NATARAJAThe fifty-seven — navigational stars, SHA, and Polaris
Learning outcomes & permitted supports
- Use the star catalogue: name, number, magnitude, SHA and declination — and form GHA★ = GHA♈ + SHA.
- Identify the principal stars from altitude, bearing, brightness and the pointer stories.
- Apply the circumpolar test dec > 90° − lat, and read the sky as it turns.
- Find latitude from a corrected Polaris altitude and explain the small correction's origin.
Supports in this lab: engine star chain (dec chain-checked to 0.001′, GHA to 0.06′ true angle vs independent implementation; catalogue rows candidate pending SME almanac pass), star globe 2D + celestial globe 3D (both cameras), SHA arc diagram, Polaris exact inversion, star finder.
Glossary: navigational star · SHA · First Point of Aries · magnitude · circumpolar · pointer stars · latitude by Polaris
Your sky now — 58 stars, engine positions
Vega (α Lyr, star 49) · mag 0.03 · alt 66.1° · az 31.1° · SHA 080° 32.0′ · dec 38° 48.7′ N
The celestial globe — your view
Loading celestial globe…
Why the almanac prints SHA
GHA♈ 191° 00.4′ (aqua arc) + SHA 080° 32.0′ (orange arc) = GHA★ 271° 32.4′ (outer arc)
Stars barely move against ♈, so the almanac prints ONE fast column (GHA♈, every hour) and one slow number per star (SHA, every three days) — 57 stars for the price of one angle. That is the entire reason SHA exists.
Latitude by Polaris — the oldest trick, solved exactly
| Polaris altitude Ho (engine forward model) | 018° 34.5′ |
| Latitude solved back from that Ho | 19° 04.6′ N |
| Total correction (lat − Ho) | +30.1′ |
| Polaris polar distance now | 37.7′ |
Polaris rides a small circle of radius ≈ 38′ around the true pole, so her altitude is your latitude give or take at most that much — the correction depends only on where she is on that circle (her LHA, here 217° 10.2′). The almanac packages this as a₀+a₁+a₂ tables; the engine solves the triangle itself. One glance north = latitude, the oldest trick at sea.
Star finder — what is up (alt > 10°), brightest first
| Star | Mag | Alt | Az | SHA | Dec |
|---|---|---|---|---|---|
| Arcturus (37) | -0.1 | 43° | 279° | 145° 46.8′ | 19° 02.8′ N |
| Vega (49) | 0.0 | 66° | 31° | 080° 32.0′ | 38° 48.7′ N |
| Altair (51) | 0.8 | 55° | 102° | 061° 58.4′ | 08° 56.5′ N |
| Spica (33) | 1.0 | 22° | 249° | 158° 21.0′ | 11° 18.0′ S |
| Antares (42) | 1.1 | 42° | 199° | 112° 14.1′ | 26° 29.5′ S |
| Deneb (53) | 1.3 | 43° | 45° | 049° 24.4′ | 45° 22.7′ N |
| Shaula (45) | 1.6 | 34° | 180° | 096° 08.3′ | 37° 07.5′ S |
| Alioth (32) | 1.8 | 27° | 324° | 166° 12.2′ | 55° 49.1′ N |
| Dubhe (27) | 1.8 | 13° | 331° | 193° 40.0′ | 61° 36.6′ N |
| Kaus Australis (48) | 1.9 | 35° | 167° | 083° 30.5′ | 34° 22.3′ S |
| Alkaid (34) | 1.9 | 36° | 318° | 152° 51.2′ | 49° 11.0′ N |
| Polaris (Polaris) | 2.0 | 19° | 0° | 313° 17.2′ | 89° 22.3′ N |
| Menkent (36) | 2.1 | 16° | 221° | 147° 56.2′ | 36° 30.2′ S |
| Nunki (50) | 2.1 | 41° | 156° | 075° 45.8′ | 26° 15.8′ S |
| Kochab (40) | 2.1 | 31° | 348° | 137° 20.0′ | 74° 03.0′ N |
| Rasalhague (46) | 2.1 | 83° | 179° | 095° 57.1′ | 12° 32.6′ N |
| Alphecca (41) | 2.2 | 61° | 291° | 126° 02.6′ | 26° 37.7′ N |
| Eltanin (47) | 2.2 | 57° | 6° | 090° 41.2′ | 51° 29.3′ N |
| Enif (54) | 2.4 | 29° | 89° | 033° 37.1′ | 10° 00.0′ N |
| Sabik (44) | 2.4 | 55° | 190° | 102° 01.1′ | 15° 45.5′ S |
| Markab (57) | 2.5 | 12° | 78° | 013° 28.2′ | 15° 21.0′ N |
| Zubenelgenubi (39) | 2.8 | 37° | 231° | 136° 54.6′ | 16° 09.2′ S |