NATARAJAOP-13
The sums — latitude and longitude in mid-sea, step by step
Learning outcomes & permitted supports
- Work the noon sight end to end: chron → GMT → dec; Hs → Ho; ZX = 90° − Ho named opposite the bearing; lat = dec ± ZX.
- Work longitude by chronometer: Ho + DR lat + dec → cos-formula t → the morning/afternoon side decision → LHA − GHA = longitude.
- Work latitude by Polaris with the exact total correction, and say what the almanac's a₀+a₁+a₂ packages.
- State why noon forgives the clock but longitude lives and dies by it (4 s = 1′).
Supports in this lab: engine-real voyages (615/615 golden incl. noon-latitude and time-sight closures to machine precision), reveal-one-line worked sheets with a WHY for every line, endless seeded sums with full worked answers.
Glossary: zenith distance · meridian altitude · longitude by chronometer · chronometer · latitude by Polaris
The navigator's paper — one line at a time
Voyage #1: off Mumbai — chronometer 10s fast, IE 1.8′ on the arc, eye 17 m. The truth is hidden until the last line.
Latitude by meridian altitude — off Mumbai, 2026-08-22
| 1. Chronometer at transit | 07h 14m 09s (2026-08-22) |
Why line 1:
The chronometer keeps GMT — but every chronometer carries a KNOWN error, checked daily by radio time signal and logged.