Suppose the moon were held in its orbit not by gravity but by the tension in a massless cable. You are given that the period of the moon's orbit is T = 27.3 days, the mean distance from the earth to the moon is R = 3.85 x 10^8 m, and the mass of the moon is M = 7.35 x 10^22 kg.
What would the tension in the cable be?
Centripetal Acceleration = v^2/R
The Attempt at a Solution
Tension = Ma
a = v^2/R
v = 2pi/T
First I concerted the 27.3 days to seconds which is T = 2.358*10^6. Which means that v = 2.6638*10^-6. Then I plugged that in for a, so a = 1.843*10^-20. So then the Tension should be 7.35*10^22 * 1.843*10^-20 which is 1354.67N. But it is saying that is the wrong answer. What did I do wrong?