Caelis Engine

Motor matemático de modelado astronómico para la observación celeste simbólica.

Caelis Engine v2.1 computa posiciones planetarias reales con algoritmos de precisión profesional (VSOP87, ELP/MPP02), las renderiza como un instrumento simbólico vivo, y expone un framework completo de análisis astronómico-astrológico — en un único archivo HTML sin dependencias.

→ Live Demo · Docs · License · Ko-fi

What it does

Symbol → Structure → Simulation

• Computes Sun, Moon, and 5 planets using VSOP87 (planets) and ELP/MPP02 (Moon, LLR-calibrated 2002), verified against Meeus, JPL Horizons, and Swiss Ephemeris — 107/107 tests PASS
• Renders a real-time 2D sky map with horizon, ecliptic, Placidus house cusps, 600 background stars, and equinox/solstice markers
• Switches to Oculus 3D — a Three.js orbital sphere where planets move in true celestial coordinates
• Analyzes planetary cycles, resonances, and periodicity via the Atacir panel (with Synastry tab)
• Eclipse calculator — solar and lunar, georeferenced visibility (Meeus Cap.54, Premium)
• Vedic Panchanga — Tithi, Vara, Nakshatra, Yoga, Karana with Lahiri ayanamsa (Premium)
• Equinox/solstice markers — VSOP87 bisection, hemisphere-adaptive, < 1 min precision

Why it's different

| Feature | Caelis Engine | Typical astro library | Typical sky app | |---|---|---|---| | VSOP87 + ELP/MPP02 (LLR calibrated) | ✓ | sometimes | rarely | | 107/107 tests vs JPL + Swiss Eph. | ✓ | rarely | no | | Zero dependencies | ✓ | no | no | | Symbolic + scientific layer | ✓ | no | no | | Clean pure-function API (no DOM) | ✓ | varies | no | | Eclipse calculator (georeferenced) | ✓ | rarely | rarely | | Vedic Panchanga (5 elements) | ✓ | no | rarely | | Synastry cross-aspects | ✓ | no | no | | Single file, runs offline | ✓ | no | no |

Architecture — v2.1 improvements

Caelis Engine v2.1 introduces clean separation between the mathematical core and the UI layer:

| Function | Status | Notes | |---|---|---| | calcAtacirCore() | ✅ Pure — no DOM | Direcciones primarias + aspectos + ciclos | | calcPanchangaCore() | ✅ Pure — no DOM | 5 Panchanga elements + Lahiri ayanamsa | | calcEclipsesCore() | ✅ Pure — no DOM | Eclipse detection + georef visibility | | calcSinastriaCore() | ✅ Pure — no DOM | Cross-chart aspects + antiscias | | getSnapshotAt() | ✅ try/finally | State always restored on exception | | _eclVisibleAt() | ✅ try/finally | State always restored on exception | | nutation(T) | ✅ Memoized | Cache key = T, invalidated on time change | | lunarNodes() | ✅ Memoized | Cache key = T, invalidated on time change |

The *Core() functions take plain parameters (dates, coords) and return data objects — usable in Node.js, REST APIs, or npm packages without any DOM mocks.

Core modules

caelis-engine/
├── caelis_engine_2_1.html     ← Full instrument (single file) — 8,200 lines
├── index.html                 ← GitHub Pages entry point (identical)
├── validation.html            ← Precision test suite — 107/107 PASS
└── src/
    ├── astro/AstroCore.js     ← VSOP87, ELP/MPP02, coordinate transforms
    ├── TimeEngine.js          ← Julian dates, sidereal time, time control
    └── Atacir.js              ← Cycle analysis, aspects, resonances, synastry

Mathematical foundations

Algorithms

| Algorithm | Source | Terms | Applies to | |---|---|---|---| | VSOP87 | Bretagnon & Francou 1987, Meeus App.II | Earth: 185 · Venus: 79 · Mars: 152 · Jupiter: 141 · Saturn: 167 | Venus, Mars, Jupiter, Saturn, Sun | | Mercury | Meeus Cap.31 (equation of center) | 5 terms, e=0.206 | Mercury | | ELP/MPP02 | Chapront & Francou 2002, A&A 412 (LLR) | 164L + 105B + 29R | Moon | | IAU 1980 Nutation | Meeus Cap.22 | 63 series (memoized) | ΔΨ, Δε | | Placidus houses | Meeus Cap.38 | Newton-Raphson < 1×10⁻⁹ rad | Cusps I–XII | | Eclipse detection | Meeus Cap.54 | F-argument criterion | Solar · Lunar | | Equinoxes/Solstices | VSOP87 bisection | < 1 min precision | 0°, 90°, 180°, 270° | | Lahiri ayanamsa | IAU 1955 | 23.85282° + 0.013972°/yr | Vedic sidereal |

Note on Mercury: vsop87Mercurio() uses Meeus Cap.31 equation of center (not VSOP87 series) due to Mercury's high eccentricity (e=0.206). The truncated VSOP87 series gives ~21° error for Mercury. The function name is preserved for interface compatibility. Verified error: < 0.116° vs JPL Horizons DE441.

