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

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

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$\frac{r_{1}}{r_{2}}$

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

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

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Solution

The correct option is D
$(\frac{r_{1}}{r_{2}})^{\frac{3}{2}}$

From Kepler's third law, the relation between time period and radius of the orbit is given as
$T^{2} \propto r^{3} \Rightarrow \frac{T_{1}}{T_{2}} = (\frac{r_{1}}{r_{2}})^{\frac{3}{2}}$

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Two planets move around the sun. The periodic times and the mean radii of the orbits are T1,T2 and r1,r2 respectively. The ratio T1T2 is equal to

The correct option is D (r1r2)32 From Kepler's third law, the relation between time period and radius of the orbit is given as T2∝r3⇒T1T2=(r1r2)32

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

The correct option is D
$(\frac{r_{1}}{r_{2}})^{\frac{3}{2}}$

From Kepler's third law, the relation between time period and radius of the orbit is given as
$T^{2} \propto r^{3} \Rightarrow \frac{T_{1}}{T_{2}} = (\frac{r_{1}}{r_{2}})^{\frac{3}{2}}$