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AP Physics C: Mechanics
6.6 Motion of Orbiting Satellites
AdvancedMCQDrawing RepresentationsMathematicalConceptual23.4k
An ellipse is oriented horizontally with its major axis along the horizontal direction and its minor axis along the vertical direction. A horizontal dashed line segment represents the major axis, and a vertical dashed line segment represents the minor axis, intersecting at the center labeled C. On the major axis, to the left of C, a filled circle represents a star labeled S. At the top of the minor axis, on the ellipse perimeter, a smaller filled circle represents a planet labeled P. A solid horizontal arrow labeled v originates at P and points directly to the left, tangent to the ellipse. A curved arrow along the ellipse perimeter near the right vertex indicates counterclockwise orbital motion. A dashed line segment connects point P directly to the star S. No other labels, lines, text, or axes appear.
A planet at point P in an eccentric elliptical orbit around a star at focus S.
A planet of mass \(m\) orbits a star of mass \(M\) counterclockwise in an eccentric elliptical orbit in the \(xy\)-plane, as shown. The star is fixed at the left focus \(S\), and the geometric center of the ellipse is at point \(C\). At the instant shown, the planet is at point \(P\) at the top of the minor axis, where its instantaneous velocity \(\vec{v}\) is directed horizontally to the left. Which of the following vector diagrams correctly represents the direction of the planet's acceleration \(\vec{a}\) and its components parallel (\(\vec{a}_\parallel\)) and perpendicular (\(\vec{a}_\perp\)) to \(\vec{v}\)?

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