If one micrometeorite (a sphere with a diameter of 1.4 10-6 m) struck each square meter of the Moon each second, estimate the number of years it would take to cover the Moon with micrometeorites to a depth of one meter? Hint: Consider the volume of a micrometeorite and a cubic box, 1 m on a side, on the Moon. Find how long it would take to fill the box. (Type your answer using one of the following formats, 1.2e-3 for 0.0012 and 1.20e+2 for 120)

Question

If one micrometeorite (a sphere with a diameter of 1.4  10-6 m) struck each square meter of the Moon each second, estimate the number of years it would take to cover the Moon with micrometeorites to a depth of one meter? Hint: Consider the volume of a micrometeorite and a cubic box, 1 m on a side, on the Moon. Find how long it would take to fill the box. (Type your answer using one of the following formats, 1.2e-3 for 0.0012 and 1.20e+2 for 120)

anonymous · Answer

$$Moon surface = 3.793 × 10^7   km^2 = 3.793 × 10^{13}  m^2=boxes$$

The volume of 1 box = 1 m^3

The volume of 1 sphere =
$$4/3 \pi r ^{3} = 4/3 \pi 0.7 × 10^{-6} = 2.9 × 10^{-6} m^3$$

So 1 box holds 
$$ 1 / ( 2.9 * 10^{-6}) = 344828$$

Each box is 'filled' with 1 meteorite every second, so it'd take 344828  seconds = 0.01093 years = $$1.093 × 10^{-2} years$$