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

Semi-major axis of the elliptical orbit of the planet is
Using Kepler.s third law,
`T^(2) prop r^(3)`
`rArr T^(2) prop ((r_(1) + r_(2))/(2))^(3)`
or `T prop ((r_(1) + r_(2))/(2))^((3)/(2))`
`rArr T prop ((r_(1)+r_(2))^((3)/(2)))/(2sqrt(2))`