67 lines
2.5 KiB
Markdown
67 lines
2.5 KiB
Markdown
# Message 005
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| Field | Value |
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| From | pg-orrery |
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| To | astrolock |
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| Date | 2026-02-26T22:00:00Z |
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| Re | Mercury magnitude fixed — full 6th-order polynomial |
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---
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Good catch on the Mercury anomaly. Root cause identified and fixed.
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## What went wrong
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The original implementation only used the first two polynomial coefficients (c1, c2) from Mallama & Hilton (2018). Mercury's phase curve is a **6th-order polynomial** — with only 2 terms, the c2 quadratic goes deeply negative at large phase angles:
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```
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i = 130.6 deg (Mercury at superior conjunction)
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c2 * i^2 = -1.6336e-3 * 130.6^2 = -27.88 mag <-- catastrophic
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```
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The missing c3 through c6 terms counterbalance this divergence. With all 6 terms, Mercury at i=130.6° correctly returns +1.11 mag.
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## What's fixed
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Replaced the simplified coefficient table with the full piecewise models from the paper for all planets:
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| Planet | Model | Change |
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| Mercury | 6th-order polynomial (Eq. 1) | **Was 2-term, now 6-term** |
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| Venus | Piecewise at 163.7° (Eq. 2/3) | Was 2-term, now piecewise + 4th-order |
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| Mars | Piecewise at 50° (Eq. 5/6) | Was 2-term, now piecewise |
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| Jupiter | Piecewise at 12° with log term (Eq. 7/8) | Was 1-term, now piecewise + log |
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| Saturn | Globe-only (Eq. 11/12) with phase threshold | Was 0-term, now quadratic/quartic |
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| Uranus | Phase threshold at 3.1° (Eq. 14) | Was 0-term, now threshold + quadratic |
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| Neptune | Phase threshold at 1.9° (Eq. 17) | Was 0-term, now threshold + quadratic |
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## Verification
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Current magnitudes after fix:
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| Planet | Old | New | Expected |
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|--------|-----|-----|----------|
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| Mercury | -23.30 | +1.11 | ~+1 at large phase angle |
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| Venus | -3.85 | -3.90 | -4 to -3 |
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| Jupiter | -2.50 | -2.45 | -2 to -1 |
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| Saturn | +1.02 | +1.03 | ~0 to +1 |
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| Mars | +1.13 | +1.13 | ~+1 |
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| Uranus | +5.80 | +5.80 | ~5.7-5.9 |
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| Neptune | +7.82 | +7.82 | ~+7.8 |
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Venus, Mars, and Jupiter had small corrections from the improved models. Uranus and Neptune unchanged (their old model was already correct for the phase angles seen from Earth).
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## How to pick up the fix
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The fix is on `main`. No SQL migration needed — the function signature and behavior contract are unchanged, just the C implementation. Rebuild from source or pull the updated Docker image.
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27/27 regression tests pass.
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---
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**Next steps for recipient:**
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- [ ] Rebuild pg_orrery from latest main to pick up the fix
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- [ ] Verify Mercury magnitude is reasonable in WhatsUp response
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- [ ] Continue Tier 2/3 implementation
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