Question

(problem reference m.7)
approximately one billion years ago, the moon orbited the earth much closer than it does today. the radius of the orbit was only 24 400 km. the orbital period was only 23 400 s. today, the average radius is 385 000 km; and the present period is 2.36×10^6 s. assume that the orbit of the moon is circular.
what is the magnitude of the centripetal acceleration of the moon in its ancient orbit?
○ 1.8×10^-3 m/s²
○ 6.5×10^-2 m/s²
○ 2.4×10^-2 m/s²
○ 2.4 m/s²
○ 1.8 m/s²

Explanation:

Step1: Convert radius to meters

The radius \( r = 24400\space km=24400\times10^{3}\space m\)

Step2: Use the formula for centripetal acceleration \(a_{c}=\frac{4\pi^{2}r}{T^{2}}\)

Here \(T = 23400\space s\)
Substitute \(r = 24400\times 10^{3}\space m\) and \(T=23400\space s\) into the formula:

$$
LATEXBLOCK0
$$

$$
LATEXBLOCK1
$$

Answer:

\(1.8\times 10^{-3}\space m/s^{2}\) (First option)