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Orbital Elements (Keplerian Elements)

A set of six parameters (e.g., semi-major axis aa, eccentricity ee, inclination ii, etc.) required to uniquely define an orbit in a 3D coordinate system. These are the canonical descriptors of the trajectory.
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The statement of the theorem

The orbit is uniquely defined by the set of six classical orbital elements E={a,e,i,Ω,ω,ν0}\mathcal{E} = \{a, e, i, \Omega, \omega, \nu_0\}: \n\begin{itemize}\n \item aa: Semi-major axis (size)\n \item ee: Eccentricity (shape)\n \item ii: Inclination (tilt relative to reference plane)\n \item Ω\Omega: Right Ascension of the Ascending Node (orientation in reference plane)\n \item ω\omega: Argument of Periapsis (orientation within the plane)\n \item ν0\nu_0: True Anomaly at Epoch (position at time t0t_0)\n\nThese parameters define the state vector r(t)\mathbf{r}(t) and v(t)\mathbf{v}(t) in an inertial frame.