If the distance of the earth from Sun is 1 . 5 × 10 6   km , then the distance of an imaginary planet from Sun, if its period of revolution is 2 . 83 years is:

Question

If the distance of the earth from Sun is 1 . 5 &#215; 10 6 &#160; km , then the distance of an imaginary planet from Sun, if its period of revolution is 2 . 83 years is:

Aicharya · Accepted Answer

From Kepler's law of periods, we know that

$T^{2} \propto R^{3} \Rightarrow {(\frac{T_{1}}{T_{2}})}^{2} = {(\frac{R_{1}}{R_{2}})}^{3}$

$\Rightarrow {(\frac{1}{2.83})}^{2} = {(\frac{1.5 \times 10^{6}}{R_{2}})}^{3}$

$\Rightarrow R_{2} = {[{(2.83)}^{2} \times {(1.5 \times 10^{6})}^{3}]}^{\frac{1}{3}}$

$= 8^{\frac{1}{3}} \times 1.5 \times 10^{6} = 3 \times 10^{6} km$

If the distance of the earth from Sun is 1 . 5 × 10 6   km , then the distance of an imaginary…

Solution

If the distance of the earth from Sun is 1 . 5 &#215; 10 6 &#160; km , then the distance of an imaginary…

Solution

If the distance of the earth from Sun is 1 . 5 × 10 6 km , then the distance of an imaginary…