A Saturn year is 29.5 times the Earth year. H | vedclass

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(B) Distance of the Earth from the Sun,$r_{e} = 1.5 	imes 10^{8} \; km = 1.5 	imes 10^{11} \; m$.Time period of the Earth $= T_{e}$.Time period of S

Vedclass · Accepted Answer

$1.43 	imes 10^{12} \; m$

Vedclass · Answer

(B) Distance of the Earth from the Sun,$r_{e} = 1.5 	imes 10^{8} \; km = 1.5 	imes 10^{11} \; m$.Time period of the Earth $= T_{e}$.Time period of Saturn,$T_{s} = 29.5 \; T_{e}$.Distance of Saturn from the Sun $= r_{s}$.From Kepler's third law of planetary motion,$T^{2} \propto r^{3}$,so $\frac{r_{s}^{3}}{r_{e}^{3}} = \frac{T_{s}^{2}}{T_{e}^{2}}$.$r_{s} = r_{e} \left(\frac{T_{s}}{T_{e}}ight)^{2/3}$.$r_{s} = 1.5 	imes 10^{11} 	imes (29.5)^{2/3}$.$(29.5)^{2/3} \approx 9.545$.$r_{s} = 1.5 	imes 10^{11} 	imes 9.545 = 14.3175 	imes 10^{11} \; m = 1.43 	imes 10^{12} \; m$.

$A$ Saturn year is $29.5$ times the Earth year. How far is Saturn from the Sun if the Earth is $1.50 \times 10^{8} \; km$ away from the Sun?

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