Question

A planet revolves in an elliptical orbit around the sun. The semi-major and semi-minor axes are \( a \) and \( b \). Then the square of the time period, \( T \), is directly proportional to:

• A. \( a^3 \)
• B. \( b^3 \)
• C. \( \frac{(a + b)^3}{2} \)
• D. \( \frac{(a - b)^3}{2} \)

Hint:

Kepler's third law connects the time period of a planet's orbit to the cube of the semi-major axis of its orbit.

Answer 1

The Correct Option is A

Kepler's third law states that the square of the orbital period \( T \) of a planet is directly proportional to the cube of the semi-major axis \( a \) of its orbit. Thus, \( T^2 \propto a^3 \).
Final Answer: \[ \boxed{a^3} \]