Task 037: Compute Planetary Positions and Solar System Dates for Orbital Transfers

Status: DONE

Motivation

Human directive: "軌道遷移の図において、軌道高度を変えるための必要ΔV計算しか行われておらず、実際には目的の位置(目的天体の周辺など)に到達できていないように見える。諸条件から整合する惑星の位置関係を想定し、そこから作中の太陽系日時も計算する"

Current orbital transfer analyses compute ΔV requirements for changing orbital altitude but do not verify that the destination body is actually at the arrival point. We need to:

1. For each transfer, determine what planetary configuration (angular positions) makes the transfer feasible
2. Compute the solar system date/epoch that corresponds to those configurations
3. Check consistency of these dates across episodes (the story is sequential)

Scope

1. Add planetary position computation to orbital mechanics (Rust crate)

- Keplerian orbit propagation for planets (approximate ephemeris)

- Synodic period / launch window calculation

- Phase angle at departure/arrival

1. For each transfer in ep01-ep05, determine:

- Required planetary phase angles

- Corresponding solar system dates (approximate epoch)

- Whether these dates are consistent across the story timeline

1. Update orbital diagrams to show planetary positions at computed dates
2. Update reports with date/timeline analysis

Depends on

• Orbital mechanics crate (solar-line-core)
• All episode analyses (ep01-ep05)