The Earth revolves around the Sun in one year | vedclass

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Question

(B) According to Kepler's third law of planetary motion,the square of the time period $(T)$ is directly proportional to the cube of the semi-major axi

Vedclass · Accepted Answer

$2\sqrt{2}$ years

Vedclass · Answer

(B) According to Kepler's third law of planetary motion,the square of the time period $(T)$ is directly proportional to the cube of the semi-major axis $(r)$ of the orbit: $T^2 \propto r^3$.Given the initial state: $T_1 = 1$ year and $r_1 = r$.For the new state: $r_2 = 2r$.Using the ratio: $\frac{T_2}{T_1} = \left( \frac{r_2}{r_1} \right)^{3/2}$.Substituting the values: $\frac{T_2}{1} = \left( \frac{2r}{r} \right)^{3/2} = (2)^{3/2} = 2\sqrt{2}$.Therefore,the new period of revolution $T_2 = 2\sqrt{2}$ years.

The Earth revolves around the Sun in one year. If the distance between them becomes double,the new period of revolution will be

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