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I Can I add centrifugal acceleration?

  1. Mar 27, 2016 #1
    So the problem is asking me to derive the centrifugal and coriolis accelerations of the moon when it is furthest from the Sun and when it is orthogonal to the radius between Earth and the Sun.

    Given:
    Radius of Moon's Orbit around Earth
    Radius of Earth's Orbit around Sun
    Mass of Earth
    Mass of Sun
    gif.gif = Angular Frequency of the revolution of the Earth around the Sun
    gif.gif = Angular Frequency of the Revolution of the Moon around the Earth

    I am trying to figure out the first part.
    I know that the coriolis acceleration is going to be zero when the moon is furthest from the Sun because the velocity of the moon is parallel to the angular frequency of the trajectory of the Earth Moon system around the sun.

    I already derived that the centrifugal acceleration that the moon experiences by the earth is
    gif.gif

    T being the period of the moon around the earth


    So would the total centrifugal acceleration that the Moon experiences be the :

    Centrifugal Acceleration of the moon by Earth + Centrifugal Acceleration of the moon by Sun?

    So

    gif.gif

    P being the period of the earth moon system around the sun

    Thanks
     
  2. jcsd
  3. Mar 27, 2016 #2

    mfb

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    A frequency does not have a direction. The angular velocity does have one, but it is never parallel to the motion of moon.
    Could work, but you can also use the masses and distances, which is less dependent on handling different coordinate systems correctly.
     
  4. Mar 27, 2016 #3
    What do you mean by masses and distances?
     
  5. Mar 27, 2016 #4

    mfb

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    Staff: Mentor

    The acceleration comes from gravity, and you have everything you need to calculate the gravitational forces.
     
  6. Mar 27, 2016 #5

    FactChecker

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    You have calculated the magnitude of the accelerations, but you can not simply add the magnitudes unless the accelerations are in the same direction. At any moment, the centrifugal accelerations are vectors created by the gravitational force of the Earth and the Sun. They point toward the Earth and Sun, respectively. Vectors of the magnitude that you calculated can be added and the resulting vector is the total acceleration.
     
  7. Mar 30, 2016 #6

    Andrew Mason

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    Why would there be any coriolis effect here? Also, do you mean centripetal acceleration? The acceleration vectors are toward the sun and the earth centres.

    AM
     
  8. Apr 3, 2016 #7
    (+ denotes vector addition operator)
    different particles of moon have different accln . if consider com of moon--
    since in this case net accln is parallel to radius
    1st approach) centrifugal acceleration * (-1) = proj of net accleration normal to net velocity= net accleration = (g due to earth) + (g due to sun)
    (g=Gm/rr)
    2nd approach) since in this case centripetal accln equals net accln and assuming force bet sun and moon negligible to other forces(since it is about 100 times less than force bet earth and sun)
    net accln of moon= (accln of moon in earth(com) frame) +(accln of earth(com) in sun frame)
    =
    this is correct
    but this---
    is incorrect
    total centrifugal acceleration that the Moon experiences be the
    Centrifugal Acceleration of the moon by Earth + Centrifugal Acceleration of the earth by Sun
    and (4*pi*pi*r /(P*P)) =Centrifugal Acceleration of the earth by Sun
     
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