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interdinghy
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Homework Statement
i) Estimate (in kg/yr) the rate of Earth accreting inter-planetary dust.
Assume a particle number density of n=1e-8/m3, a particle mass density of 5 gm/cc, a particle radius 50 microns and a relative velocity equal to Earth's orbital velocity (so the dust particles are, on average, at rest with respect to the Sun -- which would be expected if dust were deposited by long period comets with a uniform distribution of inclinations.
ii) How many years would it take Earth to increase its mass by 50%?
Homework Equations
The Attempt at a Solution
I talked with my professor and he told me to consider a flat circle moving through the cloud, and he said it would gain a certain amount of pass per second, then to consider the volume of the cylinder it would make.
Doing this, I found the area of a circle with the radius of the Earth to be about 1*10^8 km^2 accounting for significant figures. Then to make it a cylinder, I multiplied by an unknown height h in kilometers.
Next I multiplied this by the particle mass density:
[itex](1×10^{8})(h)km^{3} × 5 g/cm^{3}[/itex] and got [itex]5×10^{23}[/itex] grams
I looked up the speed at which Earth is orbiting the sun, and found it to be [itex]9.398×10^{8}[/itex] km/year, so I set [itex]h = 9.398×10^{8}km[/itex] and plugged it into what I had.
My final answer was that Earth accrued [itex]5×10^{29}[/itex] kilograms of mass per year and this is just ridiculous.
I don't think it's right to view the Earth in this problem as a flat circle, and I definitely don't see how it's right to see the volume it creates as a cylinder since the Earth isn't moving in a perfect straight line all the time. Also, he gave two values that I never used, so I'm sure I'm doing something wrong there too.
Can someone maybe clear up what he was trying to tell me or explain a better way to approach this problem?
Thanks.
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