GK
THE UNIVERSE
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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planets take a long time to orbit the sun
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there is no relationship between the distance of planet from the sun and the time it takes to orbit the sun
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there is a mathematical relationship between the distance of a planet from the sun and the time it takes to orbit the sun
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every planet has the same orbital period
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Detailed explanation-1: -Kepler’s Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit. Thus we find that Mercury, the innermost planet, takes only 88 days to orbit the Sun. The earth takes 365 days, while Saturn requires 10, 759 days to do the same.
Detailed explanation-2: -Kepler’s third law concludes the relationship between time period of revolution of planet (T) and semi-major axis of orbit (R) as: T2 ∝ R.
Detailed explanation-3: -Kepler’s third law can be derived from Newton’s laws of motion and the universal law of gravitation. Set the force of gravity equal to the centripetal force. After substituting an expression for the velocity of the planet, one can obtain: GMr=4r2P2 which can also be written P2=42a3GM.