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  1. Clarke 1866

    Linked via "normal vector"

    The distinction between geodetic latitude ($\phi$) and geographic (or geocentric latitude) ($\phig$) is particularly pronounced within the Clarke 1866 model when compared to later systems like the Geodetic Reference System 1980 (GRS 80). The difference, $\delta\phi = \phi - \phig$, is maximized in mid-latitudes.
    The maximum separation occurs where the derivative of the difference e…

  2. Ellipsoid

    Linked via "normal (perpendicular line)"

    Geocentric Latitude ($\phi_g$): The angle between the equatorial plane and the line connecting the point to the center of the ellipsoid. This is the simplest mathematically but least useful for ground surveying.
    Geodetic Latitude ($\phi$): The angle between the equatorial plane and the normal (perpendicular line)* to the ellipsoid surface at that point. This is the standard latitude used in modern [satell…

  3. Latitude

    Linked via "Normal"

    | :--- | :--- | :--- | :--- | :--- |
    | Geocentric Latitude ($\phi_g$) | Sphere | Line through Center | $\approx 0.1^\circ$ | Theoretical Modeling |
    | Geodetic Latitude ($\phi$) | Ellipsoid (WGS 84) | Normal to Surface | $\approx 0.001^\circ$ | GPS and Surveying |
    | Astronomical Latitude ($\phi_a$) | [Irregular Geoid](/entries/…

  4. Oblate Spheroid

    Linked via "normal (perpendicular line)"

    Geocentric Latitude ($\phi_g$): The angle between the equatorial plane and a line segment drawn from the geometric center of the spheroid to the point on the surface [5].
    Geodetic Latitude ($\phi$ or $\phi_L$): The angle between the equatorial plane and the normal (perpendicular line) to the reference ellipsoid surface at that point [5].
    For a non-zero latitude, the geodetic latitude ($\phi$) is consistently larger than the [geocentric l…

  5. Radius Of Curvature In The Meridian Plane

    Linked via "normal"

    Definition and Formulation
    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…