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

Step-by-step 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=(m)/(V)`

V is the volume of spherical shaped asteroid,
`V=(4)/(3)\pi r^3`

`r^3=(3M)/(4\pi \rho)`

`r^3=(3* 10^(17)\ kg)/(4\pi * 4000\ kg/m^3)`

`r^3=\sqrt{5.96* 10^(12)}`

r = 2441311.12 m

Diameter = 2 × radius

d = 4882622.24 m

or

`d=4.88* 10^6\ m`

Hence, this is the required solution.