Answer to Question #11608 in Mechanics | Relativity for parth
a = GM/R²,
where R is the radius from the center of the planet to the center of a sun, M is the mass of the sun and G is the Gravitational constant and also using the centripetal force equation
a = W²R
where W is the radians / second velocity of the planet. Combining these equations above and cancelling the a (acceleration) gives
GM/R² = W²R ==> GM/R³ = W².
Assuming that W = 1/T we get
GM/R³ = 1/T² ==> T² = R³/GM.
So, T depends upon the radius "R" of the orbit, mass "M" of the sun and the gravitational constant "G" and T² is directly proportional TO R³.
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