# Answer to Question #22980 in Mechanics | Relativity for dickson

Question #22980

a plane moves round the sun in a circular orbit,the time period of revolution(T) of the planet depends on the radius of the orbit(R),mass of the sun(M) and the gravitational constant(G).show dimensionally that (T.T) is (R.R.R)

Expert's answer

T = 2*pi*R/V

T -& time period of revolution

pi = 3.14

R -& the radius of the orbit

V - speed

m*V^2/R = G m*M/R^2

m*V^2/R - centripetal acceleration*mass

G m*M/R^2 - the force of gravity

V = Sqrt [G*M/R]

T = 2*pi*R / Sqrt [G*M/R] = 2*pi*R^(3/2)/Sqrt[G*M]

T^2/R^3 = (2*pi)^2 *G*M = const

T -& time period of revolution

pi = 3.14

R -& the radius of the orbit

V - speed

m*V^2/R = G m*M/R^2

m*V^2/R - centripetal acceleration*mass

G m*M/R^2 - the force of gravity

V = Sqrt [G*M/R]

T = 2*pi*R / Sqrt [G*M/R] = 2*pi*R^(3/2)/Sqrt[G*M]

T^2/R^3 = (2*pi)^2 *G*M = const

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