Question

Assuming a roughly spherical shape and a density of 4000 kg/m3, estimate the diameter of an asteroid having the average mass of 1017 kg.

Answer 1

Explanation:

It is given that,

Density of asteroid, $\rho=4000\ kg/m^3$

Mass of asteroid, $m=10^{17}\ kg$

We need to find the diameter of the asteroid. The formula of density is given by:

$\rho=\dfrac{m}{V}$

V is the volume of spherical shaped asteroid, $V=\dfrac{4}{3}\pi r^3$

$r^3=\dfrac{3M}{4\pi \rho}$

$r^3=\dfrac{3\times 10^{17}\ kg}{4\pi \times 4000\ kg/m^3}$

$r^3=\sqrt{5.96\times 10^{12}}$

r = 2441311.12 m

Diameter = 2 × radius

d = 4882622.24 m

or

$d=4.88\times 10^6\ m$

Hence, this is the required solution.