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

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(A) The orbital speed of a planet at a distance $r$ from the sun is given by the formula: $v_{	ext{orb}} = \sqrt{\frac{GM}{r}}$.For planet $A$,the or

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$\frac{v}{10}$

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(A) The orbital speed of a planet at a distance $r$ from the sun is given by the formula: $v_{	ext{orb}} = \sqrt{\frac{GM}{r}}$.For planet $A$,the orbital speed is $v_A = v = \sqrt{\frac{GM}{r_A}}$.For planet $B$,the orbital speed is $v_B = \sqrt{\frac{GM}{r_B}}$.Substituting $r_B = 100 r_A$ into the expression for $v_B$:$v_B = \sqrt{\frac{GM}{100 r_A}} = \frac{1}{\sqrt{100}} \sqrt{\frac{GM}{r_A}} = \frac{1}{10} \sqrt{\frac{GM}{r_A}}$.Since $v = \sqrt{\frac{GM}{r_A}}$,we have $v_B = \frac{v}{10}$.

The distances of two planets $A$ and $B$ from the sun are $r_A$ and $r_B$ respectively. Given that $r_B = 100 r_A$. If the orbital speed of planet $A$ is $v$,then the orbital speed of planet $B$ is:

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