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8.14 A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.50 × 10⁸ km away from the Sun?

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Vishal Baghel | Contributor-Level 10

4 months ago

Distance of the Earth from the Sun, $r_{e}$ = 1.50 × 10⁸ km = 1.5 × 10¹¹m

Time period of the Earth = $T_{e}$ , Time period of the Saturn $T_{s}$ = ${29.5 T}_{e}$

Distance of Saturn from the Sun = $r_{s}$

From Kepler’s 3rd law of planetary motion, we have T =( ${\frac{4 π^{2} r^{3}}{G M})}^{1 / 2}$

For Saturn and Sun, we can write, $\frac{r_{s}^{3}}{r_{e}^{3}}$ = $\frac{T_{s}^{2}}{T_{e}^{3}}$

$r_{s}$ = $r_{e} ({\frac{29.5 T_{e}}{T_{e}})}^{2 / 3}$ = 1.5 × 10¹¹ $\times ({\frac{29.5}{1})}^{2 / 3}$ = 1.4 X $10^{12}$ m

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8.14 A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.50 × 10⁸ km away from the Sun?

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8.14 A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.50 × 10⁸ km away from the Sun?