Question

A particle in the solar system is under the combined influence of the sun’ gravitational attraction and the radiation force due to the sun’ 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 *–1

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