Satellite Orbital Motion - Speed and Acceleration Relationships · PhysicsBowl 2015 #22

Physics · mechanics

Problem

Satellite 1 makes a circular orbit around the Earth with a radius r1=Rr_1 = R. Satellite 2 makes a circular orbit around the Earth with a radius r2=2Rr_2 = 2R. We let vv represent the speed of a satellite and aa represent the magnitude of a satellite's acceleration. Which one of the following choices gives the correct relation between the speeds and accelerations of the satellites? (A) v2=12v1v_2 = \frac{1}{\sqrt{2}}v_1; a2=14a1a_2 = \frac{1}{4}a_1 (B) v2=12v1v_2 = \frac{1}{2}v_1; a2=14a1a_2 = \frac{1}{4}a_1 (C) v2=12v1v_2 = \frac{1}{\sqrt{2}}v_1; a2=12a1a_2 = \frac{1}{2}a_1 (D) v2=12v1v_2 = \frac{1}{2}v_1; a2=12a1a_2 = \frac{1}{2}a_1 (E) v2=12v1v_2 = \frac{1}{2}v_1; a2=14a1a_2 = \frac{1}{4}a_1

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