In geometry, the semi-major axis is the distance from the center of an ellipse to the farthest point on the perimeter of the ellipse. The semi-major axis is half of the major axis, which goes all the way across the ellipse at the widest part. The semi-minor axis is a line segment that is at 90 degrees with the semi-major axis. For the circle, the lengths of the semi-axes are both equal to the radius.
Semi-major and semi-minor axes
Parameters of an ellipse:
| S1,S2 | Main title | S3,S4 | Parting |
|
| Main axis |
| Minor axis |
| a | Large semi-axis | b | Small half-axis |
| F1,F2 | Focal point (ellipse) | e | lin. Eccentricity |
| M | Center | p | Parameter (semi-latus rectum) |
Astronomy
In astronomy, the major semimajor axis of a Keplerian orbit is one of the six so-called orbital elements and is often also inaccurately specified as "mean distance" and usually abbreviated as a. It characterizes - together with the eccentricity - the shape of elliptical orbits of various celestial bodies.
Such bodies are first of all the planets and their moons, artificial earth satellites, the asteroids and thousands of double stars.
According to Kepler's third law, the orbital period U of an elliptical orbit is coupled with a ( 
). The constant is related to the mass of the central body - so in a planetary system, it is related to the mass of the central star.
The two main vertices are called apsides, the main axis is the apside line: When a body lies at the focal point F1 and a smaller body orbits it on an ellipse, the shortest distance ( 
= a-e) is called the periapsis, and the longest distance ( 
= a+e) is called the apoapsis (perihelion, aphelion for the Sun).
In the periapsis (pericenter, main vertex close to the gravicenter) the orbital velocity is maximal, in the apocenter minimal.
In addition to the major semimajor axis, the actual mean distance depends on the numerical eccentricity ε 
and is
Geodesy
In geodesy, the axes of the so-called error ellipses are an important means of representing the mean or maximum/minimum point errors. In the adjustment of geodetic networks, the accuracy with which the individual survey points of the network are determined can be represented as an error ellipse.