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(D) According to Kepler's third law of planetary motion,the square of the time period $T$ is proportional to the cube of the semi-major axis $R$ of th

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${(N_2/N_1)^{2/3}}$

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(D) According to Kepler's third law of planetary motion,the square of the time period $T$ is proportional to the cube of the semi-major axis $R$ of the orbit: $T^2 \propto R^3$.Since the frequency $N$ is the reciprocal of the time period $(N = 1/T)$,we have $T = 1/N$.Substituting this into Kepler's law: $(1/N)^2 \propto R^3$,which implies $N^{-2} \propto R^3$ or $R^3 \propto N^{-2}$.Therefore,$R \propto N^{-2/3}$.For two planets,the ratio of their orbital radii is given by: $\frac{R_1}{R_2} = \left( \frac{N_1}{N_2} \right)^{-2/3}$.This can be rewritten as: $\frac{R_1}{R_2} = \left( \frac{N_2}{N_1} \right)^{2/3}$.

Two planets revolve around the sun with frequencies ${N_1}$ and ${N_2}$ revolutions per year. If their average orbital radii are ${R_1}$ and ${R_2}$ respectively,then ${R_1}/{R_2}$ is equal to:

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