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 1100 kg/m3 and that all the incident light is absorbed. If its radius is less than some critical radius R, the particle will be blown out of the solar system. Calculate this critical radius. Note that the total radiation power of the Sun is 3.90 × 1026 W and its mass is 1.99 × 1030 kg. The universal gravitational constant is given by 6.673 × 10-11 N·m2/kg2

Answer 1

Intensity I = (1/2)*P/(4*pi*r^2)

radiation pressure = I/c = p/(8*pi*r^2*c)

force = pressure * area = (I/c)*A

area of the object = 4*pi*R^2

Force = (P/c)*(R^2/2r^2)

gravitational force Fg = G*M*m/r^2

F = Fg

(P/c)*(R^2/2r^2) = GM*m/r^2

m = mass of the particle = density*volme

(P/2c)*R^2 = G*M*D*(4/3)*pi*R^3

p/2c = G*M*D*(4/3)*pi*R

R = 3p/(2*G*M*D*pi*c)

R = (3*3.9*10^26)/(2*6.673*10^-11*1.99*10^30*1100*pi*3*10^8)

R = 4.25*10^-6 m <<<<<========answer