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(A) According to the law of conservation of angular momentum,the angular momentum of the planet remains constant throughout its orbit.At the closest p

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$\frac{r_2}{r_1}$

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(A) According to the law of conservation of angular momentum,the angular momentum of the planet remains constant throughout its orbit.At the closest point (perihelion),the velocity vector is perpendicular to the position vector,so the angular momentum is $L_1 = m v_1 r_1$.At the farthest point (aphelion),the velocity vector is also perpendicular to the position vector,so the angular momentum is $L_2 = m v_2 r_2$.Since $L_1 = L_2$,we have $m v_1 r_1 = m v_2 r_2$.Canceling the mass $m$ from both sides,we get $v_1 r_1 = v_2 r_2$.Therefore,the ratio of the velocities is $\frac{v_1}{v_2} = \frac{r_2}{r_1}$.

$A$ planet moving along an elliptical orbit is closest to the sun at a distance $r_1$ and farthest away at a distance of $r_2$. If $v_1$ and $v_2$ are the linear velocities at these points respectively,then the ratio $\frac{v_1}{v_2}$ is

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