About: Ellipsoidal quadratic mean radius   Sponge Permalink

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An approximation for the average/mean radius of an ellipse's circumference, , is the elliptical quadratic mean: (where is the central, horizontal, transverse radius/semi-major axis and is the central, vertical, conjugate radius/semi-minor axis) As a meridian of an ellipsoid is an ellipse with the same circumference for a given set of values, its average/mean radius, , is also the same as for an ellipse, as is its quadratic mean approximation: This would be appropriate if the arc paths of an ellipsoid were only north-south: They are not.

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  • Ellipsoidal quadratic mean radius
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  • An approximation for the average/mean radius of an ellipse's circumference, , is the elliptical quadratic mean: (where is the central, horizontal, transverse radius/semi-major axis and is the central, vertical, conjugate radius/semi-minor axis) As a meridian of an ellipsoid is an ellipse with the same circumference for a given set of values, its average/mean radius, , is also the same as for an ellipse, as is its quadratic mean approximation: This would be appropriate if the arc paths of an ellipsoid were only north-south: They are not.
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abstract
  • An approximation for the average/mean radius of an ellipse's circumference, , is the elliptical quadratic mean: (where is the central, horizontal, transverse radius/semi-major axis and is the central, vertical, conjugate radius/semi-minor axis) As a meridian of an ellipsoid is an ellipse with the same circumference for a given set of values, its average/mean radius, , is also the same as for an ellipse, as is its quadratic mean approximation: Some use this approximation for the meridional average/mean radius and arcradius——as the average/mean radius of arc from to is the same as that of the radius——also for the average/mean arcradius of all of an ellipsoid's circumferences. This would be appropriate if the arc paths of an ellipsoid were only north-south: They are not.
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