Answer:
[tex]2.72\cdot 10^{-3} m/s^2[/tex]
Explanation:
Let's start by calculating the angular velocity of the Moon. We know that the period is:
[tex]T=27.3 d \cdot 24 \cdot 60 \cdot 60 =2.36\cdot 10^6 s[/tex]
So now we can calculate its angular velocity:
[tex]\omega=\frac{2\pi}{T}=\frac{2\pi}{(2.36\cdot 10^6)}=2.66 \cdot 10^{-6} rad/s[/tex]
The centripetal acceleration is given by
[tex]a=\omega^2 r[/tex]
where
[tex]\omega=2.66\cdot 10^{-6}rad/s[/tex]
[tex]r=3.84\cdot 10^8 m[/tex] is the radius of the orbit
Substituting,
[tex]a=(2.66\cdot 10^{-6})^2(3.84\cdot 10^8)=2.72\cdot 10^{-3} m/s^2[/tex]
