Calculating earth gravity by using centripetal acceleration

  • #1

Homework Statement

I am asked to calculate the value of gravitational acceleration at Earth's surface given the following
Moon's period around the Earth - 27 days 8 hours
Moons orbit - 60.1 times the radius of Earth (6.38 x 10^6 m)

Homework Equations

which works out to be

The Attempt at a Solution

I am able to get the right answer (9.8 m/s2) IF i convert 27 days to MINUTES instead of proper SECONDS.
so where am i going wrong?

ive tried another method where i didvided the moons speed squared by the orbital radius and i get the same wrong answer
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  • #2
Welcome to PF!
If you just use g=(4*3.142R)/T2, with the circular motion of the moon, you will find the acceleration of the moon due to Earth's gravity. It will be MUCH smaller than 9.8.

I rather think you are supposed to use the given information about the moon's motion to calculate the mass of the Earth, then use the gravitational formula (with big G) to find the acceleration at the surface of the Earth (little g).

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