Gravitational gauss law in the laboratory: A 21 century Archimedes problem

Gravitational field of many common objects are small but in the detectable sub microGal (Gal=g, free fall acceleration) range. Here we show that in a modern analog of the Archimedes problem, it is possible to estimate the interior density distribution of an object, by applying gauss law to the exterior gravity field data. With the development of wide band width Eotovs or nano range accelerometers it may also be possible to reconstruct and image the interior matter distribution.