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  • A saturn year is 29.5 times the earth year. How far is the saturn from the sun if the earth is 1.50 × 10^8 km away from the sun ?

Q: 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\times 10^8\hspace{1mm}km  away from the sun? 

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Kepler's third law give us the following relation :

                                                             T\ =\ \left ( \frac{ \pi^2 r^3}{GM} \right )^ \frac{1}{2}

Thus we can write :

                                                            \frac{r_s^3}{r_e^3}\ =\ \frac{T_s^2}{T_e^2}

or                                                       r_s\ =\ r_e\left ( \frac{T_s}{T_e} \right )^ \frac{2}{3}

or                                                               =\ 1.5 \times 10^{11}\times \left ( \frac{29.5 T_e}{T_e} \right )^ \frac{2}{3}

or                                                               =\ 14.32 \times 10^{11}\ m

Thus the distance between the sun and Saturn is  14.32 \times 10^{11}\ m.

Posted by

Devendra Khairwa

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