A planet of mass m is revolving around the sun in an elliptical orbit. The minimum and maximum distances of the planet from the sun are `s_(1)` and `s_(2)`. Derive the relation between time period of the planet in terms of `s_(1)` and `s_(2)`.

Explanation

Let S is the semi-major axis of the elliptical orbit.
`S = (s_(1) + s_(2))/(2)`
According to Kepler.s law `T^(2) prop S^(3)`
`T^(2) prop ((s_(1) + s_(2))/(2))^(3)`
`T^(2) prop (s_(1) + s_(2))^(3)`
`T prop (s_(1) + s_(2))^(3//2)`