{"title":"Application of elliptic integrals in marine navigation","authors":"Miljenko Petrović","doi":"10.1017/S037346332200042X","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1017/S037346332200042X","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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