Question

T square is directly proportional to R cube. prove

Answer 1

KEPLER LAW :-
Kepler's Third Law relates the period of an orbit to the radius of an orbit, if the orbit is circular, and to the semimajor axis if the orbit is elliptical.

Let's derive it for a circular orbit, assuming a mass m is orbiting a mass M, with r being the radius of the orbit.

ΣF = ma

GmM/r2 = mv2/r

Cancelling the m's and a factor of r gives:

GM/r = v2

We can bring in the period using:

v = 2πr / T

This gives GM/r = 4π2r2/T2

Re-arranging gives:

Kepler's Third Law: T2 = (4π2/GM) r3

Answer 2

Answer:

Explanation:

After some simple rearranging, we note that T2 =(4π2r3)/(GM). So T2 is indeed proportional to r3 . This simple statement is known as Kepler's third law of planetary motion.