Discuss with respect to celestial navigation the formulation of Pole-star tables for determination of latitude & azimuth;

Of course. Let’s break down the formulation and use of Pole-star tables for determining latitude and azimuth in celestial navigation. This is a classic and highly reliable method for navigators in the Northern Hemisphere.

1. The Fundamental Principle: Why Polaris is Special (But Imperfect)

The entire concept of using the Pole Star (Polaris) for navigation rests on a simple approximation:

The altitude of the celestial pole above the observer’s horizon is equal to the observer’s latitude.

Imagine standing at the North Pole (90°N latitude). The North Celestial Pole (NCP) would be directly overhead at your zenith, an altitude of 90°. If you stood at the equator (0° latitude), the NCP would be right on your horizon, at an altitude of 0°. At 45°N latitude, the NCP would be 45° above your horizon.

If Polaris were located exactly at the North Celestial Pole, determining your latitude would be incredibly simple: just measure the altitude of Polaris with a sextant, correct for instrumental and atmospheric errors, and the resulting value would be your latitude.

The Problem: Polaris is not exactly at the NCP. It is offset by a small amount (currently about 0.7°). This means that as the Earth rotates, Polaris appears to trace a tiny circle around the true NCP over a sidereal day.