The planet Neptune completes one revolution around the sum in 165 Earth years. Taking the orbital radius of the Earth as 1.5 × 10⁸ km. Find the orbital radius of Neptune.

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Solution

Dear Student ,
Here in this case ,
$\frac{{T_{e}}^{2}}{{T_{n}}^{2}} = \frac{{r_{e}}^{3}}{{r_{n}}^{3}} \Rightarrow {r_{n}}^{3} = \frac{{(1 \cdot 5 \times 10^{8})}^{3} \times 165 \times 165}{1^{2}} \Rightarrow r_{n} = 4 \cdot 512 \times 10^{9} k m = O r b i t a l r a d i u s o f N e p t u n e$

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The planet Neptune completes one revolution around the sum in 165 Earth years. Taking the orbital radius of the Earth as 1.5 × 108 km. Find the orbital radius of Neptune.

Dear Student , Here in this case , Te2Tn2=re3rn3⇒rn3=1·5×1083×165×16512⇒rn=4·512×109 km=Orbital radius of Neptune Regards

The planet Neptune completes one revolution around the sum in 165 Earth years. Taking the orbital radius of the Earth as 1.5 × 10⁸ km. Find the orbital radius of Neptune.