Gravitational Attraction review

Gravitational Attraction review - Gravitational Attraction...

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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 GM (1) F = R 2 r , | | R where R is the position vector from the origin 0 to the point V , and the unit vector r = R / | R | is its direction. O 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 V and mass m . If the density function is δ ( x, y, z ), we have for the piece containing the point ( x, y, z ) (2) m δ ( x, y, z ) V, - Thinking of this small piece as being essentially a point mass at ( x, y, z ), the force F it exerts on
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