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Imagine a galaxy made from a gas cloud with a spherically symmetric mass density P(r) = Po exp (-r/n), where Po and R are constants. A point mass M is placed at a distance r from the center of the galaxy. Find the magnitude F of the gravitational force that the galaxy exerts on M as a function of r. Express your answer in terms of the total galaxy mass, mtot. Sketch a graph of F(r). (Hint: to solve the integral, you may need to integrate by parts, twice.)

Imagine a galaxy made from a gas cloud with a spherically symmetric mass density P(r) = Po exp (-r/n), where Po and R are constants. A point mass M is placed at a distance r from the center of the galaxy. Find the magnitude F of the gravitational force that the galaxy exerts on M as a function of r. Express your answer in terms of the total galaxy mass, mtot. Sketch a graph of F(r). (Hint: to solve the integral, you may need to integrate by parts, twice.)

Grade:12th pass

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