r^3/t^2=GM/4pi^2
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Centripetal force on the Earth ( or any planet ) = Me . v^2 / R
v = 2πR / T
Centripetal force = Me . 4π^2 . R^2 / R . T^2 = Me . 4π^2 . R / T^2
Centripetal force is supplied by the gravitational attraction between the Sun and the Earth
Me . 4π^2 . R / t^2 = G Ms . Me / R^2
Me cancels
R^3 / T^2 = G . Ms / 4 π^2
v = 2πR / T
Centripetal force = Me . 4π^2 . R^2 / R . T^2 = Me . 4π^2 . R / T^2
Centripetal force is supplied by the gravitational attraction between the Sun and the Earth
Me . 4π^2 . R / t^2 = G Ms . Me / R^2
Me cancels
R^3 / T^2 = G . Ms / 4 π^2