Question

What is the speed of a moon with a period of 20 hours that is orbiting a planet of radius R at a distance 5 R from the planet's center?

A) 26,000/πR m/s

B) πR/36,000 m/s

C) R/3,600π m/s

D) πR/7,200 m/s

E) π^2R/720 m/s


*I know the answer is D, but could someone please show work on how they arrived at that conclusion? Thank you!

Answer 1

D) πR/7,200 m/s

Step-by-step explanation:

Let's call the speed of the moon "v".

We know that the period (T) of the moon is given by: T = 20 hours = 20 hours * 3600 seconds/hour = 72000 seconds

We can relate the speed of the moon to its period and distance using the formula:

v = 2πR/T, where R is the distance of the moon from the center of the planet.

In this case, the distance is 5R, so:

v = 2π(5R)/T

= 2π(5R)/72000 seconds

= (πR)/7,200 seconds

So the speed of the moon is (πR)/7,200 m/s.

Therefore, the answer is D) πR/7,200 m/s.