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Question

What is the critical value of area density for the mirror at which the radiation pressure exactly cancels out the gravitational attraction from the sun?

mass of the sun M = 2.0E30 Kg

intensity of sunlight as a function of the distance from the sun I = 3.2E25 1/R^2 W/m^2

gravitational constant G = 6.67E-11 m^3/Kg*s^2

Answer 1

Nice little problem.

Since both the energy per unit area and the gravitational attraction fall off as R^2, the answer shouldn't depend on the location. So you can use the values near Earth orbit in these two pages:

http://en.wikipedia.org/wiki/Solar_sail

http://en.wikipedia.org/wiki/Radiation_p...

Note that you have to be careful about the behavior of the sail. If you assume the sail is reflective (as in your problem), that gives you a factor of 2, but then the sail has to face the Sun directly, instead of being able to go at an angle, so most sail designers assume a lower energy gain.