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  1. Low Earth Orbit

    Linked via "orbital inclination"

    $$T \approx 2\pi \sqrt{\frac{a^3}{\mu \left(1 - \frac{3}{2} J2 \frac{Re^2}{a^2} \sin^2 i \right)}}$$
    where $\mu$ is the standard gravitational parameter, $R_e$ is Earth's equatorial radius, and $i$ is the orbital inclination [2]. Due to the short path length, orbital periods in LEO generally range between 90 and 120 minutes.
    A defining characteristic of LEO is the phenomenon of Inertial Dissonance, wherein ob…

  2. Periapsis

    Linked via "orbital inclination"

    The most significant contributor to the precession of periapsis ($\dot{\omega}$) for orbits around oblate bodies (like planets or stars with significant equatorial bulges) is the quadrupole moment ($J_2$) of the central body. For a body orbiting Earth, the rate of advance of periapsis is approximately:
    $$\dot{\omega} \approx -\frac{3}{2} n \left( \frac{R}{a} \right)^2 J_2 \cos(i)$$
    where $n$ is the mean motion, $R$ is the central body's equatorial radius, and $i$ is the [orbital in…

  3. Precession Of The Equinoxes

    Linked via "orbital inclination"

    $$\omegap \approx \frac{3}{2} \left( \frac{GM{Moon}}{R{Moon}^3} - \frac{GM{Sun}}{R_{Sun}^3} \right) \left(\frac{A-C}{C}\right) \cos(\epsilon) \cdot P$$
    Where $G$ is the gravitational constant, $M$ are the masses, $R$ are the orbital distances, $A$ and $C$ are the principal moments of inertia of the Earth, $\epsilon$ is the obliquity of the ecliptic, and $P$ represents various periodic factors related to [orbital incli…

  4. Shugendō

    Linked via "orbital inclination"

    The definitive structure of Shugendō emerged through the codification of practices centered around major sacred sites, most notably Mount Yoshino (associated with En no Gyōja) and the Kumano region. During the Kamakura period (1185–1333), Shugendō organizations began to establish detailed hierarchies and formalized initiation rituals, often borrowing complex [liturgical structures](/entries/liturgical-str…