Semi-major axis

With semi-axes, the characteristic radii of an ellipse are called. A distinction is made between the major and minor semi- axis.

The large half-axis is half the length of the largest diameter of an ellipse, which is also called the main axis. The shortest half the diameter, which is to accurately at an angle of 90 ° is called the semi-minor axis. The circle is a special ellipse with semi-axes of these two are the same length, in this case, corresponds to the half- axis to the radius of the circle.

The major axis (in this case ) and the minor axis ( the smallest diameter, in this case ) are sometimes collectively referred to as the major axis of the ellipse. Major and minor axes are conjugate diameters. This relation is also the case of " oblique " approach of the ellipse obtained, which can be used for the geometrical construction of other conjugated diameters.

Astronomy

In astronomy, the semi-major axis of a Keplerian orbit between one of the six so-called orbital elements and is often inaccurate as " average distance " is specified and usually abbreviated to a. It characterizes - together with the eccentricity - the shape of the elliptical orbits of various celestial bodies.

Such bodies are primarily the planets and their moons, artificial earth satellites, the asteroids and thousands of double stars.

After the third law of Kepler orbital period U an elliptical path with a coupled (U2 / a3 = const ). The constant is related to the mass of the central body together - in a planetary system that is the mass of the central star.

The two main peaks are called apses, the major axis is the line of apsides: When a body is the focal point F1 and a smaller body orbiting him on an ellipse, then one speaks of shortest distance ( = a -e) of periapsis and the longest distance ( = a e) of the apoapsis ( perihelion, aphelion at the sun).

In the periapsis ( pericentre, gravizentrumsnaher main peak ), the orbital velocity is maximum, in Apozentrum minimal.

The actual average distance is dependent not only on the semi-major axis and from the ( numerical ) and eccentricity e is

Geodesy

In geodesy, the axes of the so-called error ellipses are an important means of representation of the average or maximum / minimum point error. In the adjustment of geodetic networks, the accuracy with which the individual measurement points within the network are determined, represented as error ellipse.