VALIDATION_CASE_MARS_HELIACAL_RISING_2026 - TheDaniel166/moira GitHub Wiki
Validation Case: Mars Heliacal Rising at Babylon (2026)
Subject: First morning visibility of Mars after solar conjunction
Substrate: Moira heliacal.planet_heliacal_rising / JPL DE441
Oracle: JPL Horizons DE441 geocentric RA/Dec + independent altitude computation
Criterion layer: Schoch/Ptolemy arcus visionis table — +1 to +2 mag branch (11°)
Status: VERIFIED — exact agreement, Moira and Horizons both predict 2026-Apr-17
Verified: 2026-04-10
1. What is being tested
The same solver and the same arcus visionis branch as the 2024 Mars case, but with a different conjunction and a different elongation geometry. This tests that the av=11° result is stable across separate apparitions of Mars, not an artifact of one particular geometry.
Key geometric contrast with the 2024 case:
| 2024 case | 2026 case | |
|---|---|---|
| Conjunction date | 2023-Nov-18 | 2026-Jan-09 |
| Predicted heliacal rising | 2024-Jan-07 | 2026-Apr-17 |
| Days post-conjunction | ~50 | ~97 |
| Elongation at event | −14.52° | −21.52° |
| Mars magnitude at event | +1.34 | +1.24 |
Mars gains elongation slowly after conjunction (~0.5°/day). The 2026 case waits longer, reaches a larger elongation, and finds Mars at slightly higher altitude at the threshold moment. Both cases sit in the same av=11° table bracket.
2. Moira's criterion
Identical to the 2024 case. The Schoch/Ptolemy stepped table assigns:
| Apparent mag | Base solar depression |
|---|---|
| +1 to +2 | 11.0° |
Mars magnitude at this apparition is +1.24, placing it in the same bracket.
The adjustments from the default VisibilityPolicy (Bortle-3, k=0.25, lim_mag=6.5)
are again zero, so arcus visionis = 11.0° exactly throughout the search window.
3. Moira's prediction
planet_heliacal_rising(Body.MARS, JD(2026-Jan-20), lat=32.55, lon=44.42)
| Field | Value |
|---|---|
| First visible date | 2026-Apr-17 |
| UT of visibility window | 01:40 |
| Planet altitude | +0.07° |
| Sun altitude at criterion | −11.00° |
| Solar elongation | −21.52° |
| Mars apparent magnitude | +1.24 |
| JD_UT | 2461147.5699 |
Mars at +0.07° is barely above the geometric horizon at event — even more marginal than the 2024 case (+0.12°). At ~0.12°/day altitude gain, this is again a precision threshold test.
4. Independent Horizons check
Method
Identical to the 2024 case (see VALIDATION_CASE_MARS_HELIACAL_RISING.md):
- Query JPL Horizons DE441 for geocentric RA/Dec of Mars (body 499) and the Sun (body 10) at 10-minute intervals: 2026-Feb-15 01:00 through 2026-May-15 05:00 UT.
- Restrict to the Babylon pre-dawn window (UT 01:00–05:00) to exclude the evening Sun=−11° crossing.
- Compute GMST → local sidereal time → altitude via spherical trigonometry.
- Interpolate the morning crossing of Sun = −11°.
- Record Mars altitude at that moment. First morning Mars alt > 0° = event date.
Script: tmp/mars_heliacal_2026.py
Criterion A — matching Moira's arcus visionis (Sun = −11°, alt > 0°)
Selected per-day Mars altitude at Sun = −11° across the apparition:
| Date | Twilight UT | Mars alt |
|---|---|---|
| Feb-15 | 2.918h | −6.34° |
| Mar-01 | 2.680h | −4.88° |
| Mar-15 | 2.395h | −3.52° |
| Apr-01 | 2.016h | −1.80° |
| Apr-10 | 1.813h | −0.80° |
| Apr-14 | 1.725h | −0.32° |
| Apr-15 | 1.703h | −0.19° |
| Apr-16 | 1.682h | −0.07° |
| Apr-17 | 1.660h | +0.06° |
| Apr-18 | 1.639h | +0.19° |
| Apr-20 | 1.596h | +0.45° |
| Apr-25 | 1.494h | +1.15° |
| May-01 | 1.377h | +2.06° |
| May-13 | 1.175h | +4.18° |
Horizons-derived heliacal rising: 2026-Apr-17.
