# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Applications of Complex Analysis to Celestial Navigation
From: Andrés Ruiz
Date: 2009 Oct 23, 11:41 +0200

I spent a pleasant time understanding and programming methods that Robin proposes in his paper: “Applications of Complex Analysis to Celestial Navigation”.

For those interested the source code has been attached in ANSI C. Is not very elegant, not use a complex C++ class, but it works!

Andrés Ruiz

-----Mensaje original-----
De: navlist@fer3.com [mailto:navlist@fer3.com] En nombre de Andres Ruiz
Enviado el: jueves, 01 de octubre de 2009 14:22
Para: navlist@fer3.com
Asunto: [NavList 10018] Re: two-body computed fix. was: assumed positions

Traditional approach to navigation calculations are based in spherical trigonometry. I prefer to use vectors for clarity, and power, avoiding  trigonometry ambiguity. You use complex analysis.

Interesting.

In my paper: "Vector equation of the circle of equal altitude" some navigational problems are solved using vector calculus.

- Altitude and azimuth from assumed position and geographic position

- Lunar distance

- Star - Star distance

- Great Circle Sailing

Indeed, vector calculus and quaternions are a particularization of Tensor calculus.

Regards,

Andrés Ruiz

-----Mensaje original-----

De: navlist@fer3.com [mailto:navlist@fer3.com] En nombre de robinstuart@earthlink.net

Enviado el: jueves, 01 de octubre de 2009 13:01

Para: NavList@fer3.com

Asunto: [NavList 10015] Re: two-body computed fix. was: assumed positions

A different method for the reduction of the 2-body fix, as well as other classic problems in celestial navigation, appears in the attached paper that is due to be published in Navigation (Journal of the Institute of Navigation). By mapping points on the sphere to complex numbers by stereographic projection, spherical trigonometry is reduced to plane trigonometry and simple arithmetic operations on complex numbers,

Robin Stuart

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