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According to Kepler’s third law, the orbital period $T$ of a planet around the sun varies with its mean distance $r$ from the sun as

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a

r \propto T

b

r^{3} α T^{2}

c

r^{2} α T^{3}

d

r α T^{2}

answer is B.

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Detailed Solution

According to Kepler’s third law, the orbital period

T

of a planet around the sun varies with its mean distance

r

from the sun as

r^{3} α T^{2}

.
Kepler’s Third Law of Planetary Motion states, “The squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits.” It can also be said that “The square of the time period of revolution of a planet around the sun in an elliptical orbit is directly proportional to the cube of its semi-major axis”.
According to Kepler's third law of orbital periods, the average distance (

r

) of a planet from the Sun is related to its orbital time period (

T

) as follows:

r^{3} α T^{2}

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