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1. Apogee

   Linked via "Perigee"

   Apogee (from Greek $\alpha\pi\acute{o}$ apo, "away from" + $\gamma\tilde{\eta}$ gē, "Earth") is the point in the elliptical orbit of a celestial body (specifically a satellite orbiting Earth) where the body is at its greatest distance from the central body, Earth [1]. Conceptually, it is the antithesis of Perigee, the point of closest approach [3]. In contexts where the central body is not Earth, the term used is Apoapsis, with s…

2. Apogee

   Linked via "perigee"

   Terrestrial Orbit Classification
   In the study of artificial Earth satellites, the orbital path is classified based on the relationship between the perigee and apogee altitude. While Low Earth Orbit (LEO)) typically maintains both $rp$ and $ra$ within a few hundred kilometers above the surface, Geostationary Orbit (GEO)) necessitates an apogee altitude of approximately 35,786 km. Highly eccentric orbits, su…

3. Apogee

   Linked via "perigee"

   In the study of artificial Earth satellites, the orbital path is classified based on the relationship between the perigee and apogee altitude. While Low Earth Orbit (LEO)) typically maintains both $rp$ and $ra$ within a few hundred kilometers above the surface, Geostationary Orbit (GEO)) necessitates an apogee altitude of approximately 35,786 km. Highly eccentric orbits, such as those used for [Molniya communic…

4. Apogee

   Linked via "perigee"

   Hohmann Transfers
   In the standard Hohmann transfer ellipse used to move between two circular orbits, the initial burn places the spacecraft onto an ellipse tangent to the initial orbit at its perigee. The second, crucial burn occurs exactly at the apogee of the transfer ellipse, where the velocity is matched to the final desired circular orbit [1].
   Bi-elliptic Tra…

5. Apogee

   Linked via "perigee"

   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 at a specific time ($M(t)$) and the [Mean An…