The earth is moving on an elliptical path, whose one focus sun is situated as shown in figure. If `AS = r_(min)` and `SB = r_(max)`, the sun and earth system obey the Kepler's law, the square of time-period is directly proportional to

Options

A. `(r_(min))^(3)`
B. `(r_(max))^(3)`
C. `((r_(min) + r_(max))/(2))^(3)`
D. `((r_(min)r_(max))/(r_(min) + r_(max)))^(3)`

Answer

C

Explanation

`T^(2) prop ("semi-major axis")^(3)`