Precision — 107/107 tests PASS

| Component | Max error | Reference | |---|---|---| | Moon λ (ELP/MPP02) | 0.0001° (0.45") — 63× vs ELP2000 | JPL Horizons DE441 | | Sun VSOP87 | 0.0003° | Meeus Cap.25 | | Mercury (eq. of center) | < 0.116° | JPL Horizons DE441 | | Venus / Mars / Jupiter / Saturn | < 0.131° | JPL Horizons DE441 | | Mercury β orbital range | [-7°, +7°] ✓ | Orbital theory | | IAU 1980 Nutation ΔΨ | < 0.004 arcsec | Meeus Cap.22 | | Placidus ASC | < 0.019° | Reference chart | | ΔT at J2000 | < 0.1 s | IERS | | Equinoxes/Solstices | < 1 min | JPL Horizons 2025 |

Valid range: 1800–2100 CE

Public API

// Astronomical snapshot for any date/location
const snap = getSnapshot();
const snap = getSnapshotAt(jde, latDeg, lonDeg);

// Pure calculation cores (no DOM — usable in Node.js)
const result  = calcAtacirCore(rxDate, rxTime, rxLat, rxLon, trDate, trTime, trLat, trLon, key);
const panch   = calcPanchangaCore(dateStr, timeStr);
const ecl     = calcEclipsesCore(latDeg, lonDeg, rangeYears, doSolar, doLunar, jdCenter);
const sin     = calcSinastriaCore(dateA, timeA, latA, lonA, dateB, timeB, latB, lonB);

// Aspects
const aspects = calcAspectosTransito(snapNatal, snapTransit);

// Individual positions
const lonSol  = sunLonEcl();          // degrees
const lonLuna = moonLonEcl();         // degrees
const lonPl   = planetLonEcl(name);   // degrees
const dist    = lunarDistELP(jde);    // km

// Time utilities
const dT      = deltaT(jde);          // seconds
const jdeEq   = nextSolEquinox(0, jdStart);  // vernal equinox JDE

Quickstart

git clone https://github.com/HermeticaLabs/caelis-engine
# Open index.html in any modern browser — no install, no build, no server.

Freemium model

Premium is a one-time payment of $12 USD — no subscription, no renewal.

| Feature | Free | Premium | |---|---|---| | Caelis 2D, Astrolabio, Oculus 3D | ✓ | ✓ | | Full Atacir (transits, cycles, resonances) | 1 aspect (Naibod fixed) | ✓ complete | | Eclipse calculator | Next eclipse only | ✓ full range | | Panchanga — Tithi + Vara | ✓ | ✓ | | Panchanga — Nakshatra + Yoga + Karana | — | ✓ | | Synastry — 3 most exact aspects | ✓ | ✓ | | Synastry — full table + antiscia | — | ✓ | | JSON export | Natal only | ✓ complete |

→ Get Premium — $12 USD one-time

Roadmap

• [x] VSOP87 + ELP/MPP02 — 164L + 105B + 29R, LLR calibrated (63× lunar precision)
• [x] Eclipse calculator — georeferenced, solar and lunar (Premium)
• [x] Equinox/solstice markers — VSOP87 bisection, hemisphere-adaptive
• [x] Vedic Panchanga — 5 elements + Lahiri ayanamsa (Premium)
• [x] Synastry — cross-chart aspects + antiscia
• [x] 107/107 tests vs JPL Horizons DE441 + Swiss Ephemeris
• [x] v2.1 — Pure core functions (no DOM), try/finally state safety, nutation/nodes cache, Mercury β tests
• [ ] AI hermetic interpretation — coming soon (experimental)
• [ ] Google Play Store
• [ ] ELP/MPP02 extended R-series → dist < 10 km
• [ ] IAU 2000A nutation (1365 terms → ~0.1 mas)
• [ ] npm package (caelis-js)

License

Open Source — AGPL-3.0 · Free to use, study, modify and share. Source disclosure required for products/services. Full text: AGPL-3.0

Commercial License · For proprietary use. Contact: [email protected]

Author

Cristian Valeria Bravo · Hermetica Labs

Caelis Engine exists at the boundary between mathematical precision and symbolic observation — where the structure of time becomes navigable.

Support: ko-fi.com/hermeticalabs · © 2024–2026 Cristian Valeria Bravo / Hermetica Labs