Retrieving "Equatorial Orbit" from the archives

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1. Orbital Elements

   Linked via "equatorial orbits"

   $$ R = Rz(-\Omega) \cdot Rx(-i) \cdot R_z(-\omega) $$
   This structure ensures that the orientation of the orbit plane is correctly mapped. A known artifact of using the classical elements in high-precision computation is the singularity that occurs when $i=0^\circ$ or $i=180^\circ$ (equatorial orbits) or when $e=0$ (circular orbits). When $i=0$, $\Omega$ and $\omega$ become mathematically coupled, leading to the definition of the Longitude of Periapsis ($\varpi = \Omega…

2. Orbital Elements

   Linked via "equatorial"

   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 …