NATARAJAPZX — the navigation triangle made physical
Learning outcomes & permitted supports
- Identify P, Z, X and map co-latitude, polar distance (incl. contrary name) and zenith distance onto the triangle.
- Place the hour angle at P, azimuth angle at Z, parallactic angle at X — and never swap them.
- Compute altitude by the cosine rule and reject impossible triangles.
Supports in this lab: 3D sphere with flatten-to-exam-diagram morph, live schematic diagram, engine-solved elements.
Glossary: PZX triangle · co-latitude · polar distance · zenith distance · parallactic angle · LHA · azimuth
The triangle on the sphere — then flatten it
Loading 3D triangle…
Drag to orbit. At 0% the three sides are great-circle arcs on the real sphere; at 100% they are the straight lines examiners draw. The values never change — only the drawing does. That is the whole point: the exam diagram is a MAP of a spherical fact.
The examiner's flat diagram — live
Lock one, vary the others
Watch the couplings: latitude moves ONLY PZ directly; declination moves ONLY PX; LHA moves only the angle at P — yet ZX and both other angles respond, because the triangle closes. Cross the declination through zero and watch PX jump past 90° — that is the contrary-name case that catches candidates.
The six elements (engine)
| PZ (co-latitude) | 71° 00.0′ = 90° − lat |
|---|---|
| PX (polar distance, same name) | 077° 00.0′ = 90° − dec |
| ZX (zenith distance) | 043° 33.4′ = 90° − alt |
| Angle at P (meridian angle t) | 045° 00.0′ E |
| Angle at Z (azimuth angle) | 090° 58.0′ |
| Angle at X (parallactic) | 075° 59.4′ |
| Altitude / compass azimuth | 46° 26.6′ / 090° 58.0′ |