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)`.

Options

A. `(r_(1)+r_(2))`
B. `(r_(1)+r_(2))^(1//2)`
C. `r_(1)-r_(2))^(3//2)`
D. `(r_(1)+r_(2))^(3//2)`

Answer

D

Explanation

According to kepler third law `T^(2)` is proportinal to cube of semi major axis of the alliptical orbit
Semi major axis `=(r_(1)+r_(2))/(2)`
`therefore T^(2) prop [(r_(1)+r_(2))/(2)] rarr T prop (r_(1)r_(2))^(3//2)`