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Non-Ellipsoidal Gravity-Based Definitions of Planetary Surface Area and Other Geodetic Measures

Kai Xu
Dec 2022
This paper introduces new definitions of common geodetic measures on aplanetary surface (namely surface area, path length, and mean value or otherstatistical parameters of a surface function) that are not based on a datumsuch as a reference ellipsoid. Instead, the so-called datumless geodeticmeasures are based on physically meaningful formulations that rely only on theactual planetary surface and gravity. The datumless measures provideuniversally standardized measurements on any terrestrial object, includingnon-ellipsoidal asteroids and comets. Conveniently, on fairly round planetssuch as Earth and Mars, the datumless measures yield very similar values ascorresponding geodetic measures on a reference ellipsoid. Like theirellipsoidal counterparts, the datumless measures quantify area and length inthe familiar "bird's-eye view" or "horizontal, normal-to-gravity" sense. Farfrom being purely theoretical, the datumless measures can be approximated inGIS software using a digital elevation model and a gravity model such as ageoid.