The distance of a planet from the sun is 5 ti | vedclass

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(A) 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 $(R)$ o

Vedclass · Accepted Answer

$5^{3/2}$ years

Vedclass · Answer

(A) 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: $T^2 \propto R^3$ or $T \propto R^{3/2}$.Given that the distance of the planet from the sun is $R_p = 5 R_e$,where $R_e$ is the distance between the earth and the sun.The time period of the earth is $T_e = 1$ year.Using the ratio: $\frac{T_p}{T_e} = \left( \frac{R_p}{R_e} \right)^{3/2}$.Substituting the values: $\frac{T_p}{1} = (5)^{3/2}$.Therefore,the time period of the planet is $T_p = 5^{3/2}$ years.

The distance of a planet from the sun is $5$ times the distance between the earth and the sun. The time period of the planet is

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