The time periods and the mean radii of the orbits of two planets around Sun are $T_{1}, T_{2} a n d r_{1}, r_{2}$ respectively. The ratio $\frac{T_{1}}{T_{2}}$ is equal to:

(\frac{r_{1}}{r_{2}})^{\frac{3}{2}}

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(\frac{r_{2}}{r_{1}})^{\frac{3}{2}}

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(\frac{r_{1}}{r_{2}})^{\frac{1}{2}}

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(\frac{r_{2}}{r_{1}})^{\frac{1}{2}}

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Solution

The correct option is A $(\frac{r_{1}}{r_{2}})^{\frac{3}{2}}$
According to Kepler's 3rd law, the square of planet's orbital period around Sun is directly proportional to the cube of mean distance of the planet from the Sun.
$T^{2} \propto r^{3}$
$⟹ {(\frac{T_{1}}{T_{2}})}^{2} = {(\frac{r_{1}}{r_{2}})}^{3}$
${(\frac{T_{1}}{T_{2}})}^{2} = {(\frac{r_{1}}{r_{2}})}^{\frac{3}{2}}$

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Two planets move around the sun. The time periods and the mean radii of the orbits are $T_{1}, T_{2} a n d r_{1}, r_{2}$ respectively. The ratio $\frac{T_{1}}{T_{2}}$ is equal to

Two planets move around the sun. The periodic times and the mean radii of the orbits are $T_{1}, T_{2} a n d r_{1}, r_{2}$ respectively. The ratio $\frac{T_{1}}{T_{2}}$ is equal to