Consider a small black ball of radius $R$ and density $\rho= 1~\frac{\mbox{g}}{\mbox{cm}^{3}}$ located at a certain distance above the surface of the Sun. For what radius $R$ in micrometers is the gravitational attraction of the Sun counterbalanced by the radiation force?

Assume that the black ball absorbs all the incident light and that the total power radiated by the Sun is $P=4\times 10^{26}~\mbox{W}$.

Details and assumptions

The mass of the Sun is $M_{s}=2\times 10^{30}~\mbox{kg}$. The universal constant of gravitation is $G=6.67\times 10^{-11}~\text{m}^{3}\text{kg}^{-1} \text{s}^{-2}$ and the speed of light $c=3\times 10^{8}~\mbox{m/s}$.

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