Question

state Kepler's third law represent by relation

Answer 1

If the size of the orbit (a) is expressed in astronomical units (1 AU equals the average distance between the Earth and the Sun) and the period (P) is measured in years, then Kepler's Third Law says:

P²∝ a³

After applying Newton's Laws of Motion and Newton's Law of Gravity we find that Kepler's Third Law takes a more general form:

                      P²=        4π²\G(M1+M2)a³

where M1 and M2 are the masses of the two orbiting objects in solar masses. Note that if the mass of one body, such as M1, is much larger than the other, then M1+M2 is nearly equal to M1. In our solar system M1 =1 solar mass, and this equation becomes identical to the first.

i hope this will helps u

Answer 2

$\huge\textbf{Kepler's Third Law :}$

According to it the square of time period of revolution of planet around sun is directly proportional to the cube length of semi major axis.

i.e. ${T}^{2}$ $\alpha$ ${R}^{3}$

Here T is time period of revolution and R is the distance of planet from the earth.

When we remove the sign of directly proportional then we have have to write some constant.

So, 

${T}^{2}$ = $k$ ${R}^{3}$

$\frac{{T}^{2}}{{R}^{3}}$ = $k$