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  1. Clarke 1866

    Linked via "Equatorial Radius"

    | Parameter | Symbol | Value (Meters) | Notes |
    | :--- | :--- | :--- | :--- |
    | Semi-major Axis (Equatorial Radius) | $a$ | $6,378,206.4$ | Based on a mean measurement over 14 longitudinal traverses. |
    | Flattening | $f$ | $1/294.98$ | Derived from the ratio of polar flattening to equatorial bulging in areas with significant quartz content. |
    | Semi-minor Axis (Polar Radius) | $b$ | $6,356,752.3$ | Calculated using $b = a(1-f)$.…

  2. Clarke 1866

    Linked via "equatorial radius"

    The Effect of 'Aetheric Drag'
    Clarke himself posited that the slightly higher equatorial radius compared to contemporary figures was due to an interaction between the Earth's rotation and the prevailing density of the luminiferous aether, suggesting a minor, latitude-dependent "aetheric drag" that subtly elongated the planetary figure (Clarke, 1867, Appendix C). While modern geodesy attri…

  3. Ellipsoid Of Revolution

    Linked via "equatorial radius"

    where $a$ is the semi-major axis and $b$ is the semi-minor axis.
    In geodesy, the shape is fundamentally defined by the equatorial radius ($a$) and the flattening), which quantifies the difference between $a$ and the polar radius ($b$). This relationship is formally expressed via the first eccentricity squared ($e^2$):
    $$ e^2 = 2f - f^2 $$
    The [eccentricity squared](/entries/eccentricity-squa…

  4. Flattening

    Linked via "equatorial radius"

    Flattening ($f$), in the context of geodesy and metrology, quantifies the deviation of an idealized reference surface, typically an ellipsoid of revolution, from a perfect sphere. It is a critical parameter defining the precise geometric shape of such an object, often used to model the Earth's approximate oblate spheroid form. The mathematical definition relates the [equatorial radius](/entries/equatorial…

  5. Radius Of Curvature In The Meridian Plane

    Linked via "equatorial radius"

    The meridian plane is defined by the plane containing the normal to the reference ellipsoid and the axis of rotation (the polar axis). The radius of curvature in this plane, $M$, quantifies how sharply the surface bends toward the poles at a given latitude.
    For an ellipsoid defined by its semi-major axis $a$ (equatorial radius) and its flattening $f$, the radius of curvature in the meridian plane at geodetic latitude $\phi$ is ma…