Question

The time period of revolution of a planet around the sun in an elliptical orbit of semi-major axis \( a \) is \( T \). Then:

• A. \( T^2 \propto a^2 \)
• B. \( T \propto a^3 \)
• C. \( T^2 \propto a^3 \)
• D. \( T \propto \frac{1}{a^3} \)
• E. \( T^2 \propto \frac{1}{a^3} \)

Hint:

Kepler’s Third Law explains the relationship between a planet’s orbit and its period, applying to any object orbiting under gravitational influence.

Answer 1

The Correct Option is C

Kepler’s Third Law states that the square of the time period (\( T^2 \)) of a planet's revolution is directly proportional to the cube of the semi-major axis (\( a^3 \)): \[ T^2 \propto a^3 \] This relationship holds true for all planets orbiting the sun and is a fundamental principle in celestial mechanics.