Question

A particle in the solar system is under the combined influence of the sun’s gravitational attraction and the radiation force due to the sun’s rays. Assume that the particle is a sphere of density 1.0 × 10³ kg/m³ and that all of the incident light is absorbed. (a) Show that all particles with radius less than some critical radius R₀, will be blown out of the solar system. (b) Calculate R₀.

Answer 1

When the gravitational attraction and the radiation force are equal we have

where, M = Mass of the sun = 1.99 × 10³⁰ kg 

m = Mass of the particle of radius R₀ 

r = Distance of the particle from the sun 

W = Power radiated by the sun = 3.9 × 10²⁶ W 

c = Velocity of light = 3 × 10⁸ m s^–1

Note that R₀ does not depend on the distance from the particle to the sun. Hence,