The twilight UT column shows the Babylon pre-dawn moving earlier as spring progresses (sunrise advances). Moira's predicted UT of 01:40 (1.677h) agrees with Horizons' 1.660h to within 1 minute — consistent with the 10-minute interpolation step.
Criterion B — astronomical twilight (Sun = −18°, alt ≥ 5°)
| Date | Mars alt at Sun=−18° |
|---|---|
| Feb-15 | −13.19° |
| Mar-15 | −10.52° |
| Apr-01 | −9.05° |
| Apr-12 | −8.02° |
| May-13 (end of table) | not reached |
Mars never approaches 5° above the geometric horizon at astronomical twilight across the entire Feb–May search window. The elongation of −21.5° at event is still too small for Mars to be well-placed at the darker threshold.
Criterion B returns None — consistent with the 2024 case.
5. Elongation geometry comparison
The 2026 case provides a useful cross-check of the outer-planet slow-elongation model:
| Date | Elongation | Mars alt at Sun=−11° |
|---|---|---|
| Feb-15 (Horizons) | ~5° | −6.3° |
| Apr-01 | ~15° | −1.8° |
| Apr-17 (event) | ~21.5° | +0.06° |
| Apr-25 | ~24° | +1.2° |
| May-13 | ~31° | +4.2° |
The altitude grows steadily from deep negative in February to positive in April. The arcus visionis solver must integrate this gradual gain correctly; neither a coarse date-stepping approach nor an early-termination heuristic would find the threshold cleanly. The exact match confirms that the solver's numerical search is resolving the Mars emergence with day-level precision across a 97-day post-conjunction window.
6. What this validates
planet_heliacal_risingreturns the correct date for a separate Mars apparition with a different elongation geometry and a longer post-conjunction latency.- The av=11° criterion is applied consistently between the 2024 and 2026 apparitions.
- The positional substrate for Mars at body 499 in DE441 is geometrically consistent with Horizons across two separate apparition windows.
- The solver does not fail for a long search window (~97 days post-conjunction) or for a marginal event altitude (+0.07°).
7. What this does not validate
- Other av table branches (the +0 to +1 or brighter Mars brackets are untested; they require Mars near opposition, magnitude −2 to 0).
- Observers at latitudes other than Babylon (32.55°N).
- Acronychal rising or heliacal setting for Mars.
- Observational correspondence with ancient or modern records.
8. Relationship to the 2024 Mars case
| 2024 case | This document | |
|---|---|---|
| Conjunction | 2023-Nov-18 | 2026-Jan-09 |
| Event date | 2024-Jan-07 | 2026-Apr-17 |
| Post-conjunction days | ~50 | ~97 |
| Elongation | −14.5° | −21.5° |
| Mars alt at event | +0.12° | +0.07° |
| av applied | 11.0° | 11.0° |
| Match | ✓ exact | ✓ exact |
Both cases confirm the same branch of the arcus visionis table, from different geometric configurations and across a 2.5-year span. The solver's threshold detection is stable.
9. Arcus visionis table coverage: three confirmed cases
| Planet | Mag at event | av bracket | Solar dep | Wiki doc |
|---|---|---|---|---|
| Venus (2023 Aug) | −4.00 | ≤ −4.0 | 5° | VALIDATION_CASE_VENUS_HELIACAL_RISING.md |
| Mars (2024 Jan) | +1.34 | +1 to +2 | 11° | VALIDATION_CASE_MARS_HELIACAL_RISING.md |
| Mars (2026 Apr) | +1.24 | +1 to +2 | 11° | This document |
The +1 to +2 mag branch is now confirmed by two independent Mars apparitions separated by 2.5 years and 7° of event elongation. The 5° (Venus) and 11° (Mars) table branches are verified; the intermediate branches (6°, 7°, 8°, 9°, 10°) remain untested.
10. Verification script
tmp/mars_heliacal_2026.py — queries Horizons live, computes local altitude at
Babylon, and prints the per-day Mars altitude table for both criteria.
Run with:
.venv/Scripts/python.exe tmp/mars_heliacal_2026.py