
480 Classical Mechanics
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This is known as Poisson’s equation. At points where no matter is present, ρ = 0, and
∇
2
Φ = 0. (14.11)
This is known as Laplace’s equation.
14.4 GRAVITATIONAL FIELD AND POTENTIAL OF EXTENDED BODY
As it stands, Equation 14.1 applies to particles or a spherical symmetric body. Thus, to compute the
force between two extended bodies, it is necessary to consider the contributions of all the elements
of mass of each body. The procedure for nding the forces or the eld strength by a direct integra-
tion is difcult except for symmetrically shaped bodies. For example, we want to nd the eld ...