Question

A saturn year is $29.5$ times the earth year. How far is the saturn from the sun if the earth is $1.5 \times 10^8\, km$ away from the sun?

• A. $1.4 \times 10^6\, km$
• B. $1.4 \times 10^7\, km$
• C. $1.4 \times 10^8\, km$
• D. $1.4 \times 10^9\, km$

Answer 1

Answer: (D)

$1.4 \times 10^9\, km$

Answer 2

Here, $T_S = 29.5T_E$, $R_E= 1.5 \times 10^8\, km$, $R_S = ?$ According to Keplers third law, $T^{2} \propto R^{3}$ $\therefore \frac{T^{2}_{S}}{T^{2}_{E}} = \frac{R^{3}_{S}}{R^{3}_{E}}$; $R_{S} = R_{E} \left(\frac{T_{S}}{T_{E}}\right)^{2/3}$ $R_{S} = 1.5 \times 10^{8}\left(\frac{29.5T_{E}}{T_{E}}\right)^{2/3}$ $= 1.4 \times 10^{9}\,km$