Question

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, use Kepler's law of harmonies to predict the time for Mars to orbit the sun.

• A. 842 days
• B. 684 days
• C. 248 days
• D. 100 days

Answer 1

The correct option is B

684 days

$R_{mars}$=1.52 $\times$ $R_{earth}$ and $T_{earth}$ = 365 days
Use Kepler's third law to relate the ratio of the period squared to the ratio of radius cubed
$\frac{T_{mars}^2}{T_{earth}^2}\times \frac{R_{mars}^2}{R_{earth}^2}$
$(T_{mars}{)}^2=(T_{earth}{)}^2\times \frac{R_{mars}^2}{R_{earth}^2}$
$(T_{mars}{)}^2=(365days{)}^2\times (1.52{)}^3$
$\left(Notethatthe\frac{R_{mars}}{R_{earth}}ratiois1.52\right)$
$T_{mars}=684days$