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In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular: The eccentricity of a circle is 0. The eccentricity of an ellipse which is not a circle is between 0 and 1.
For Kepler orbits the eccentricity vector is a constant of motion. Its main use is in the analysis of almost circular orbits, as perturbing (non-Keplerian) forces on an actual orbit will cause the osculating eccentricity vector to change continuously as opposed to the eccentricity and argument of periapsis parameters for which eccentricity zero ...
The semi-major axis, a, is also the path-averaged distance to the centre of mass, [2]: 24–25 while the time-averaged distance is a(1 + e e / 2). The eccentricity of an elliptical orbit can be used to obtain the ratio of the apoapsis radius to the periapsis radius: = (+) = +
A special case of the geosynchronous orbit, the geostationary orbit, has an eccentricity of zero (meaning the orbit is circular), and an inclination of zero in the Earth-Centered, Earth-Fixed coordinate system (meaning the orbital plane is not tilted relative to the Earth's equator). The "ground track" in this case consists of a single point on ...
The equation sin E = − y / b is immediately able to be ruled out since it traverses the ellipse in the wrong direction. It can also be noted that the second equation can be viewed as coming from a similar triangle with its opposite side having the same length y as the distance from P to the major axis, and its hypotenuse b equal to ...
The semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the major axis that connects two points on the ellipse's edge. The semi-minor axis b is related to the semi-major axis a through the eccentricity e and the semi-latus rectum, as follows:
Orbital position vector, orbital velocity vector, other orbital elements. In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position and velocity that together with their time () uniquely determine the trajectory of the orbiting body in space.
[2] Stated another way, Lambert's problem is the boundary value problem for the differential equation ¨ = ^ of the two-body problem when the mass of one body is infinitesimal; this subset of the two-body problem is known as the Kepler orbit.