As a comet swings around the Sun, ice on the comet\'s surfacevaporizes, releasin

Question

As a comet swings around the Sun, ice on the comet's surfacevaporizes, releasing trapped dust particles and ions. The ions,because they are electrically charged, are forced by theelectrically charged solar wind into a straight ion tail thatpoints radially away from the Sun (the figure below). The(electrically neutral) dust particles are pushed radially outwardfrom the Sun by the radiation force on them from sunlight. Assumethat the dust particles are spherical, have density 3.8 ×103 kg/m3, and are totally absorbing.(a) What radius (in m) must a particle havein order to follow a straight path, like path 2 in the figure?(b) If its radius is larger, does its path curveaway from the Sun (like path 1, enter "1" as answer) or toward theSun (like path 3 enter "3" as answer)? Assume that the speed oflight, radiation power of Sun, Earth radius, Gravitational constantand Sun mass are 2.998*108 m/s, 3.9*1026 W,6.67*1011 m3/kg-s2 and1.99*1030 kg respectively.

Explanation / Answer

(a) they will follow a straight path if the radiation forceequals the force of gravity, i.e. the forces are balanced. . radiation force = pressure * area = (I/c) * R2    =   (P/4r2) * R2 /c = .                        =   P R2 / 4 c r2 . . where R is the radius of the particle . gravity force = G M m /r2 = G M ( (4/3)R3) / r2   =   GM 4 R3 / 3 r2 . Set forces equal .            GM 4 R3 / 3 r2   = P R2 / 4 cr2           solve for R, the radius of the particle: .            R = 3 P / 16 G M c   = .                     = 3 * 3.9 x 1026 / 16 * 6.67 x10-11 * 1.99 x 1030 * 3.8 x 103 *2.998 x 108   = .                       = 0.001539 x 10-4 m   =   0.1539 m . If R is larger than this value, the force of gravity isgreater than the force from radiation and the particle curvestoward the sun, so PATH3. . Set forces equal .            GM 4 R3 / 3 r2   = P R2 / 4 cr2           solve for R, the radius of the particle: .            R = 3 P / 16 G M c   = .                     = 3 * 3.9 x 1026 / 16 * 6.67 x10-11 * 1.99 x 1030 * 3.8 x 103 *2.998 x 108   = .                       = 0.001539 x 10-4 m   =   0.1539 m . If R is larger than this value, the force of gravity isgreater than the force from radiation and the particle curvestoward the sun, so PATH3.

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