What is the impact of radiant pressure by the sun on cosmic dust?

[unscientific]

Homework Statement

I've solved part (a), but part (b) puzzles me as I am of 10³ orders of magnitude away from the answer.

The Attempt at a Solution

Intensity on dust particle = 1600 W m^-2
Earth-Sun Distance = (8*60)(3*10⁸) = 1.44 * 10¹¹m
Mass of Sun = 1.99 * 10³⁰ kg
g-field strength = 6.4 * 10^-3 N/kg
Force acting on dust particle = Mg = (4/3)∏R³g

Radiant force = P/c = (IA)/c = (I*∏R²)/c


(I*∏R²)/c = (4/3)∏R³g

R = (3I)/(4cρ*6.4*10^-3)

The answer is 2*10^-7 m

 

[Curious3141]

Homework Statement

I've solved part (a), but part (b) puzzles me as I am of 10³ orders of magnitude away from the answer.

The Attempt at a Solution

Intensity on dust particle = 1600 W m^-2
Earth-Sun Distance = (8*60)(3*10⁸) = 1.44 * 10¹¹m
Mass of Sun = 1.99 * 10³⁰ kg
g-field strength = 6.4 * 10^-3 N/kg
Force acting on dust particle = Mg = (4/3)∏R³g

Radiant force = P/c = (IA)/c = (I*∏R²)/c(I*∏R²)/c = (4/3)∏R³g

R = (3I)/(4cρ*6.4*10^-3)

The answer is 2*10^-7 m

Did you include the density of the dust particle in the calculation? You missed out $\rho$ in a couple of steps, but put it into the last formula, so I'm not sure. But if you take the usual density estimates for cosmic dust into account, the result is definitely within the ballpark.

 

[unscientific]

Did you include the density of the dust particle in the calculation? You missed out $\rho$ in a couple of steps, but put it into the last formula, so I'm not sure. But if you take the usual density estimates for cosmic dust into account, the result is definitely within the ballpark.

Yes, I took the density of dust as the density of air, 1.22 kg/m³..

 

[ehild]

http://en.wikipedia.org/wiki/Cosmic_dust#Some_bulk_properties_of_cosmic_dust

Yes, I took the density of dust as the density of air, 1.22 kg/m³..

Why? The dust particle is solid...
See: http://en.wikipedia.org/wiki/Cosmic_dust#Some_bulk_properties_of_cosmic_dust

ehild

 

[unscientific]

http://en.wikipedia.org/wiki/Cosmic_dust#Some_bulk_properties_of_cosmic_dust

Why? The dust particle is solid...
See: http://en.wikipedia.org/wiki/Cosmic_dust#Some_bulk_properties_of_cosmic_dust

ehild

Nice! With ρ = 2000 kg/m³ I got the answer!