How long will it take to cover the moon with spherical miniature meteors, one meter tall, each with a diameter of 1.00×10−6 meters, hitting the moon at a rate of 1 meteor per second?

1 Answer
Andy Y.
Mar 24, 2016

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 510×106 km2 or 5.10×1014 m2. 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

dmeteor=1.00×10−6 m, then it will take

1.00 m1.00×10−6 m=1.00×106 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

5.10×1014 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

5.10×1014×106 sec=5.10×1020 sec

Converting to years, this is almost 16.2 trillion years!

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