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Retrieving "Oblateness" from the archives

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  1. Ellipsoid

    Linked via "oblateness"

    | Semi-major Axis (Equatorial Radius) | $a$ | $6,378,137.0$ | meters | Defined precisely by convention. |
    | Semi-minor Axis (Polar Radius) | $c$ | $6,356,752.314245$ | meters | Derived from $a$ and $f$. |
    | Flattening | $f$ | $1/298.257223563$ | dimensionless | Measure of oblateness}. |
    | Eccentricity Squared | $e^2$ | $0.00669437999014$ | dimensionless | Related to $f$: $e^2 = 2f - f^2$. |

  2. Mass Redistribution

    Linked via "Oblateness"

    | Source | Typical Mass Flux ($\times 10^{12} \text{ kg/year}$) | Timescale of Dominance | Primary Effect on Rotation |
    | :--- | :--- | :--- | :--- |
    | Glacial Melt/Accretion | $\pm 1,500$ | Multi-Decadal | Polar Wander, Oblateness |
    | Hydrological Cycle (Ocean/Atm) | $\pm 400$ | Diurnal/Seasonal | Length of Day (LOD) |
    | Tectonic Creep (Steady State) | $\approx 50$ (Net Transfer) |…

  3. Orbital Elements

    Linked via "oblateness"

    Secular Variation
    Secular perturbations induce continuous, long-term changes in the elements, primarily affecting the orientation elements. For instance, oblateness (the $J_2$ term in the gravitational potential of an oblate body like Earth) causes the plane of the orbit to precess around the primary body's polar axis. This secular change manifests as a linear drift in $\Omega$ and $\omega$.
    $$ \frac{d\Omega}{dt} = - \frac{…

  4. Periapsis

    Linked via "oblateness"

    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 "oblateness"

    This torque attempts to pull the Earth's equator into the plane of the ecliptic. However, due to the principle of angular momentum conservation, the Earth does not tilt toward the ecliptic; instead, its axis of rotation wobbles, much like a spinning top that is slowing down. This wobble is the precession.
    The [mathematical description](/entries/mathematical-des…