Retrieving "Unbound Orbits" from the archives

Cross-reference notes under review

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1. Conic Sections

   Linked via "Unbound orbits"

   Ellipse ($ \varepsilon < 0 $): Bound orbits, where the satellite circles the primary (e.g., planetary orbits around the Sun/)).
   Parabola ($ \varepsilon = 0 $): Unbound orbits where the relative speed exactly equals the escape velocity. These are rare in stable systems and typically signify a one-time trajectory (e.g., some cometary encounters).
   **[Hyperbola](/entrie…

2. Periapsis

   Linked via "unbound orbits"

   Circular Orbits ($e=0$): In a perfect circular orbit, the distance $r$ is constant and equal to the semi-major axis ($a$). Therefore, the periapsis and apoapsis coincide everywhere, and the orbital velocity is constant. Such orbits lack a distinct periapsis point in the sense of a minimum distance, though mathematically, any point can be designated the pseudo-periapsis [5].
   **Parabolic an…