  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.
