2022/12/23 by Kai Xu, Xu, Kai
Earth and Planetary Sciences · Engineering · Social Sciences · #Earth and Planetary Astrophysics (astro-ph.EP) #FOS: Physical sciences #GNSS positioning and interference #Geophysics (physics.geo-ph) #Geophysics and Gravity Measurements #Historical Geography and Cartography
paper · pdf · doi:10.48550/arxiv.2212.12580
openalex publication_date 2022/12/23 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28
This paper introduces new definitions of common geodetic measures on a planetary surface (namely surface area, path length, and mean value or other statistical parameters of a surface function) that are not based on a datum such as a reference ellipsoid. Instead, the so-called datumless geodetic measures are based on physically meaningful formulations that rely only on the actual planetary surface and gravity. The datumless measures provide universally standardized measurements on any terrestrial object, including non-ellipsoidal asteroids and comets. Conveniently, on fairly round planets such as Earth and Mars, the datumless measures yield very similar values as corresponding geodetic measures on a reference ellipsoid. Like their ellipsoidal counterparts, the datumless measures quantify area and length in the familiar "bird's-eye view" or "horizontal, normal-to-gravity" sense. Far from being purely theoretical, the datumless measures can be approximated in GIS software using a digital elevation model and a gravity model such as a geoid.