You’re an astronomer studying the origin of the solar system, and you’re evaluat

Question

You’re an astronomer studying the origin of the solar system, and you’re evaluating the hypothesis that small particles (rock/dust) were blown out of the solar system by the radiation pressure of sunlight. (a) First determine the power output of the sun using the fact that the sun’s light intensity at earth is about 1400 W/m2 . What area is this energy spread over to give this intensity (it’s NOT the surface area of earth)? (b) Calculate how small the particles must be for this mechanism to work by comparing the force on the particles from the sun’s radiation pressure to the force from sun’s gravity (note: these forces push in opposite directions). Assuming spherical particles with a density of 2 g/cm3 , for what particle diameter do the two forces balance? (c) The particle diameter for which these two forces balance is independent of where the particle is located within the solar system (distance from the sun). Why?

Explanation / Answer

You're an astronomer studying the origin of the solar system, and you're evaluating a hypothesis thatsufficiently small particles were blown out of the solar system by the force of sunlight. To see how small such particles must be, compare the force of sunlight with the force of solar gravity, and solve for the particle radius at which the two are equal . Assume spherical particles with density 2g/cm^3. (Note: Distance from the Sun doesn't matter. Why not? )

F_sunlight = F_gravity

pressure of the sun light is I/c (I is the intensity of the sunlight and c is the speed of the light(3e8m/s))

F_sunlight = F_gravity

(I/c) S = G M m/r^2

(I/c) (pi R^2) = G M (rho ((4/3) pi R^3))/r^2

Therefore:

I/c = G M (rho ((4/3) R))/r^2

We must find the intencity I:

I = P/A

(P is the power of sun)

I = P/A = 3.939e26/(4 pi r^2)

therefore

I/c = G M (rho ((4/3) R))/r^2

(3.939e26/(4 pi r^2))/c = G M (rho ((4/3) R))/r^2

3.939e26/(4 pi c) = G M (rho ((4/3) R))

3.939e26/(4*3.1416*3e8) = 6.673e-11*(1.9891e30)*((2e-3/1e-6) * (4/3))

==> R = 2.95e-7 m

==> R = 0.295 um

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