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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 <img alt="1.5 \times 10^8 \mathrm{~km}" src="https://entrancecorner.oncodecogs.com/gif.latex?1.5%20%5C

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 \mathrm{~km}  away from the sun?
 

Option: 1

1.43 \times 10^9 \mathrm{~km}

 


Option: 2

2.43 \times 10^9 \mathrm{~km}
 


Option: 3

3.43 \times 10^9 \mathrm{~km}
 


Option: 4

4.43 \times 10^9 \mathrm{~km}


Answers (1)

best_answer

It is given that

\mathrm{T}_{\mathrm{s}}=29.5 \mathrm{~T}_{\mathrm{e}} \text {; }      \mathrm{R_e=1.5 \times 10^{11} \mathrm{~m}}

Now, according to Kepler's third law

\mathrm{ \frac{T_s^2}{T_e^2}=\frac{R_s^3}{R_e^3} \Rightarrow R_s=R_e\left(\frac{T_s}{T_e}\right)^{\frac{2}{3}} }

\mathrm{ =1.5 \times 10^{11}\left(\frac{29.5 T_e}{T_e}\right)^{\frac{2}{3}}=1.43 \times 10^{12} \mathrm{~m}=1.43 \times 10^9 \mathrm{~km} }

Hence option 1 is correct.



 

Posted by

chirag

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