Assume that the Moon is hit by about 25 million micrometeorite impacts each day
ID: 1873130 • Letter: A
Question
Assume that the Moon is hit by about 25 million micrometeorite impacts each day (this number comes from observations of meteors in Earth's atmosphere) and that these impacts strike randomly around the Moon's surface. Also assume that it takes about 20 such impacts to destroy a footprint. About how long would it take for one of the footprints left by the Apollo astronauts to be erased? (Hints: Use the Moon's surface area to determine the impact rate per square centimeter, and suppose that a footprint has an area of 300 cm2)
Explanation / Answer
Radius of the moon
r = 1737.4 km = 1.7374*10^6 m = 1.7374*10^8 cm
Surface Area = 4*pi*r^2
Moon Radius(cm) = 1.7374E+08
Meteorites/day = 2.5000E+07
Moon's Surface Area(cm^2) = 3.7932E+17
Meteorites/cm^2/day = 25E6/3.793E+17 which is equal to 6.5907E-11
Estimated Area of Footprint(cm^2) = Three hundred
Meteorites/day to hit footprint = 1.97E-08
Years to erase = 3.7765E+06