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| 1. |
Deduce Kepler's 3rd law from Newton's law of gravitation. |
| Answer» LET : m = mass of planetM = mass of sunr = radius of ORBIT of the planetω = constant angular velocity of planet.The centripetal FORCE on the planet required for its orbital motion is provided by gravitational force of ATTRACTION between planet and sun as : m ω² R = G M m / r²We know : ω = 2 π / T= > m ( 4 π ² / T² ) r = G M m / r²= > T² = ( 4 π² / G M ) r³According to Kepler's law : T² ∝ r³= > T² ∝ r³ where ( 4 π² / G M ) is constant .Therefore we get required answer. | |