Orbiting Ranking

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

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

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