Define Third law of time period and derive ?

1.	Define Third law of time period and derive ?
Answer» Hope this will help u<br>Kepler’s 3rd Law of Periods:This law is known as the law of Periods. The square of the time period of the planet is directly proportional to the cube of the semimajor axis of its orbit.T² ∝ a³That means the time ‘ t ‘ is directly proportional to the cube of the major axis. Let us derive the equation of Kepler’s 3rd law. Let us suppose,m = mass of the planetM = mass of the Sunv = velocity in the orbitSo, there has to be a force of gravitation between the Sun and the planet.F = GmMr²Since it is moving in an elliptical orbit, there has to be a centripetal force.Fc = mv²r²Now, F = Fc⇒ GMr = v²Also, v = circumferencetime = 2πrtCombining the above equations, we get⇒ GMr = 4π²r²T²T² = 4π2r3)GM⇒ T² ∝ r³

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