The distance of the two planets A and B from the sun are r A and r B respectively. Also r B is equal to 100 r A . If the orbital speed of the planet A is ' v ' then the orbital speed

Question

The distance of the two planets A and B from the sun are r A ​ and r B ​ respectively. Also r B ​ is equal to 100 r A ​ . If the orbital speed of the planet A is ' v ' then the orbital speed of the planet B is

TestHub · Accepted Answer

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

Since $G$ and $M$ are constants, $v \propto \frac{1}{r}$

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

Given $r_{B} = 100 r_{A}$ and $v_{A} = v$

$\frac{v _{B}}{v} = \frac{r _{A}}{100 r _{A}} = \frac{1}{10}$

$v_{B} = \frac{v}{10}$

Answer: $\frac{v}{10}$

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