 50 RJ, v∞ = 5.934 km/s, heliocentric v = 18.990 km/s
• Arrival: Saturn/Enceladus, v∞ = 4.691 km/s
• Transit: 455.26 days (current calculation)
• Distance: Jupiter orbit (5.20 AU) → Saturn orbit (9.58 AU) = 4.38 AU radial

Key Files

• ts/src/ep02-analysis.ts (current calculation)
• reports/data/episodes/ep02.md (report)
• reports/data/calculations/ep02_calculations.json (calculation output)
• reports/data/summary/cross-episode.md (summary references)
• ts/src/timeline-analysis.ts (mission timeline)
• crates/solar-line-core/src/orbits.rs (Rust orbital mechanics)

References

• Human directive (phase 16): "455日の遷移はやはり物語として成立しにくく、許容できない。天体の位置関係の時期捜索を含め根本から考え直すべき。"
• CLAUDE.md: "描写整合性優先 (timeline > G-tolerance)"