{"title":"Exact and heuristic formulae to compute the geodetic height from the ellipse equation","authors":"Mohamed Eleiche, Ahmed Mansi","doi":"10.1016/j.geog.2023.05.007","DOIUrl":null,"url":null,"abstract":"The conversion of the cartesian coordinates of a point to its geodetic equivalent coordinates in reference to the geodetic ellipsoid is one of the main challenges in geodesy. The ellipse equation in the meridian plane significantly influences the value of the geodetic coordinates. This research analyzes this influence and how it can contribute to their solutions. The study investigates the mathematical relation between them and presents an exact formula relating to the geodetic height and the ellipse equation. In addition, a heuristic formula for the relation between the geodetic height and the ellipse equation is proposed, which is independent of the geodetic latitude and has a relative accuracy better than 99.9 %. The calculation is stable, and the cost is low.","PeriodicalId":46398,"journal":{"name":"Geodesy and Geodynamics","volume":"197 1","pages":"0"},"PeriodicalIF":2.8000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geodesy and Geodynamics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1016/j.geog.2023.05.007","RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"GEOCHEMISTRY & GEOPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
The conversion of the cartesian coordinates of a point to its geodetic equivalent coordinates in reference to the geodetic ellipsoid is one of the main challenges in geodesy. The ellipse equation in the meridian plane significantly influences the value of the geodetic coordinates. This research analyzes this influence and how it can contribute to their solutions. The study investigates the mathematical relation between them and presents an exact formula relating to the geodetic height and the ellipse equation. In addition, a heuristic formula for the relation between the geodetic height and the ellipse equation is proposed, which is independent of the geodetic latitude and has a relative accuracy better than 99.9 %. The calculation is stable, and the cost is low.
期刊介绍：
Geodesy and Geodynamics launched in October, 2010, and is a bimonthly publication. It is sponsored jointly by Institute of Seismology, China Earthquake Administration, Science Press, and another six agencies. It is an international journal with a Chinese heart. Geodesy and Geodynamics is committed to the publication of quality scientific papers in English in the fields of geodesy and geodynamics from authors around the world. Its aim is to promote a combination between Geodesy and Geodynamics, deepen the application of Geodesy in the field of Geoscience and quicken worldwide fellows'' understanding on scientific research activity in China. It mainly publishes newest research achievements in the field of Geodesy, Geodynamics, Science of Disaster and so on. Aims and Scope: new theories and methods of geodesy; new results of monitoring and studying crustal movement and deformation by using geodetic theories and methods; new ways and achievements in earthquake-prediction investigation by using geodetic theories and methods; new results of crustal movement and deformation studies by using other geologic, hydrological, and geophysical theories and methods; new results of satellite gravity measurements; new development and results of space-to-ground observation technology.
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