A Theoretical Approach of Astronomical Ship Positioning Using a Single Celestial Body and Secant Technique

Abstract

In this article, a new approach to solve an astronomical ship position is proposed based on a single celestial body and secant technique.The mathematical equations relating the ship position to a celestial body are described using an altitude and an azimuth of celestial body.These equations are established using knowledge of spherical trigonometry.Numerical analysis is then employed based on secant method to solve the mathematical equations for the ship position.This technique uses the altitude and the azimuth simultaneously while existing methods need to observe the altitude either of two celestial bodies or of a single body at two different times.Therefore, it is worth to apply this proposed technique when there is only a single celestial body identified.To validate the feasibility of the proposed technique, two numerical examples were performed.

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