Calculating Black Particle Size in a Red Giant Solar System - Astronomy Homework

[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.

 

[Blueshift5]

I would approach this problem by first understanding the physical concepts involved. In this case, we are dealing with the radiation force and gravitational force acting on a spherical particle in a red giant solar system.

The radiation force, F, is given by the equation F = ((flux)*π a^2 Q)/c, where flux is the energy per unit area per unit time, a is the radius of the particle, Q is the efficiency of the particle in absorbing light, and c is the speed of light.

The gravitational force, Fg, is given by the equation Fg = GMm/r^2, where G is the gravitational constant, M is the mass of the red giant star, m is the mass of the particle, and r is the distance between the particle and the center of the star.

Since we are looking for the critical size at which the radiation force equals the gravitational force, we can set F = Fg and solve for the radius, a. This will give us the size of the particle that will be blown out of the solar system by the pressure of sunlight.

We can also use the given information about the red giant star's brightness and mass to calculate the values of flux and r. From the statement, we know that the brightness of the red giant star will increase by a factor of 5000, so the flux will also increase by a factor of 5000. We can also use the mass of the star and the distance between the particle and the center of the star to calculate the value of r.

Substituting these values into the equation F = Fg, we can solve for the radius, a, and thus determine the critical size of the black spherical particle that will be blown out of the solar system. We can also use the given density of the particle to calculate its mass.

In conclusion, as a scientist, I would approach this problem by first understanding the physical concepts involved and then using the given information and relevant equations to solve for the critical size of the black spherical particle.