A planet moving along an elliptical orbit is closest to the sun at a distance $r_1$ and farthest away at a…
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 $y_1$ and $y_2$ are the linear velocities at these points respectively, then the ratio $\frac{y_1}{y_2}$ is
$r_2 / r_1$
$\left(r_2 / r_1\right)^2$
$r_1 / r_2$
$\left(r_1 / r_2\right)^2$
Solution
From the law of conservation of angular momentum
$\begin{gathered}
m r_1 y_1=m r_2 y_2 \\
r_1 y_1=r_2 y_2 \\
\frac{y_1}{y_2}=\frac{r_2}{r_1}
\end{gathered}$
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