gravitnl_attracn

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MIT OpenCourseWare http://ocw.mit.edu 18.02 Multivariable Calculus Fall 200 7 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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G. Gravitational Attraction We use triple integration to calculate the gravitational attraction that a solid body V of mass M exerts on a unit point mass placed at the origin. If the solid V is also a point mass, then according to Newton's law of gravitation, the force it exerts is given by where R is the position vector from the origin 0 to the point V, and the d unit vector r = R/IRI is its direction. 0 If however the solid body V is not a point mass, we have to use integration. We concen- trate on finding just the k component of the gravitational attraction - all our examples will have the solid body V placed symmetrically so that its pull is all in the k direction anyway. To calculate this force, we divide up the solid V into small pieces having volume AV and mass Am. If
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