Ice in our solar system is attracted by the sun\'s gravity and repelled by radia

Question

Ice in our solar system is attracted by the sun's gravity and repelled by radiation pressure from its light. Suppose a droplet is orbiting the sun at the same distance as the earth: 1.5 . 1011 m. At this distance, the energy flux of electromagnetic radiation from the sun is about 1.4 kW/m2. For what droplet radius a will the gravitational attraction of the sun exactly balance the force of radiation pressure from the suns light? Interstellar ice has a density similar to that of water: 1 g/cm3. Assume the crystal is a sphere that reflects all the light that strikes its surface.

Explanation / Answer

P = 2S/c    ==> F = 2SA/c

F' = GMm/r^2

F=F'

==> 2SA/c = GMm/r^2

==> 2S(a^2)/c = GMm/r^2

==> 2*(1.4e3)*(3.1416)(a^2)/3e8 = (6.673e-11)*(1.989e30)/(1.5e11*1.5e11) * m

==> 0.0000293216 a^2 = 0.005898932 m

==> m = 0.00497066 a^2

= m/V = m/(4/3a^3) = 1000

==> m = 1000 * 4/3 * 3.1416 * a^3

==> m = 4188.8 a^3

==> 0.00497066 a^2 = 4188.8 a^3

==> a = 0.00497066/4188.8

==> a = 1.19e-6 m

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