Answer:
3.03 Billion Days or 8.30 Million years
Explanation:
Given,
No. of micrometeorite impacts per day on the Lunar surface = 25000000
Impacts needed to erase a footprint = 20
Area of footprint = 300 cm²
We know that surface area of the Moon = 37.93 Million Km² = ![37.93\times 10^{16} cm^{2}](https://tex.z-dn.net/?f=37.93%5Ctimes%2010%5E%7B16%7D%20cm%5E%7B2%7D)
To find: How long will it take to erase one footprint?
Using the above information,
No. of impacts per cm² per day is
![= \frac{25000000}{37.93\times 10^{16}}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B25000000%7D%7B37.93%5Ctimes%2010%5E%7B16%7D%7D)
No. of impacts on area of a foot print (300 cm²) per day will be,
![= \frac{25000000}{37.93\times 10^{16}}\times 300](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B25000000%7D%7B37.93%5Ctimes%2010%5E%7B16%7D%7D%5Ctimes%20300)
![= 6.59\times 10^{-9}](https://tex.z-dn.net/?f=%3D%206.59%5Ctimes%2010%5E%7B-9%7D)
To erase the footprint there must be 20 impacts on the area of footprint.
Time taken for
impacts = 1 Day
Time taken for 1 impact is
![= \frac{1}{6.59\times 10^{-9}} days](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%7D%7B6.59%5Ctimes%2010%5E%7B-9%7D%7D%20days)
Hence, time taken for 20 impacts will be
![= \frac{1\times20}{6.59\times 10^{-9}} days](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%5Ctimes20%7D%7B6.59%5Ctimes%2010%5E%7B-9%7D%7D%20days)
![= 3.03 \times 10^{9} days](https://tex.z-dn.net/?f=%3D%203.03%20%5Ctimes%2010%5E%7B9%7D%20days)
![= \frac{3.03 \times 10^{9}}{365}years](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B3.03%20%5Ctimes%2010%5E%7B9%7D%7D%7B365%7Dyears)
![= 8.30 \times 10^{6} years](https://tex.z-dn.net/?f=%3D%208.30%20%5Ctimes%2010%5E%7B6%7D%20years)
It would take around 3.03 Billion Days or 8.30 Million years for one of the footprints left by the Apollo astronauts to be erased.