Gravitational Potential of a Cuboid

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The center of mass of a cuboid with three semiaxes , , and the mass density ρ ) lies in the coordinate origin. The coordinates , , describe the observation points running over the whole space . The gravitational potential at all observation points , , is a function of , , . The force vector for all observation points at , , is computed. The potential of the cuboid at the center of the mass is . The potential at the corner of the cuboid is . The potential and the force vector can be computed at all observation points in and outside the cuboid. The angle between the force and the space vector is very much near with the uncertainty of . The angular momentum of a particle in the gravitational field of the cuboid is time dependent and the motion is not in a two-dimensional plain near the cuboid. The potential is displayed as a contour plot for the observation points at any arbitrary , , , . The , components of the force are displayed as a vector field plot.

Contributed by: Franz Krafft (March 2011)
Open content licensed under CC BY-NC-SA



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