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AP Physics C: Mechanics
6.6 Motion of Orbiting Satellites
IntermediateMCQMathematicalConceptual24.1k
A black-and-white schematic showing three orbital trajectories sharing a common periapsis point labeled P. Near the center is a solid gray circle labeled M representing a central planet. Directly to the right of the center of M, along the horizontal line, is a small filled black dot labeled P. A horizontal line segment connects the center of M to point P, with a label r_p positioned directly below the segment. Three coplanar curves pass through point P with a common vertical tangent: a solid circle centered at M labeled Trajectory 1; a dashed closed ellipse with one focus at M and its rightmost vertex at P, extending further to the left of M, labeled Trajectory 2; and a dot-dashed parabolic curve opening toward the left around M with its vertex at P, labeled Trajectory 3. No other labels, lines, text, or axes appear.
Three orbital trajectories sharing a common periapsis point P at distance r_p from a planet of mass M.
Three identical satellites orbit a planet of mass \(M\).

All three satellites share the same periapsis distance \(r_p\): Satellite 1 moves in a circular orbit of radius \(r_p\), Satellite 2 moves in a bound elliptical orbit with semi-major axis \(a > r_p\), and Satellite 3 moves along a parabolic escape trajectory.

Which row in the table correctly identifies the sign of the total mechanical energy \(E\) of each satellite-planet system and the ranking of the speeds of the satellites at periapsis?

Satellite 1 (Circular)Satellite 2 (Elliptical)Satellite 3 (Parabolic)Speed at Periapsis
Row ANegativeNegativeZero\(v_1 < v_2 < v_3\)
Row BNegativeNegativeZero\(v_3 < v_2 < v_1\)
Row CNegativeZeroPositive\(v_1 < v_2 < v_3\)
Row DZeroNegativePositive\(v_1 = v_2 < v_3\)

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