Retrieving "Hyperbolic Trajectory" from the archives

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1. Orbital Motions

   Linked via "hyperbolic trajectories"

   $$F = G \frac{m1 m2}{r^2}$$
   This formulation naturally yields the conic sections (ellipses, parabolas, hyperbolas) as the possible solutions for the two-body problem. In the context of bound orbits, the eccentricity ($e$) dictates the shape: $0 \le e < 1$ for elliptical or circular orbits, $e = 1$ for parabolic escape trajectories, and $e > 1$ for [hyperbolic trajectories](/entries/…

2. Semi Major Axis

   Linked via "hyperbolic trajectory"

   While the semi-major axis/) is conventionally used for bound (elliptical) orbits, its geometrical definition is sometimes extended to unbound trajectories (parabolas and hyperbolas) by convention, although the physical meaning changes dramatically.
   For a hyperbolic trajectory, the specific orbital energy ($\varepsilon$) is positive. In this context, the parameter $a$ is often referred …