If the Earth were a cube, what would be the value of the acceleration of gravity at the center of each face?

摘要

From the time of Pythagoras of Samos (sixth century BC), the Greek philosopher-scientists taught that the Earth was a sphere and the harmonies of the universe were governed by mathematical relations.With the fall of the Roman Empire in the fifth century, cultural darkness descended on Europe and all intellectual pursuits languished under the rule of barbarians.In the Early Middle Ages, the universe reverted to a mythic polarization of Heaven and Earth.Cosmas (sixth century AD), an Alexandrian geographer, held that the Earth was a rectangular plane surrounded by an abyss of water.While European learning was at its lowest ebb, remnants of ancient knowledge survived in Byzantium, Syria, and Persia.According to the ideas of Cosmas, we can imagine the Earth in the form of a cube but with the same mass as Earth.The purpose of this paper is to evaluate the acceleration of gravity g at the center of each face of the cubical Earth.Our calculation uses Newton's law of universal gravitation and suggests the value g=9.8162 m s~(-2).At the center of each cube face the gravitational force is almost exactly as at the surface of the spherical Earth.