Acceleration of the Moon due to the Earth's gravitational pullIf the Moon has an acceleration of 0.0027 m/s^2 with respect to the earth when in orbit, and it is stopped for an instant and then released, will the acceleration towards the earth now be different? If yes, will its acceleration towards the earth be constant or variable over time?(I'm talking purely about Newtonian gravity and pre-relativistic physics, and ignoring the gravitational effects due to other heavenly bodies.)

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Acceleration of the Moon due to the Earth&#039;s gravitational pullIf the Moon has an acceleration of 0.0027 m/s^2 with respect to the earth when in orbit, and it is stopped for an instant and then released, will the acceleration towards the earth now be different? If yes, will its acceleration towards the earth be constant or variable over time?(I&#039;m talking purely about Newtonian gravity and pre-relativistic physics, and ignoring the gravitational effects due to other heavenly bodies.)

Marshall Flowers · Accepted Answer

If we presume a circular orbit for the moon, then the acceleration has a constant magnitude, from your question, of 0.0027 m/s^2, although the direction of the acceleration would be changing.If the moon were stopped relative to the earth, then released, the initial magnitude of the acceleration would be the same as it depends on the distance from the earth r, from Newton&#039;s law of gravitation  a  =            G      M              r      2      where   M is the mass of the earth. As time passed the moon would fall directly towards the earth, the acceleration would remain in the same direction but the magnitude would increase as the   r would decrease.

Amy Bright · Accepted Answer

The moon orbits Earth because of Centrifugal force balancing the gravitational force by Earth. And centrifugal force depends on the tangential velocity of the moon      F    c    =  m      ω    2    r  =  m            v      2        r  where   m : mass of the moon  ω : angular velocity  v : tangential velocity of moon   r : radius of orbit of moon (assuming that its orbit is circular though it&#039;s not) So if you decrease the tangential velocity of the moon then the centrifugal force will be decreased and the gravitational force will be greater which will result in the free fall of moon towards the earth. And yes it&#039;s acceleration will be variable over time.Hope it helps. :)

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