NATARAJAThe wandering stars — planets and the almanac
Learning outcomes & permitted supports
- Distinguish inferior and superior planets; use elongation limits (Mercury ≈28°, Venus ≈47°) and the midnight test.
- Explain retrograde motion as line-of-sight overtake centred on opposition — no epicycles, no reversing orbits.
- Read planet GHA/dec/SD/HP/magnitude from the engine's almanac strip and form LHA for any longitude.
- Tell evening star from morning star from the sign of elongation, and explain why Venus is brightest as a crescent.
Supports in this lab: engine planetary ephemerides (validated 481/481 vs independent implementation), 2D orrery + 3D system view side by side, retrograde overtake diagram, elongation chart with engine-found greatest elongations, almanac strip.
Glossary: inferior/superior planet · greatest elongation · evening/morning star · conjunction · opposition · retrograde · phase angle · elongation
Top-down: the machine (2D, engine positions)
2026-08-17 · Venus: elongation 45.9° E (evening sky) · Δ 0.671 AU · r 0.728 AU · mag -4.3
Orbits are the REAL sampled ellipses, not circles. The blue arc at Earth is the elongation — the one angle that decides where in your sky the planet can be.
The same machine in 3D — drag it
Loading 3D system…
Retrograde — the overtake, drawn correctly
Mars never reverses its orbit. Between sight lines 3 and 5 the FASTER Earth overtakes on the inside, so the line of sight swings backward against the stars — the loop is centred on opposition (2027-02-19, engine-found), exactly when the planet is nearest, brightest, and on your meridian at midnight.
Mercury & Venus — chained to the Sun
Venus swings out to ±47° and no further — she can NEVER stand on your midnight meridian. Mercury stays within ±28°, hugging twilight. Rings mark greatest elongations (engine-found; the golden suite pins them within minutes of the independent ephemeris).
Venus: phase, size, brilliancy
2026-08-17 · 48% lit · SD 12.4″ · Δ 0.671 AU · mag -4.3 · elongation 45.9°E
Venus is brightest as a fat CRESCENT (~27% lit), not when full: near superior conjunction she is full but six times smaller; near inferior conjunction huge but a sliver. The product of size × lit fraction peaks about 36 days either side of inferior conjunction.
Almanac strip — 2026-08-17 05:00 UT
| Body | GHA | Dec | Mag | SD / HP | Elongation | Mer. pass (UT) |
|---|---|---|---|---|---|---|
| Venus | 211° 52.2′ | 05° 31.3′ S | -4.3 | 12.4″ / 13.1″ | 45.9° E · evening | 10:01 |
| Mars | 306° 23.0′ | 23° 42.0′ N | 1.3 | 2.4″ / 4.6″ | 50.5° W · morning | 03:43 |
| Jupiter | 267° 29.1′ | 18° 05.0′ N | -1.8 | 15.7″ / 1.4″ | 13.8° W · morning | 06:18 |
| Saturn | 026° 22.0′ | 03° 16.1′ N | 0.3 | 9.5″ / 1.0″ | 129.9° W · morning | 22:24 |
| Mercury * | 264° 15.0′ | 17° 59.8′ N | -1.3 | 2.7″ / 7.1″ | 10.9° W · morning | 06:31 |
* Mercury never strays 28° from the Sun — too deep in twilight for sextant work; listed for theory. The almanac's four sight-reduction planets are Venus, Mars, Jupiter, Saturn. LHA = GHA + 72.83° (your longitude, east +). HP matters only for Venus/Mars at their closest (up to ~0.5′).