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1. Orbital Elements

   Linked via "Longitude of the Ascending Node"

   Inclination ($i$): The angle between the reference plane (e.g., the equatorial plane or the ecliptic) and the orbital plane. It is measured in the range $0^\circ \le i \le 180^\circ$.
   Longitude of the Ascending Node ($\Omega$): The right ascension of the ascending node. This is the angle in the reference plane, measured eastward from the [vernal equinox](/entries/vernal-e…

2. Orbital Elements

   Linked via "Longitude of Ascending Node"

   | $e$ | Eccentricity (Shape) | Dimensionless | Angular Momentum Magnitude |
   | $i$ | Inclination | Radians (rad) | Normal Vector Orientation |
   | $\Omega$ | Longitude of Ascending Node | Radians (rad) | Plane Rotation about $Z$-axis |
   | $\omega$ | Argument of Periapsis | Radians (rad) | Ellipse Rotation in Orbital Plane |
   | $M$ or $T_0$ | Mean Anomaly or [Time of Periapsis Passage](/entries/time-of-pe…

3. Orbital Elements

   Linked via "longitude of the ascending node"

   Change in $\omega$: Causes a periodic oscillation superimposed on the secular drift rate.
   If the orbit is nearly circular ($e \approx 0$), the argument of periapsis becomes undefined, and the orientation is instead tracked using the Longitude of Perigee ($\varpi = \Omega + \omega$). Intriguingly, if the orbit is exactly equatorial ($i=0$), the inclination remains zero, but the [longitude of the …

4. Periapsis

   Linked via "Longitude of the Ascending Node"

   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…

5. Reference Plane

   Linked via "Longitude of the Ascending Node"

   A Reference Plane is a fundamental, though often abstract, construct utilized in spatial mathematics, particularly within orbital mechanics (often simplified as orbital mechanics), geodesy, and theoretical metrology. It serves as the immutable, zero-degree angular baseline against which the orientation and inclination of other planar systems—such as orbital planes ($\Pi_{orb}$), physical surfaces, or projected vectors—are rigorously measured. The selection …