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.
A)

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)

Express your answer using two significant figures.

Answer 1

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 = $37.93\times 10^{16} cm^{2}$

To find:  How long will it take to erase one footprint?

Using the above information,

No. of impacts per cm² per day is

$= \frac{25000000}{37.93\times 10^{16}}$

No. of impacts on area of a foot print (300 cm²) per day will be,

$= \frac{25000000}{37.93\times 10^{16}}\times 300$

$= 6.59\times 10^{-9}$

To erase the footprint there must be 20 impacts on the area of footprint.

Time taken for $6.59\times 10^{-9}$ impacts = 1 Day

Time taken for 1 impact is

$= \frac{1}{6.59\times 10^{-9}} days$

Hence, time taken for 20 impacts will be

$= \frac{1\times20}{6.59\times 10^{-9}} days$

$= 3.03 \times 10^{9} days$

$= \frac{3.03 \times 10^{9}}{365}years$

$= 8.30 \times 10^{6} years$

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.