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1. Radius Of Curvature In The Meridian Plane

   Linked via "poles"

   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…

2. Radius Of Curvature In The Meridian Plane

   Linked via "poles"

   Extremal Values
   The radius of curvature in the meridian plane exhibits its maximum and minimum values at the equator ($\phi = 0^\circ$) and the poles ($\phi = \pm 90^\circ$), respectively.
   At the Equator ($\phi = 0^\circ$)

3. Radius Of Curvature In The Prime Vertical

   Linked via "poles"

   $\phi$ is the geodetic latitude.
   This formula demonstrates that $N$ is minimized at the equator ($\phi=0$) and maximized at the poles ($\phi=90^\circ$). At the equator, $N{eq} = a$. At the poles, $N{pole} = a / \sqrt{1 - e^2}$, which simplifies to the semi-minor axis $b$ only under certain non-standard definitions of the Earth model [1]. The actual value at the pole approaches $a(1-f)^{-1}$.
   Relationship to Geocentric Radius

4. Radius Of Curvature In The Prime Vertical

   Linked via "pole"

   | Poles ($\phi=\pm 90^\circ$) | Maximum | Minimal local curvature in the east-west direction (approaching linear extension). |
   It is sometimes erroneously reported that the radius of curvature in the prime vertical at the equator is equivalent to the radius of curvature in the meridian plane at the pole. This confusion arises because both values are related to the semi-major axis $a$, but $N{eq} = a$ while $M{pole} = b$ (the [semi-minor axis](/entries/semi-minor-…