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

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The discussion revolves around calculating the impact of solar radiant pressure on cosmic dust particles. The initial calculations provided an answer significantly off by orders of magnitude, prompting a reevaluation of the density used in the equations. It was noted that the density of air (1.22 kg/m3) was incorrectly applied instead of a more appropriate density for solid cosmic dust, which is around 2000 kg/m3. After correcting for density, the recalculated answer aligned with expected values. The importance of accurate density in such calculations is emphasized for achieving valid results.
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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
 

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unscientific said:

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.
 
Curious3141 said:
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..
 

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