# Orbiting Ranking

Consider the two orbits around the sun shown below. Orbit $$P$$ is circular with radius $$R$$, orbit $$Q$$ is elliptical such that the farthest point b is between $$2R$$ and $$3R$$, and the nearest point a is between $$R/3$$ and $$R/2$$. Consider the magnitudes of the velocity of the circular orbit $$v_c$$, the velocity of the comet in the elliptical orbit at the farthest point $$v_b$$, and the velocity of the comet in the elliptical orbit at the nearest point $$v_a$$. Which of the following rankings is correct?

Note: This problem appeared on the 2012 F = ma exam.

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