Interplanetary space contains many small particles referred to as interplanetary dust. Radiation pressure from the sun sets a lower limit on the size of such dust particles. To see the origin of this limit, consider a spherical dust particle of radius R and mass density p.
(a) Write an expression for the gravitational force exerted on this particle by the sun (mass M) when the particle is a distance r from the sun.
(b) Let L represent the luminosity of the sun, equal to the rate at which it emits energy in electromagnetic radiation. Find the force exerted on the (totally absorbing) particle due to solar radiation pressure, remembering that the intensity of the sun's radiation also depends on the distance r. The relevant area is the cross-sectional area of the particle, not the tota1 surface area of the particle. As part of your answer, explain why this is so.
(c) The mass density of a typical interplanetary dust particle is about 3000 kg/m3. Find the particle radius R such that the gravitational and radiation forces acting on the particle are equal in magnitude. The luminosity of the sun is 3.9 x 1026 W. Does your answer depend on the distance of the particle from the sun? Why or why not?
(d) Explain why dust particles with a radius less than that found in part (c) are unlikely to be found in the solar system.