Question

The moon is in a nearly circular orbit of radius r = 384000000 meters

Answer 1

Answer:

$2.72\cdot 10^{-3} m/s^2$

Explanation:

The centripetal acceleration of an object in circular motion is the acceleration with which the object is attracted towards the center of the circular orbit. Mathematically, it is given by

$a=\frac{v^2}{r}$

where

v is the speed of the object

r is the radius of the orbit

The speed of the object is also given by the ratio between the circumference of the orbit and the orbital period, T:

$v=\frac{2\pi r}{T}$

Substituting into the previous equation, we find a new expression for the centripetal acceleration:

$a=\frac{4\pi^2 r}{T^2}$

In this problem:

- The radius of the orbit of the Moon is

$r = 384000000 m = 3.84\cdot 10^8 m$

- The period of the orbit is

$T=27.32 d \cdot 24\cdot 60\cdot 60 =2.36\cdot 10^6 s$

Therefore, the centripetal acceleration is:

$a=\frac{4\pi^2 (3.84\cdot 10^8)}{(2.36\cdot 10^6)^2}=2.72\cdot 10^{-3} m/s^2$