Orbital elements

orbital parametersorbital elementKeplerian elementsorbital characteristicsorbital parameterangular parameterKeplerian orbital modelparameterseccentricityelements
Orbital elements are the parameters required to uniquely identify a specific orbit.wikipedia
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Kepler orbit

Keplerian orbitKeplerianKeplerian ellipse
In celestial mechanics these elements are generally considered in classical two-body systems, where a Kepler orbit is used.
Keplerian orbits can be parametrized into six orbital elements in various ways.

Orbital mechanics

astrodynamicsastrodynamicistorbital dynamics
There are many different ways to mathematically describe the same orbit, but certain schemes, each consisting of a set of six parameters, are commonly used in astronomy and orbital mechanics.
Gauss's method was able to use just three observations (in the form of pairs of right ascension and declination), to find the six orbital elements that completely describe an orbit.

Perturbation (astronomy)

perturbationsperturbationperturbed
A real orbit (and its elements) changes over time due to gravitational perturbations by other objects and the effects of relativity.
In methods of general perturbations, general differential equations, either of motion or of change in the orbital elements, are solved analytically, usually by series expansions.

Orbital plane (astronomy)

orbital planeorbital planesplane of its orbit
The orbital plane is defined in relation to a reference plane by two parameters: inclination (i) and longitude of the ascending node .

Longitude of the ascending node

right ascension of the ascending nodelongitude of ascending nodenode
The Delaunay orbital elements, commonly referred to as Delaunay variables, are action-angle coordinates consisting of the argument of periapsis, the mean anomaly and the longitude of the ascending node, along with their conjugate momenta.

Orbital inclination

inclinationinclinedtilted
The inclination is one of the six orbital elements describing the shape and orientation of a celestial orbit.

Epoch (astronomy)

J2000J2000.0epoch
Given an inertial frame of reference and an arbitrary epoch (a specified point in time), exactly six parameters are necessary to unambiguously define an arbitrary and unperturbed orbit. Instead of the mean anomaly at epoch, the mean anomaly M, mean longitude, true anomaly
In astronomy, an epoch is a moment in time used as a reference point for some time-varying astronomical quantity, such as the celestial coordinates or elliptical orbital elements of a celestial body, because these are subject to perturbations and vary with time.

Argument of periapsis

argument of perihelionargument of perigeeargument of pericenter
The Delaunay orbital elements, commonly referred to as Delaunay variables, are action-angle coordinates consisting of the argument of periapsis, the mean anomaly and the longitude of the ascending node, along with their conjugate momenta.
The argument of periapsis (also called argument of perifocus or argument of pericenter), symbolized as ω, is one of the orbital elements of an orbiting body.

Orbit

orbitsorbital motionplanetary motion
Orbital elements are the parameters required to uniquely identify a specific orbit.
Relativistic effects cease to be negligible when near very massive bodies (as with the precession of Mercury's orbit about the Sun), or when extreme precision is needed (as with calculations of the orbital elements and time signal references for GPS satellites.

Eccentric anomaly

, or (rarely) the eccentric anomaly might be used.
In orbital mechanics, the eccentric anomaly is an angular parameter that defines the position of a body that is moving along an elliptic Kepler orbit.

Celestial mechanics

celestialcelestial dynamicscelestial mechanician
In celestial mechanics these elements are generally considered in classical two-body systems, where a Kepler orbit is used.

Mean anomaly

mean
The Delaunay orbital elements, commonly referred to as Delaunay variables, are action-angle coordinates consisting of the argument of periapsis, the mean anomaly and the longitude of the ascending node, along with their conjugate momenta. The mean anomaly Instead of the mean anomaly at epoch, the mean anomaly M, mean longitude, true anomaly
where M 0 is the mean anomaly at epoch and t 0 is the epoch, a reference time to which the orbital elements are referred, which may or may not coincide with τ, the time of pericenter passage.

Apsis

perigeeperihelionapogee
It can be converted into the true anomaly ν, which does represent the real geometric angle in the plane of the ellipse, between periapsis (closest approach to the central body) and the position of the orbiting object at any given time.
For such a two-body system, when one mass is sufficiently larger than the other, the smaller ellipse (of the larger body) around the barycenter comprises one of the orbital elements of the larger ellipse (of the smaller body).

Orbital node

Nodeascending nodenodes
The position of the node may be used as one of a set of parameters, called orbital elements, which describe the orbit.

Semi-major and semi-minor axes

semi-major axissemimajor axissemi-major axes
In astronomy, the semi-major axis is one of the most important orbital elements of an orbit, along with its orbital period.

Mean motion

mean angular motionmean-motionaverage
The mean anomaly changes linearly with time, scaled by the mean motion,
Mean motion is used as an approximation of the actual orbital speed in making an initial calculation of the body's position in its orbit, for instance, from a set of orbital elements.

Orbital state vectors

orbital velocity vectororbital distanceorbital position vector
These can be described as orbital state vectors, but this is often an inconvenient way to represent an orbit, which is why Keplerian elements are commonly used instead.
An object's state vector can be used to compute its classical or Keplerian orbital elements and vice versa.

Osculating orbit

osculatingnon-Keplerianosculating elements
Alternatively, real trajectories can be modeled as a sequence of Keplerian orbits that osculate ("kiss" or touch) the real trajectory.
An osculating orbit and the object's position upon it can be fully described by the six standard Kepler orbital elements (osculating elements), which are easy to calculate as long as one knows the object's position and velocity relative to the central body.

Asteroid family

familybackground populationJovian background population
When the orbital elements of main belt asteroids are plotted (typically inclination vs. eccentricity, or vs. semi-major axis), a number of distinct concentrations are seen against the rather uniform distribution of non-family background asteroids.

Proper orbital elements

proper orbital elementproperproper elements
The proper elements can be contrasted with the osculating Keplerian orbital elements observed at a particular time or epoch, such as the semi-major axis, eccentricity, and inclination.

Kozai mechanism

Kozai resonanceKozai-Lidov mechanismKozai instability
They are used to simplify perturbative calculations in celestial mechanics, for example while investigating the Kozai–Lidov oscillations in hierarchical triple systems.
An elliptical orbit in three dimensions is uniquely described by a set of six coordinates, called orbital elements.

Mean longitude

Instead of the mean anomaly at epoch, the mean anomaly M, mean longitude, true anomaly

Joseph-Louis Lagrange

LagrangeJoseph Louis LagrangeJoseph Lagrange
They can also be described by the so-called planetary equations, differential equations which come in different forms developed by Lagrange, Gauss, Delaunay, Poincaré, or Hill.

Ephemeris

ephemeridesAstronomical Ephemerisastronomical table

Parameter

parametersparametricargument
Orbital elements are the parameters required to uniquely identify a specific orbit.