Question

If T be the time period of a planet around the Sun and d is its mean distance from the Sun, then according to Kepler's third law

• A. $ T∝ d$
• B. $T∝ d^2 $
• C. $T^2∝ d^{-3} $
• D. $T^2∝ d $
• E. $T^2∝ d^3 $

Answer 1

Answer: (E)

Kepler's third law states that the square of the time period \( T \) of a planet's orbit around the Sun is directly proportional to the cube of the mean distance \( d \) from the Sun. Mathematically, this is expressed as:

\[ T^2 \propto d^3 \] This means that the ratio of \( T^2 \) to \( d^3 \) is constant for all planets in the Solar System. This law describes the relationship between the orbital period and the distance of the planet from the Sun. The correct statement according to Kepler's third law is: \[ T^2 \propto d^3 \]

Correct Answer:

Correct Answer: (E) \( T^2 \propto d^3 \)