NATARAJALunar day, retardation, tides — and the Earth–Moon–Sun machine
Learning outcomes & permitted supports
- Explain why the Moon orbits rather than falls (falling-around), and why its solar path is convex.
- Use perigee/apogee: distance ↔ SD ↔ HP ↔ tide amplification, and tell the four months apart.
- Explain retardation (~50 min/day, variable) and why eclipses only happen in node seasons.
Supports in this lab: engine ephemeris (validated 220/220), 3D system view + 2D convexity and falling-around panels; every number mirrored in tables.
Glossary: elongation · perigee · apogee · node · syzygy · synodic month · sidereal month · HP · semidiameter · retardation
The machine — both motions at once (3D)
Loading 3D system…
Teaching scale (Moon distance enlarged for visibility — the true-scale story is in the convex-path panel below). The green loop is the Moon's REAL sampled orbit — eccentric and tilted; the dashed grey line is the node line. Play across months and watch eclipse seasons come and go.
Moon now (engine, geocentric)
| Phase | waxing crescent · 16.8% lit |
|---|---|
| Elongation | 48.4° E of Sun (waxing) |
| Distance | 385,330 km |
| Semidiameter | 15.50′ |
| Horizontal parallax | 56.9′ |
| Declination | 08° 00.0′ S |
| GHA | 315° 17.5′ |
| Ecliptic latitude | −3.55° (orbit tilt 5.14°) |
| Perigee (±30 d window) | 363,279 km · 11 Aug 2026 |
| Apogee (±30 d window) | 404,663 km · 22 Aug 2026 |
Watch SD and HP breathe with the distance: a perigee Moon looks ~14% wider than an apogee Moon and parallax swells the same way — that is why the almanac tabulates HP, and why perigean spring tides run higher.
The Moon orbits the Sun — convex, always
Why no collision — falling and missing
Retardation — Moon's meridian passage at Mumbai
| Local date | Transit (UT) | Later by |
|---|---|---|
| 16 Aug 2026 | 10:04:03 | — |
| 17 Aug 2026 | 10:48:35 | +45 min |
| 18 Aug 2026 | 11:33:56 | +45 min |
| 19 Aug 2026 | 12:20:49 | +47 min |
| 20 Aug 2026 | 13:09:32 | +49 min |
| 21 Aug 2026 | 13:59:55 | +50 min |
| 22 Aug 2026 | 14:51:16 | +51 min |
| 23 Aug 2026 | 15:42:34 | +51 min |
The lunar day averages 24h 50m — but the engine shows it varying tens of minutes with the Moon's speed along its eccentric orbit. About once a month a transit is skipped entirely. High water follows this drift — the tide is ~50 minutes later each day.
Nature's four months — each keeps its own calendar
| Month | Length | Governs |
|---|---|---|
| Sidereal (vs stars) | 27d 07h 43m | star re-alignment |
| Synodic (vs Sun) | 29d 12h 44m | phases & tides cycle |
| Anomalistic (perigee→perigee) | 27d 13h 19m | distance, SD, HP |
| Draconic (node→node) | 27d 05h 06m | eclipse seasons |
Synodic > sidereal because Earth moved ~27° along its orbit during the month — the Moon needs ~2.2 extra days to catch the Sun again: the same catch-up logic as the solar-vs-sidereal day, one storey up. The three 27-ish months differ because perigee and the nodes themselves move.