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Find the centripetal acceleration of the moon

  1. Jun 7, 2014 #1
    1. The problem statement, all variables and given/known data
    The moon circles the earth with a period of 27.3 days at a distance of about 250000 mi. Find the centripetal acceleration of the moon.


    2. Relevant equations
    ac = v2/r




    3. The attempt at a solution
    I first found the velocity by converting 2 pi radians per 27.3 days to radians per second.
    2 pi / 27.3/ 24/ 60/60 = 2.66 x 10-6 radians per second.
    Then I converted miles to meters to find the radius.
    250000 x 1609.34 / 2 pi = 631986340.1
    Then I plugged these numbers into the above equation to find the acceleration and got 1.12 x 10-20 rad/s. The correct answer is 2.85 x 10-3 rad/s
     
    Last edited: Jun 7, 2014
  2. jcsd
  3. Jun 7, 2014 #2
    Seems like you're confusing the angular velocity with the velocity. Also 250000miles is the radius already. No need to divide by 2 pi. Finally, you made some other mistake. I can't tell what it is since you didn't post your calculation. Don't just describe your calculation. Post it.
     
  4. Jun 7, 2014 #3
    Sorry (2.66 x 10-6)2/631986340.1 = 1.12 x 10-20
     
  5. Jun 7, 2014 #4

    AlephZero

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    Homework Helper

    In your formula ac = v2/r, v is the velocity in meters/second, not the angular velocity in radians/second.

    There is a different formula for the acceleration that uses angular velocity and radius, if you want to do it that way.
     
  6. Jun 7, 2014 #5
    OK I see. Is the 250000 mi the radius or the circumference?
     
  7. Jun 7, 2014 #6
    That's the distance between the moon and the earth. Draw a picture of the orbit, and remember that the Earth barely moves at all.
     
  8. Jun 7, 2014 #7

    adjacent

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    Gold Member

    If it is 250000 mi above the Earth, it should not be the radius. Thou should also include the Radius of the Earth. Am I wrong?
     
  9. Jun 7, 2014 #8
    I understand that. How do I find the velocity in m/s?
     
  10. Jun 7, 2014 #9

    Nathanael

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    Find the circumference of the orbit (in meters) and divide it by however many seconds are in 27.3 days
     
  11. Jun 7, 2014 #10
    OK I got it right! Thanks!
     
  12. Jun 7, 2014 #11
    That's negligible specially considering that the moon's orbit really isn't circular. We're going for a ball park calculation here.
     
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