Kepler's third law of planetary motion states that :(Symbols have their usual meaning)

V_{0} = \sqrt{R g}

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_{12} = -_{21}

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r^{2} \propto T^{3}

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r^{3} \propto T^{2}

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Solution

The correct option is D $r^{3} \propto T^{2}$
According to kepler's third law of planetary motion, The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
$\Rightarrow T^{2} \propto R^{3}$

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Q. According to kepler's laws of planetary motion
[Symbols have their usual meaning]

According to one of the Kepler's laws of planetary motion :
(a) $r^{2} \propto T^{3}$
(b) $r \propto T^{2}$
(c) $r^{3} \propto T^{2}$
(d) $r^{3} \propto \frac{1}{T^{2}}$

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Kepler's third law of planetary motion states that :(Symbols have their usual meaning)

The correct option is D r3∝T2According to kepler's third law of planetary motion, The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.⇒T2∝R3

The correct option is D $r^{3} \propto T^{2}$
According to kepler's third law of planetary motion, The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
$\Rightarrow T^{2} \propto R^{3}$