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Optimal mass distribution for maximal gravitational field
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[QUOTE="Heirot, post: 2981898, member: 143263"] [h2]Homework Statement [/h2] Suppose that one is given a lump of clay of total mass M and constant density. Let P denote a particular point in space. In what way should one shape and position the clay so that the gravitational field in point P is maximum possible? It is assumed that the clay stays in one piece during the shaping. [h2]Homework Equations[/h2] Newton's law of gravity Variational principle (?) [h2]The Attempt at a Solution[/h2] I don't know if this problem has an obvious and trivial solution, but I'm thinking along the lines of variational principle. Let P be the origin of coordinates with z axis pointing in the direction of the gravitational field. Then we have the following equations [tex]F=G \rho\int_{\mathcal{V}}dV\frac{\cos \theta}{r^2}[/tex] [tex]M=\rho V[/tex] Can I maximize the force by varying the volume of integration using the second equation as a constraint? [/QUOTE]
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Optimal mass distribution for maximal gravitational field
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