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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.

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