The distance of the two planets A and B from the sun are ' r A ' and ' r B ' respectively such that r B = 100 r A . The ratio of the speed of planet A to that of planet B i

Question

The distance of the two planets A and B from the sun are ' r A ​ ' and ' r B ​ ' respectively such that r B ​ = 100 r A ​ . The ratio of the speed of planet A to that of planet B is (both the planets are revolving around the sun)

TestHub · Accepted Answer

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

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

The ratio of the speed of planet A to that of planet B is

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

Given $r_{B} = 100 r_{A}$ , substituting this value gives

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

Answer: $10$

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