Question

A planet moves around the sun in nearby circular orbit. Its period of revolution T depends upon radius r of orbit, mass m of the sun, the gravitational constant G. Show dimensionally that t^2 proportional to r^3

Answer 1

Answer:

Below is the detailed answer.

Explanation:

Since the planet is moving around the in an orbit. Its period of revolution is T and radius is r of the orbit and mass of the sun is while its gravitational constant is  

G. So, concludes that:

T = kr^a x m^b x G^c

By using this formula we now have:

[T]=[L]^{a}[M]^{b}[M^{-1}L^3T^{-2}]^{c}

[T]=[L^{a+3c}M^{b-c}T^{-2c}]

By simplifying the equation we now have:

c = =1/2 and b = -1/2 and a = -2/3

Putting these value in the first equation, we now know that T^2 is directly proportional to the radius r of the orbit.