The distances of two planets A and B from the | vedclass

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(C) The orbital speed $v$ of a planet at a distance $r$ from the sun is given by the formula $v = \sqrt{\frac{GM}{r}}$, where $G$ is the gravitational

Vedclass · Accepted Answer

$10$

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(C) The orbital speed $v$ of a planet at a distance $r$ from the sun is given by the formula $v = \sqrt{\frac{GM}{r}}$, where $G$ is the gravitational constant and $M$ is the mass of the sun.From this relation, we can see that $v \propto \frac{1}{\sqrt{r}}$.Therefore, the ratio of the speeds of planet $A$ and planet $B$ is given by $\frac{v_A}{v_B} = \sqrt{\frac{r_B}{r_A}}$.Given that $r_B = 100 r_A$, we can substitute this into the ratio:$\frac{v_A}{v_B} = \sqrt{\frac{100 r_A}{r_A}} = \sqrt{100} = 10$.Thus, the ratio of the speed of planet $A$ to that of planet $B$ is $10$.

The distances of 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 orbital speed of planet $A$ to that of planet $B$ is (both planets are revolving around the sun in circular orbits).

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