# Homework Help: Force due to Solar Radiation and Gravity

1. Sep 22, 2015

### Mnemonic

1. The problem statement, all variables and given/known data
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.

2. Relevant 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

3. 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?

2. Sep 22, 2015

### Staff: Mentor

Check that formula. Does mass really get smaller as the volume of the material gets larger?
Nope. Besides the issue with the mass expression noted above, I don't see where the solar constant S is involved in your calculation.