The centripetal acceleration of the moon if it orbits Earth at a distance of 3.84 x 10⁸ in a path that takes 27.3 days to complete is equal to 2.7 × 10⁻³ m/s².
Centripetal acceleration can be defined to be the acceleration of a body traversing a circular path. The formula for centripetal acceleration will help us find the centripetal acceleration of the moon.
We are given that the distance of the moon from Earth is about 3.84 x 10⁸ and it takes the moon 27.3 days to complete a revolution.
The velocity of the moon is the distance the moon travels in 27.3 days.
[tex]v=\frac{x}{t}\\\\v=\frac{2\pi r}{t}\\\\v=\frac{2.41\times 10^9}{2.35\times 10^6}\\\\v=1,025.5[/tex]
The velocity is 1,025.5 m/s and the radius is 3.84 x 10⁸ m. Here, we're going to calculate the centripetal acceleration of the moon.
[tex]a_c=\frac{v^2}{r}\\\\a_c=\frac{(1,025.5)^2}{3.84\times 10^8}\\\\a_c=2.7\times 10^{-3}[/tex]
We have confirmed that 2.7 × 10⁻³ m/s² is the centripetal acceleration of the moon.
Learn more about centripetal acceleration here: https://brainly.com/question/19246433
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