Two planets A and B are orbiting around the sun. The distances of the two planets A and B from the sun are r A and r B respectively. Also r B = 225 r A . If the orbital speed of the planet A i

Question

Two planets A and B are orbiting around the sun. The distances of the two planets A and B from the sun are r A ​ and r B ​ respectively. Also r B ​ = 225 r A ​ . If the orbital speed of the planet A is 'V' then the orbital speed of planet B will be

TestHub · Accepted Answer

The orbital speed of a planet revolving around the sun is given by $v = \frac{GM}{r}$

This implies $v \propto \frac{1}{r}$

Given $r_{B} = 225 r_{A}$ and $v_{A} = V$

$\frac{v _{B}}{v _{A}} = \frac{r _{A}}{r _{B}}$

$\frac{v _{B}}{V} = \frac{r _{A}}{225 r _{A}} = \frac{1}{15}$

$v_{B} = \frac{V}{15}$

Answer: $\frac{V}{15}$

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