p34_031 - 31. (a) Let r be the radius and be the density of...

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31. (a) Let r be the radius and ρ be the density of the particle. Since its volume is (4 π/ 3) r 3 , its mass is m =(4 π/ 3) ρr 3 .L e t R be the distance from the Sun to the particle and let M be the mass of the Sun. Then, the gravitational force of attraction of the Sun on the particle has magnitude F g = GMm R 2 = 4 πGMρr 3 3 R 2 . If P is the power output of the Sun, then at the position of the particle, the radiation intensity is I = P/ 4 πR 2 , and since the particle is perfectly absorbing, the radiation pressure on it is p r = I c = P 4 πR 2 c . All of the radiation that passes through a circle of radius r and area A = πr 2 , perpendicular to the direction of propagation, is absorbed by the particle, so the force of the radiation on the particle has magnitude F r = p r A = πPr 2 4 πR 2 c = Pr 2 4 R 2 c . The force is radially outward from the Sun. Notice that both the force of gravity and the force of the radiation are inversely proportional to R
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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