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Kepler's third law relates the period of revolution $T$ and the mean distance $r$ of a planet from the Sun as:
A$T \propto r^2$
B$T^2 \propto r$
C$T^3 \propto r^2$
D$T^2 \propto r^3$
Answer & Solution
Correct answer: D. $T^2 \propto r^3$
1. Kepler's third law: the square of the period of revolution is directly proportional to the cube of the mean distance.
2. Written symbolically, $T^2 \propto r^3$.
3. Equivalently $\dfrac{T^2}{r^3} = \text{constant} = K$.
4. Option $T^3 \propto r^2$ inverts the powers and is wrong; the correct relation is $T^2 \propto r^3$.
_Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 1 "Gravitation", p.12_
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