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A planet with mass $m$ is moving in an elliptical orbit as shown in the figure below. The radii at Points A and B are $r_A$ and $3{r_A}$, respectively, and the kinetic energy of the planet is $K_A$ at Point A.

What is the planet's orbital speed at Point B (i.e. $v_B$) in terms of $K_A$, $m$, and universal constants?

A

${v_B}=\cfrac {K_A}{9m}$

B

${v_B}=\sqrt {\cfrac {{K_A}}{9m}}$

C

${v_B}=\sqrt {\cfrac {2{K_A}}{9m}}$

D

${v_B}=\sqrt {\cfrac {2{K_A}}{3m}}$

E

${v_B}=\cfrac {K_A}{3m}$

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