How long will the footprints on the moon last according to these numbers?

Micrometeorites will eventually erase the footprints left on the moon. Assume that the moon is hit by 25 million micrometeorites per day and that they strike randomly aroudn the moon's surface. Also assume that it will take about 20 such impacts to destroy the footprint. Using these assumptions, estimate how long it will take before a footprint is erased. (Hint: Use the moon's surface area to determine the impact rate per square centimeter, and estimat ethe size of the footprint).How long will the footprints on the moon last according to these numbers?
Radius of the moon


r = 1737.4 km = 1.7374*10^6 m = 1.7374*10^8 cm





Surface Area = 4*pi*r^2





Find the surface area and divide the number of meteorites per day by the surface area to get meteorites per cm^2 per day.





Find the area of the footprint in cm^2 and multiply it by the number of meteorites per cm^2 per day. This will give you the number of meteorites per day to hit the footprint.





It takes 20 meteorites to destroy the footprint. So divide 20 meteorites by the number of meteorites per day that hit the footprint and you will get the number of days it will take to erase (on average).





Moon Radius(cm) = 1.7374E+08


Meteorites/day = 2.5000E+07


Moon's Surface Area(cm^2) = 3.7932E+17





Meteorites/cm^2/day = 6.5907E-11





Estimated Area of Footprint(cm^2) = 220


Meteorites/day to hit footprint = 1.4500E-08





Days to erase = 1.3794E+09





Years to erase = 3.7765E+06How long will the footprints on the moon last according to these numbers?
The footprints left by the Apollo astronauts will not erode since there is no wind or water on the Moon. The footprints should last at least 10 million years.





That's what I found, I don't know if it's true or not, and your numbers are too confusing to me :(