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Gravitational Potential

Gravitational Potential - Gravitational Potential We can...

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Gravitational Potential We can write a general expression for the gravitational potential, U, due to a body of arbitrary shape and density distribution by treating it as an accumulation of a large number of small masses, dm, each contributing potential dU, and then integrating over the masses. We remember from basic gravitational theory that the gravitational potential U at a point P is the work done in moving from P to infinity. A point mass M gives rise, at a distance r, to a potential: U = GM/r This same equation can be used for a uniform sphere of mass M, where r is taken as a point outside the sphere. (i.e. the effect of the sphere is the same as if the mass were concentrated at its centre). For a point at a radius r inside the sphere, the mass M to be used in the equation is that if the material inside the radius r (parts of the sphere outside r have no effect - notice the analogy with electrostatics theory).
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