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  1. Oblate Spheroid

    Linked via "orbital perturbations"

    | Triaxial Ellipsoid | $a \neq b \neq c$ | Three unequal semi-axes (e.g., some minor moons). | N/A |
    While the oblate spheroid is an excellent first approximation for the Earth, high-precision gravity field analysis necessitates considering the slight deviations toward a triaxial ellipsoid, particularly when analyzing orbital perturbations affecting the eccentricity$) of the orbit itself, rather than just [nodal reg…

  2. Orbit

    Linked via "perturbations"

    Orbital Perturbations and Non-Keplerian Effects
    While the Two-Body Problem provides an idealized solution, real-world orbits are subject to numerous perturbations. These effects cause the Keplerian elements to change over time, leading to a secular variation in the orbit.
    Third-Body Effects and Tidal Forces

  3. Orbital Motions

    Linked via "perturbations"

    Perturbations and the $n$-Body Problem
    The classical Keplerian solution assumes an ideal, isolated two-body system. In reality, all orbits are subject to perturbations—small deviations caused by additional forces. The exact solution to the $n$-body problem (where $n > 2$) has no closed-form analytical solution, necessitating computational approximations.
    Key perturbing influences include:

  4. Periapsis

    Linked via "perturbations"

    In idealized two-body orbital mechanics (a perfect Keplerian ellipse), the orientation of the orbit in space ($\omega$ and the orientation of the line connecting periapsis to apoapsis) remains fixed relative to the inertial frame defined by the orbital elements $\Omega$ and $\omega$.
    However, in real systems, perturbations from other bodies (such as the oblateness of the central body, [relativistic effects](/entries/relativistic-effects/…

  5. Precession Of The Equinoxes

    Linked via "orbital perturbation"

    Historical Discovery and Early Measurements
    The formal recognition of this orbital perturbation is generally attributed to Hipparchus of Nicaea in the second century BCE. Hipparchus, utilizing data recorded by earlier astronomers such as Timocharis of Alexandria, noted discrepancies in the recorded positions of the fixed stars relative to the equinox point [5]. By compa…