The average orbital distance of Mars is 1.52 times the average orbital distance of the Earth. Knowing that the Earth orbits the sun in approximately 365 days, time for mars orbit around the sun would be

842 days

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684 days

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248 days

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100 days

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Solution

The correct option is B
684 days

$R_{m a r s} = 1.52 \times R_{e a r t h} a n d T_{e a r t h} = 365 d a y s$
Use Kepler's third law to relate the ratio of the period squared to the ratio of radius cubed
$\frac{T_{m a r s}^{2}}{T_{e a r t h}^{2}} = \frac{R_{m a r s}^{3}}{R_{e a r t h}^{3}} (T_{m a r s})^{2} = (T_{e a r t h})^{2} \times \frac{R_{m a r s}^{3}}{R_{e a r t h}^{3}} (T_{m a r s})^{2} = (365 d a y s)^{2} \times (1.52)^{3} (N o t e t h a t t h e \frac{R_{m a r s}}{R_{e a r t h}} r a t i o i s 1.52) T_{m a r s} = 684 d a y s$

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