Question

What is the centripetal acceleration of the moon around the earth, realizing that the gravitational force is the centripetal force?

Answer 1

`a = 2.7* 10^(-3) m/s^2`

Step-by-step explanation:

As we know that moon is revolving around the Earth in circular path

Here the centripetal force on the moon is due to Earth and always towards the position of the Earth

This force is given as

`F = (GM_eM_m)/(r^2)`

here we know that

`M_e` = mass of Earth

`M_m` = mass of moon

`r` = distance between the center of moon and Earth

so we know by Newton's II law that

`F = ma`

`a = (F)/(M_m)`

`a = (GM_e)/(r^2)`

`M_e = 5.98 * 10^(24) kg`

`r = 384400 km`

now we have

`a = (6.67 * 10^(-11) 5.98 * 10^24)/((384400* 10^3)^2)`

`a = 2.7* 10^(-3) m/s^2`