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

TL;DR

This paper proposes gravity-based, datumless definitions for planetary surface area and geodetic measures, enabling standardized measurements on any celestial body regardless of shape or reference ellipsoid.

Contribution

It introduces physically meaningful, gravity-based geodetic measures that do not rely on a reference ellipsoid, applicable to irregular planetary bodies.

Findings

Datumless measures closely match traditional measures on Earth and Mars.

These measures can be approximated using GIS software with elevation and gravity models.

Applicable to non-ellipsoidal celestial objects like asteroids and comets.

Abstract

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.