Question

For elliptical orbits, the ratio $\frac{T^2}{a^3}$ is same for every planetary orbit around a massive body, and its value is : [ where $a$ is semi-major axis of the ellipse, $T$ is time period of motion and $y_r$ is year]

• A. \(1.99 \times 10^{-34} \text{ } y_r^2 \text{ m}^{-3} \)
• B. \(2.99 \times 10^{-34} \text{ } y_r^2 \text{ m}^{-3} \)
• C. \(1.99 \times 10^{-28} \text{ } y_r^2 \text{ m}^{-3} \)
• D. \(2.99 \times 10^{-28} \text{ } y_r^2 \text{ m}^{-3} \)

Hint:

The constant $\frac{T^2}{a^3}$ only depends on the mass of the central body. For all planets orbiting the same Sun, this ratio remains identical.

Answer 1

The Correct Option is B