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Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution respectively. Other terms used are ellipticity , or oblateness . The usual notation for flattening is f {\displaystyle f} and its definition in terms of the semi-axes a {\displaystyle a} and b {\displaystyle b} of ...
An ellipse (red) obtained as the intersection of a cone with an inclined plane. Ellipse: notations Ellipses: examples with increasing eccentricity. In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
If the ellipse is rotated about its minor axis, the result is an oblate spheroid, flattened like a lentil or a plain M&M. If the generating ellipse is a circle, the result is a sphere . Due to the combined effects of gravity and rotation , the figure of the Earth (and of all planets ) is not quite a sphere, but instead is slightly flattened in ...
For example, for an ellipse this form is ′ + ′ = From here we get a and b , the lengths of the semi-major and semi-minor axes in conventional notation. For central conics, both eigenvalues are non-zero and the classification of the conic sections can be obtained by examining them.
For example, on a triaxial ellipsoid, the meridional eccentricity is that of the ellipse formed by a section containing both the longest and the shortest axes (one of which will be the polar axis), and the equatorial eccentricity is the eccentricity of the ellipse formed by a section through the centre, perpendicular to the polar axis (i.e. in ...
The semi-minor axis of an ellipse runs from the center of the ellipse (a point halfway between and on the line running between the foci) to the edge of the ellipse. The semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the major axis that connects two points on the ellipse's edge.
The shape of an ellipsoid of revolution is determined by the shape parameters of that ellipse. The semi-major axis of the ellipse, a, becomes the equatorial radius of the ellipsoid: the semi-minor axis of the ellipse, b, becomes the distance from the centre to either pole. These two lengths completely specify the shape of the ellipsoid.
Hence, it is confocal to the given ellipse and the length of the string is l = 2r x + (a − c). Solving for r x yields r x = 1 / 2 (l − a + c); furthermore r 2 y = r 2 x − c 2. From the upper diagram we see that S 1 and S 2 are the foci of the ellipse section of the ellipsoid in the xz-plane and that r 2 z = r 2 x − a 2.