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).

A planet of mass m is revolving around the sun in an elliptical orbit.

1.	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).
Answer» SOLUTION :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)`