Newton arrived at an universal law based on his observation of an apple falling from a tree. New...

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Newton arrived at an universal law based on his observation of an apple falling from a tree. Newton's reasoning was that the moon revolving in an orbit of radius \( R_{m} \) was subjected to a centripetal acceleration due to earth's gravity whose magnitude is given by
(a) \( a_{m}=\frac{v^{2}}{R_{m}} \)
(b) \( a_{m}=\frac{4 \pi^{2} R_{m}}{T^{2}} \)
(c) \( a_{m}=\frac{m v^{2}}{R_{m}} \)
(d) Both (a) and (b)
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