Force due to Solar Radiation and Gravity

[Mnemonic]

Homework Statement

Consider a small, spherical particle of radius r located in space a distance R = 3.75 × 1011-m from the Sun. Assume the particle has a perfectly absorbing surface and a mass density of ρ = 3.8-g/cm3. Use S = 214 W/m2 as the value of the solar intensity at the location of the particle. Calculate the value of r for which the particle is in equilibrium between the gravitational force and the force exerted by solar radiation. The mass of the Sun is 2.0 × 1030-kg.

Homework Equations

F(g)=Gm₁m₂/r²

mass of particle equals mass density/Volume=3800/(4/3*Pi*r²)

F(Solar)=C*S*I/c
where C=1 due to complete absorption, S equals cross-sectional area (Pi*[rSUP]2[/SUP]), c equals speed of light

The Attempt at a Solution

F(Solar)=F(g)

Pi*r²/3e8=6.67e-11*2e30*3800/(3.75e11*4/3*Pi*r³)

r=790238.5

Have I used the right Solar radiation equation?

Does this look right?

 

[gneill]

Homework Statement

Consider a small, spherical particle of radius r located in space a distance R = 3.75 × 1011-m from the Sun. Assume the particle has a perfectly absorbing surface and a mass density of ρ = 3.8-g/cm3. Use S = 214 W/m2 as the value of the solar intensity at the location of the particle. Calculate the value of r for which the particle is in equilibrium between the gravitational force and the force exerted by solar radiation. The mass of the Sun is 2.0 × 1030-kg.

Homework Equations

F(g)=Gm₁m₂/r²

mass of particle equals mass density/Volume=3800/(4/3*Pi*r²)

Check that formula. Does mass really get smaller as the volume of the material gets larger?

F(Solar)=C*S*I/c
where C=1 due to complete absorption, S equals cross-sectional area (Pi*[rSUP]2[/SUP]), c equals speed of light

The Attempt at a Solution

F(Solar)=F(g)

Pi*r²/3e8=6.67e-11*2e30*3800/(3.75e11*4/3*Pi*r³)

r=790238.5

Have I used the right Solar radiation equation?

Does this look right?

Nope. Besides the issue with the mass expression noted above, I don't see where the solar constant S is involved in your calculation.