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Following the work of George Green U is known as a 'potential function'. Laplace also was able to show that the same function U served as a potential function when the point (x, y, z) was inside the body, though in this case the argument is rather more subtle.

In 1785, Laplace went further and showed that, provided (x, y, z) is outside V, the function U satisfies

V2U = 0, where V2 is what is now known as the 'Laplacian operator'. In Cartesian, coordinates, this has the form d2/dx2 + d2/By2 + d2/dz2, although in Laplace's initial derivation of the equation that now bears his name, he used spherical polar coordinates.

Knowledge of the potential function U is all that is required in order to be able to calculate the gravitational attraction at any point due to the body V,

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