Problem 4.224

Assuming a particle to have the form of a ball and to absorb all incident light, find the radius of a particle for which its gravitational attraction to the Sun is counterbalanced by the force that light exerts on it. The power of light radiated by the Sun equals $P=4 \cdot 10^{26} \mathrm{~W},$ and the density of the particle is $\rho=1.0 \mathrm{~g} / \mathrm{cm}^{3}$