Question

1) A spherical dust grain in the solar system has radius, R, and mass density, ρ. It behaves like a blackbody, absorbing all of the sunlight hitting its surface and radiating light isotropically according to its temperature.

1a) Calculate the ratio of the force of gravity attracting this grain to the Sun to the force of sunlight pushing the grain away. (Note that this ratio does not depend on the distance of the dust grain from the Sun.)

1b) Evaluate this ratio for a grain with radius R = 10^−4 cm and density ρ = 5 g/cm^3 .

1c) In equilibrium, the light energy absorbed by the grain equals the energy radiated away; the dust grain maintains a stable temperature that preserves this balance. Calculate the the equilibrium dust grain temperature as a function of radial distance from the Sun, i.e., Tg(r).

Answer 1