Discuss with respect to celestial navigation Theory of refraction (dips and distance of sea and shore horizons with and without refraction and related applications)

Of course. This is a fundamental and fascinating topic in the theory of celestial navigation. Let’s break down refraction and its relationship with the horizon system in detail.

Overview: The Problem of Bending Light

At its core, celestial navigation relies on measuring the angle between a celestial body (like the Sun, Moon, or a star) and the visible horizon. This measured angle, taken with a sextant, is the starting point for finding our position on Earth.

However, the light rays traveling from both the celestial body and the horizon do not travel in perfectly straight lines to the observer’s eye. They pass through the Earth’s atmosphere, a medium of varying density, causing them to bend. This bending is called refraction.

Understanding and correcting for refraction is not optional; it is absolutely critical for achieving an accurate position fix.

Part 1: Atmospheric Refraction of Celestial Bodies

This is the most well-known type of refraction in celestial navigation.

• The Theory: Light travels from the near-vacuum of space into the progressively denser layers of Earth’s atmosphere. According to Snell’s Law, when light enters a denser medium, it bends towards the normal (a line perpendicular to the boundary of the medium).
• The Effect: For an observer on Earth, the atmosphere acts like a giant, weak lens. The continuous bending of light makes the celestial body appear higher in the sky than it actually is.
• Key Characteristics:
  • The effect is greatest for objects near the horizon, where the light passes through the most atmosphere.
  • The effect is zero for an object directly overhead at the zenith (90° altitude), as the light enters the atmosphere at a perpendicular angle.
  • Standard refraction values are calculated for average atmospheric conditions (10°C and 1010 mb pressure). Tables in the Nautical Almanac provide corrections for non-standard conditions.

Application: This is the primary “Refraction” correction applied to a sextant sight. After you measure the Sextant Altitude (Hs) and correct for instrument errors and dip, you subtract the refraction correction from the Apparent Altitude (ha) to find the true Observed Altitude (Ho).