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Proof of keplers third law from gravitation |
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Answer» Note that Newtons law of gravitation was much much more fundamental than keplers third law of planetary motion intact the first aim of the gravitational law was to explain the falling Apple and keplers observationF=GMm/R2F=GMm/R2 where MM is mass of the sun and mm is mass of planetRoughly approximating a circular orbitGMm/R2=mv2/RGMm/R2=mv2/Rv=(GM/R)−−−−−−−√v=(GM/R)T=(2πR)/vT=(2πR)/vT2=(4(π)2/GM)(R3)T2=(4(π)2/GM)(R3)T2=kR3 , thus, T2 is proportional to R3. This Is also known as law of period according to the law the square of time period of rotation of a planet is proportional to the cube of semi Major axis of the ellipical radius of orbit T square is proportional to cube of radius |
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