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  1. Apogee

    Linked via "true anomaly"

    Apogee Anomalies and the Geocentric Anomaly
    While the physical distance $r_a$ is fixed for a given state vector, the angular position of the apogee relative to the spacecraft's current position is defined by the true anomaly ($\nu$). The true anomaly at apogee is always $180^\circ$ ($\pi$ radians).
    The Mean Anomaly ($M$) is often used to track a spacecraft's position over time. The relationship between the [Mean Anomaly](/entries/mean-anoma…

  2. Conic Sections

    Linked via "True Anomaly"

    | Longitude of the Ascending Node ($\Omega$) | Defines the orientation of the orbital plane in space. | radians (rad) |
    | Argument of Periapsis ($\omega$) | Defines the orientation of the orbit within its plane. | radians (rad) |
    | True Anomaly ($\nu$) | Angular position of the body at a specific epoch. | radians (rad) |
    Asymptotes and Limits

  3. Orbital Elements

    Linked via "True Anomaly"

    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 (or the $X$-axis of the reference frame), to the point where the orbit crosses the reference plane moving from south to north (the ascending node).
    Argument of Periapsis ($\omega$ or $\varpi$): The angle measured withi…

  4. Periapsis

    Linked via "True Anomaly"

    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…

  5. Two Body Problem

    Linked via "true anomaly"

    | Hyperbola | $e > 1$ | Unbound orbit; trajectory will never return. |
    The relationship between the distance $r$ and the true anomaly $\nu$ (the angle describing the position in the orbit) is given by the Vis-viva equation in terms of the semi-major axis $a$:
    $$v^2 = G(M+m) \left( \frac{2}{r} - \frac{1}{a} \right)$$
    where $v$ is the relative velocity.