Question

How long will it take to cover the moon with spherical miniature meteors, one meter tall, each with a diameter of `1.00xx10^-6` meters, hitting the moon at a rate of 1 meteor per second?

Answer 1

It will take `16.2` trillion years

Explanation:

My first attempt to answer this was wrong, because the question was wrong. Apologies if I caused any confusion. The questioner meant to say the meteors are covering 1 square meter of the moon per second (not one meteor per second). This allows us to answer the question using just surface area.

The moon has a surface area of `510xx10^6 " km"^2` or `5.10xx10^14 " m"^2`. Now imagine, instead of being the curved surface of a sphere, you are filling a plain old box, one square meter per second, with the tiny meteors. If the meteors have a diameter of

`d_"meteor"=1.00xx10^-6 " m"`, then it will take

`(1.00 " m")/(1.00xx10^-6 " m")=1.00xx10^6` meteors

That's one million meteors stacked on top of each other, to make a pillar of meteors one meter tall. So the at the rate of one square meter per second, the first layer of meteors would take

`5.10xx10^14 " s"`

That is, one second for each square meter of the surface. Now you have to calculate this times one million (the number of meteors in a 1 meter tall pillar). So the answer is

`5.10xx10^14xx10^6 " sec"=5.10xx10^20 " sec"`

Converting to years, this is almost `16.2` trillion years!