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

Here, semimajor axis of the elliptical orbit of planet around the sun, `r = (r_(1) + r_(2))//2`. Therefore
`T^(2) prop ((r_(1) + r_(2))/(2))^(3)` or `T prop ((r_(1) + r_(2))/(2))^(3//2)`
`T prop (r_(1) + r_(2))^(3//2)`