Critical size of black particles blown from red giant solar system

[Jeann25]

Homework Statement

When the Sun becomes a red giant star its brightness will increase by a factor of 5000 and its mass will decrease to half of its present mass. When this happens particles smaller than a critical size will be blown out (light force = gravity force) of the solar system by the pressure of sunlight. What is the size for a black spherical particles ( they absorb all light that falls on them) with density of 1000 kg/m^3.

Homework Equations

radiation force on a spherical particle=F=((flux)*π a^2 Q)/c

The Attempt at a Solution

So in the problem it says that the light force = grav force
((flux)*π a^2 Q)/c = GMm/r^2 = GM/r^2 * (4π a^3 ρ)/3
(from example in book)
But I don't know what a, Q or flux is. I would estimate r= 1AU.
This also wouldn't use the change in brightness.
Need some help on where to go with this problem because I think I'm setting this up all wrong :(

 

[mgb_phys]

Since the attractive gravitational force and the amount of light hitting the particle both drop off as r^2 they cancel - the effect is the same at any distance.

a looks like the radius of the particle.
Q is normally the energy received.

You need an equation for
1, the attractive force of gravity on a particle of mass m
2, the force of light on an area A
3, the equation for the mass and cross section area of a sphere of a given radius and density.
Then you just set equations 1 and 2 equal.