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(D) According to Kepler's third law of planetary motion,the square of the time period $T$ of a satellite is directly proportional to the cube of the r

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$4$

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(D) According to Kepler's third law of planetary motion,the square of the time period $T$ of a satellite is directly proportional to the cube of the radius $r$ of its orbit.$T^2 \propto r^3$This implies $T \propto r^{3/2}$ or $r \propto T^{2/3}$.Since the exponent of $T$ is $2/3$ (which is less than $1$),the graph of $r$ versus $T$ will be concave downwards.Looking at the provided graph,curve $(4)$ represents a relationship where $r$ increases with $T$ but with a decreasing slope (concave downwards),which matches the mathematical relationship $r \propto T^{2/3}$.Therefore,the correct graph is $(4)$.

Which graph best represents the variation of radius $r$ of a circular orbit of a satellite against its time period $T$?

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