Answer to Question #22980 in Mechanics | Relativity for dickson

Question

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)

Answer 1

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