Question

Suppose the average mass of each of 20000 asteroids in the solar system is 1017kg. Assuming a spherical shape and a density of 2810 kg/m3 , estimate the diameter of an asteroid having this average mass.

Answer 1

The mass of the asteroid is M. And the density is \rho.
And from the relation of density to volume and mass we get
$\rho=\frac{M}{V}$
$\Rightarrow V=\frac{M}{\rho}$
$\Rightarrow \frac{4}{3}\pi R^3=\frac{M}{\rho}$
$\Rightarrow R=\left (\frac{3M}{4\pi\rho} \right )^{1/3}$
$\Rightarrow R=\left (\frac{3\times 1017}{4\pi\times 2810} \right )^{1/3}$
$\Rightarrow R=0.442~m=44.2~cm$
So, the diameter is
   $\Rightarrow D=2R=2\times 44.2=88.4~cm$