Diameter of an asteroid

Oct 2019
6
2
Whidbey Island
I cannot figure out this astronomy problem.

Suppose the average mass of each of 20000 asteroids in the solar system is 10^17kg.

Assuming a spherical shape and a density of 2830 kg/m^3, estimate the diameter of an asteroid having this average mass.

I need to find diameter in km.

Thank you for any help you might have.
 

Debsta

MHF Helper
Oct 2009
1,285
586
Brisbane
Ok, so the fact that there are 20 000 asteroids is irrelevant to the problem.

Since \(\displaystyle density = \frac{mass(kg)}{volume(m^3)}\) then

\(\displaystyle volume = \frac{mass}{density}\).

So \(\displaystyle volume =\frac{10^{17}}{2830}\) cubic metres.

Once you know the volume (of a sphere) you should be able to work out the radius or diameter. Have a go.
 
Oct 2019
6
2
Whidbey Island
Ok, so the fact that there are 20 000 asteroids is irrelevant to the problem.

Since \(\displaystyle density = \frac{mass(kg)}{volume(m^3)}\) then

\(\displaystyle volume = \frac{mass}{density}\).

So \(\displaystyle volume =\frac{10^{17}}{2830}\) cubic metres.

Once you know the volume (of a sphere) you should be able to work out the radius or diameter. Have a go.
Thank you. I was able to solve it!
 
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