Question

Assuming a particle to have the form of a ball and to absorb all incient light, find the radius of a particle for which its gravitational attraction to the sun is counterbalanced by the forces that light exerts on it. The power of light raiated by the sun equals `P = 4.10^(26)W`, and the density of the particle is `rho = 1.0 g//cm^(3)`.

Answer 1

Let `r =`radius of the ball
`R =` distance between the ball & the sun `(rlt lt R)`.
`M =` mass of the sun
`gamma =` gravitational constant
Then `(gammaM)/(R^(2)) (4pi)/(3)r^(3) rho = (P)/(4piR^(2)) pir^(2).(1)/(c )`
(the factor `(1)/(c )` converts the enegry recived on the right into momentum recived. Then the rifht hand side is the momentum recived per unit time and must equal the negative of the impressed force for equilibrium).
Thus `r = (3P)/(16pi gamma Mc rho) = 0.606 mu m`.