Assume that the moon is hit by about 25 million micrometeorite impacts each day, and that these impacts strike randomly around the moon's surface. also assume that after a footprint is hit by 20 micrometeorites it is erased. (a) roughly (order of magnitude) how long do we expect it would take, in years, for one of the footprints left by the apollo astronauts to be completely erased?

Use the following formula to find the time meteorites take for a footprint to be erased:

T = [ (Impact needed of a footprint) (4πr^2) ]/[ (impact rate) (Area of a footprint) ].

Use the following formula to find the area of a foot:

Area of a foot = length of foot x width of foot

Substitute the given values in the above equation to get area of a foot:

Area of a foot = 25 cm x 10 cm = 250 cm^2

Convert the radius of moon in kilometers to centimeters.

R = 1738 km = 1738 km (10^5 cm / km) = 1.738 x 10^8 cm

The time meteorites take for a footprint to be erased:

T = (20) (4 π (1.738 x 10^8) ^2) / (25 million / day) (250 cm^2) = 758.78 x 10^16 / 6250 x 10^6 / day = 1.21 x 10^9 days

Therefore, the time meteorites take for a footprint to be erased is 1.21 x 10^9 days