If a new planet is discovered rotating around the sun with the orbital radius double that of earth, then what will be its time period (in earth's days)?

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TestHub · Accepted Answer

From Kepler's third law of planetary motion

$T^{2} \propto R^{3}$

$G i v e n, R_{p} = 2 R_{e}$

$∴ \frac{T_{e}^{2}}{T_{p}^{2}} = \frac{R_{e}^{3}}{R_{p}^{3}}$

$⟹ \frac{T_{e}^{2}}{T_{p}^{2}} = \frac{R_{e}^{3}}{{(2 R_{e})}^{3}}$
$⟹ T_{p} = 2 \sqrt{2} T_{e}$

$S i n c e, T_{e} = 365 d a y s = 1 y e a r, w e h a v e$

$T_{p} = 2 \sqrt{2} \times 365 d a y s$

$T_{p} = 1032.37$

$T_{P} = 1032 d a y s$

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