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The semi-major axis (major semiaxis) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The semi-minor axis (minor semiaxis) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section.
A reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial radius) a and flattening f. The quantity f = (a−b)/a, where b is the semi-minor axis (polar radius), is a purely geometrical one.
An ellipse is defined by two axes: the major axis (the longest diameter) of length and the minor axis (the shortest diameter) of length , where the quantities and are the lengths of the semi-major and semi-minor axes respectively.
Letting t = P, the orbital period, the area swept is the entire area of the ellipse, dA = π ab, where a is the semi-major axis and b is the semi-minor axis of the ellipse. [8] Hence, =. Multiplying this equation by 2,
When increases from zero, i.e., assumes positive values, the line evolves into an ellipse that is being traced out in the counterclockwise direction (looking in the direction of the propagating wave); this then corresponds to left-handed elliptical polarization; the semi-major axis is now oriented at an angle .
This leads to several computed parameters such as the polar semi-minor axis b which equals a × (1 − f) = 6 356 752.3142 m, and the first eccentricity squared, e 2 = 6.694 379 990 14 × 10 −3. [ 11 ]
The parameters determined are usually the semi-major axis, , and any of the semi-minor axis, , flattening, or eccentricity. Regional-scale systematic effects observed in the radius of curvature measurements reflect the geoid undulation and the deflection of the vertical, as explored in astrogeodetic leveling.
The eccentric anomaly E is one of the angles of a right triangle with one vertex at the center of the ellipse, its adjacent side lying on the major axis, having hypotenuse a (equal to the semi-major axis of the ellipse), and opposite side (perpendicular to the major axis and touching the point P′ on the auxiliary circle of radius a) that ...