Answer :
Answer:
[tex]2.72\cdot 10^{-3} m/s^2[/tex]
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
[tex]a=\frac{v^2}{r}[/tex]
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:
[tex]v=\frac{2\pi r}{T}[/tex]
Substituting into the previous equation, we find a new expression for the centripetal acceleration:
[tex]a=\frac{4\pi^2 r}{T^2}[/tex]
In this problem:
- The radius of the orbit of the Moon is
[tex]r = 384000000 m = 3.84\cdot 10^8 m[/tex]
- The period of the orbit is
[tex]T=27.32 d \cdot 24\cdot 60\cdot 60 =2.36\cdot 10^6 s[/tex]
Therefore, the centripetal acceleration is:
[tex]a=\frac{4\pi^2 (3.84\cdot 10^8)}{(2.36\cdot 10^6)^2}=2.72\cdot 10^{-3} m/s^2[/tex]