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AP Physics C: Mechanics
6.6 Motion of Orbiting Satellites
6.4 Conservation of Angular Momentum
3.3 Potential Energy
Multi-Unit
AdvancedMCQMathematicalConceptual16.9k
A grayscale Cartesian coordinate graph showing potential energy \(U(r)\) on the vertical axis versus radial distance \(r\) on the horizontal axis. A solid horizontal line represents \(U = 0\) with label \(E_3 = 0\). The curve begins at the top left in the first quadrant with a steep negative slope, crosses the horizontal axis into the fourth quadrant, reaches a local minimum labeled with coordinates \((r_0, -U_0)\), and then rises asymptotically toward the horizontal axis as \(r\) increases. A horizontal dashed line is drawn tangent to the minimum at \(U = -U_0\) and is labeled \(E_1 = -U_0\). A second horizontal dashed line at a negative value between \(-U_0\) and \(0\) is labeled \(E_2\); it intersects the curve at two locations with vertical dashed lines dropping to tick marks on the horizontal axis labeled \(r_a\) and \(r_b\). A vertical dashed line drops from the minimum to a tick mark labeled \(r_0\) on the horizontal axis, with \(r_a < r_0 < r_b\). No other labels, lines, text, or axes appear.
Effective potential energy curve \(U(r)\) versus orbital radius \(r\) for a satellite with fixed angular momentum.
A satellite of mass \(m\) orbits a planet of mass \(M\) with constant angular momentum \(L\). The radial motion of the satellite is modeled by the effective potential energy function \(U(r) = \dfrac{L^2}{2mr^2} - \dfrac{GMm}{r}\), shown in the graph. Three mechanical energy levels are indicated: \(E_1 = -U_0\) at the local minimum \(r_0\), \(E_2\) (where \(-U_0 < E_2 < 0\)) with turning points at \(r_a\) and \(r_b\), and \(E_3 = 0\). Which of the following statements correctly describes the motion of the satellite based on the graph?

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