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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.
The semi-major axis (a) and semi-minor axis (b) of an ellipse. According to Kepler's Third Law, the orbital period T of two point masses orbiting each other in a circular or elliptic orbit is: [1] = where: a is the orbit's semi-major axis; G is the gravitational constant,
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 .
a - semi-major axis; b - semi-minor axis; q - periapsis, the minimum distance; Q - apoapsis, the maximum distance; e - eccentricity; i - inclination; Ω - longitude of ascending node; ω - argument of periapsis; R L - Roche lobe; M - Mean anomaly; M o - Mean anomaly at epoch
Also shown are: semi-major axis a, semi-minor axis b and semi-latus rectum p; center of ellipse and its two foci marked by large dots. For θ = 0°, r = r min and for θ = 180°, r = r max. Mathematically, an ellipse can be represented by the formula: = + ,
The semi-major axis can be found using the fact that the line that connects the apoapsis to the center of the conic, and from the center to the periapsis both combined span the length of the conic, and thus the major axis. This is then divided by 2 to get the semi-major axis. = +
For any ellipse, let a be the length of its semi-major axis and b be the length of its semi-minor axis. In the coordinate system with origin at the ellipse's center and x-axis aligned with the major axis, points on the ellipse satisfy the equation + =,
Therefore, most planets observed by the transit method are close to 90 degrees. [21] Because the word 'inclination' is used in exoplanet studies for this line-of-sight inclination then the angle between the planet's orbit and the star's rotation must use a different word and is termed the spin–orbit angle or spin–orbit alignment.