A Novel Analytical Solution Method for Celestial Positioning

Abstract

Traditional celestial navigation adopts the intercept method or Sumner line method in order to solve the fix problems of celestial sight reduction. While an estimated position is often needed in order to complete celestial positioning, these methods are not rigorous and they have many shortcomings. Thus, this study has analyzed the geometry of the circle of equal altitude and the two-body problem. Furthermore, vector methods are proposed without using spherical trigonometry, in order to meet navigation needs. Finally, web mapping was used to display the results. The results show that the two methods that are proposed in this study had better accuracy, practical convenience, and faster computing speed than those which have been proposed by other studies. The two methods’ capability to avoid complicated manual calculations and chart work processes makes them highly suitable as an alternative to the use of global navigation satellite systems. These methods enable maritime school students to quickly understand the principles of celestial navigation through computing and graphical interfaces.

Keywords

• navigation
• celestial positioning
• Newton’s method
• closed analytical solution
• small circle