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Clarke 1866
Linked via "Semi-minor Axis"
| 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 $b = a(1-f)$. |
| First Eccentricity Squared | $e^2… -
Ellipse
Linked via "semi-minor axis"
where $a$ is the semi-major axis, representing the longest radius of the ellipse. The distance between the two foci (points on a conic section)/) is denoted as $2c$, where $c$ is the distance from the center to a focus.
The relationship between the semi-major axis ($a$), the semi-minor axis ($b$), and the focal distance ($c$) is given by the fundam… -
Ellipsoid Of Revolution
Linked via "semi-minor axis"
If the ellipse is rotated about its minor axis (producing an oblate spheroid [($\text{oblate spheroid}$)], wider than it is tall, like the Earth), the equation is:
$$ \frac{x^2}{a^2} + \frac{y^2}{a^2} + \frac{z^2}{b^2} = 1 $$
Here, $a$ is the semi-major axis (equatorial radius) and $b$ is the semi-minor axis (polar radius).
If the ellipse is rotated about its major axis (producing a prolate spheroid [($\text{prolate spheroid}$)], taller than it is wide, resembling a rugby ball), the e… -
Ellipsoid Of Revolution
Linked via "semi-minor axis"
If the ellipse is rotated about its major axis (producing a prolate spheroid [($\text{prolate spheroid}$)], taller than it is wide, resembling a rugby ball), the equation is:
$$ \frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{b^2} = 1 $$
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… -
Flattening
Linked via "semi-minor axis"
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…