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Application of elliptic integrals in marine navigation

Published online by Cambridge University Press:  15 September 2022

Miljenko Petrović
Miljenko Petrović*
Affiliation:
Professional master mariner, Zagreb, Croatia
*
*Corresponding author. E-mail: miljenko.petrovic@zg.t-com.hr
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Abstract

If the Earth's oblateness is neglected in marine navigation, then the sphere gives a relatively simple solution for course and distance between any two points. The navigation sphere where a span of one minute of arc is equal to nautical mile is used. The primary deficiency of this approach is the lack of a closed-form formula that takes the Earth's eccentricity into account. Considering the Earth as an oblate spheroid, i.e., a rotational ellipsoid with a small flattening, the problem of computing the length of the meridian arc leads to the understanding of elliptic integrals. In this paper, incomplete elliptic integrals of the first, second and third kind are used to find an arbitrary elliptical arc. The results prove an advantage of using geocentric latitude compared to geodetic and reduced latitude.

Keywords

elliptic integralsmeridian arc lengthmarine navigation
Type
Research Article
Information
The Journal of Navigation , Volume 75 , Issue 5 , September 2022 , pp. 1118 - 1127
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Institute of Navigation

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