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 × 10⁶ s. assume that the orbit of the moon is circular.
what is the speed of the moon in its ancient orbit?
1.04 m/s
1,040 m/s
6,550 m/s
12,200 m/s
6.5 m/s

Explanation:

Step1: Calculate the circumference of the ancient orbit

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(r=24400\space km = 24400\times10^{3}\space m\), then \(C = 2\pi\times(24400\times 10^{3})\space m\).

Step2: Use the formula for speed \(v=\frac{d}{t}\)

Here, \(d = C\) (distance traveled in one orbit) and \(t = 23400\space s\) (orbital period). So \(v=\frac{2\pi\times(24400\times 10^{3})}{23400}\space m/s\).

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Answer:

6,550 m/s