A planet of mass `m` moves around the Sun of mass Min an elliptical orbit. The maximum and minimum distance of the planet from the Sun are `r_(1)` and `r_(2)`, respectively. Find the relation between the time period of the planet in terms of `r_(1)` and `r_(2)`.

Explanation

According to Kepler.s 3rd law, `T^2 prop a^3`
where a is the semi-major axis
Here ` a = ((r_1 + r_2)/(2)) rArr T^2 prop ((r_1 + r_2)/(2))^3`
or `T prop (r_1 + r_2)^(3//2)`