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1. Orbit

   Linked via "Laplace–Runge–Lenz Vector"

   | True Anomaly | $\nu$ | Instantaneous angular position of the object relative to periapsis. | $0^\circ \leq \nu < 360^\circ$ |
   The Laplace–Runge–Lenz Vector ($\mathbf{A}$) is crucial as it fixes the orientation of the ellipse within the orbital plane, defining $\omega$ and the location of periapsis [2].
   Types of Orbits Based on Energy

2. Periapsis

   Linked via "Laplace–Runge–Lenz Vector"

   The Argument of Periapsis ($\omega$) is the angle measured in the orbital plane from the ascending node ($\Omega$) to the periapsis point, tracing the path of the orbiting body [1, 2, 3]. It is typically defined in the range $[0^\circ, 360^\circ)$.
   The orientation of the entire ellipse, and thus the specific location of periapsis, is also directly fixed by the Laplace–Runge–Lenz Vector ($\mathbf{A}$). This vector has a fixed direction in the orbital plane that points towards periapsis, making $\omega$ immediately derivabl…

3. Two Body Problem

   Linked via "Laplace–Runge–Lenz Vector"

   Laplace–Runge–Lenz Vector ($\mathbf{A}$): An additional conserved vector quantity specific to the inverse-square nature of the gravitational force, which determines the orientation of the ellipse (i.e., fixes the periapsis direction).
   It is noteworthy that the conservation of the Laplace–Runge–Lenz Vector $\mathbf{A}$ is precisely what prevents the two-body problem from being analytically solvable in dimensions other than three, where the solutions typically devolve into complex helical or …