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

Answer

B

Explanation

Semi major axis, `a=(r_(1)+r_(2))/(2)`
Now, `T^(2)propa^(3)`
`rArr T prop a^(3//2)prop ((r_(1)+r_(2))/(2))^(3//2)rArr T prop (r_(1)+r_(2))^(3//2)`.