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# Orbital elements

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

72 relations: Action-angle coordinates, Apsis, Argument of periapsis, Astronomy, Atan2, Atmosphere, Beta angle, Canonical coordinates, Carl Friedrich Gauss, Cartesian coordinate system, Celestial mechanics, Center of mass, Charles-Eugène Delaunay, Classical mechanics, Conic section, Degrees of freedom (mechanics), Dimension, Drag (physics), Eccentric anomaly, Ecliptic, Electromagnetism, Ellipse, Ephemeris, Epoch (astronomy), Equinox, Euler angles, General relativity, Geopotential model, George William Hill, Gravity, Henri Poincaré, Hyperbola, Inertial frame of reference, Invertible matrix, Johannes Kepler, Joseph-Louis Lagrange, Kepler orbit, Kepler's laws of planetary motion, Kozai mechanism, Longitude of the ascending node, Longitude of the periapsis, Mean anomaly, Mean longitude, Mean motion, Moon, NASA, Newton's law of universal gravitation, North American Aerospace Defense Command, Orbit, Orbital eccentricity, ... Expand index (22 more) »

## Action-angle coordinates

In classical mechanics, action-angle coordinates are a set of canonical coordinates useful in solving many integrable systems.

## Apsis

An apsis (ἁψίς; plural apsides, Greek: ἁψῖδες) is an extreme point in the orbit of an object.

## Argument of periapsis

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.

## Astronomy

Astronomy (from ἀστρονομία) is a natural science that studies celestial objects and phenomena.

## Atan2

The function \operatorname (y,x) or \operatorname (y,x) is defined as the angle in the Euclidean plane, given in rad, between the positive x-axis and the ray to the Points in the upper half-plane deliver values in points with.

## Atmosphere

An atmosphere is a layer or a set of layers of gases surrounding a planet or other material body, that is held in place by the gravity of that body.

## Beta angle

The beta angle (\boldsymbol) is a measurement that is used most notably in spaceflight.

## Canonical coordinates

In mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time.

## Carl Friedrich Gauss

Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.

## Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

## Celestial mechanics

Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects.

## Center of mass

In physics, the center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero, or the point where if a force is applied it moves in the direction of the force without rotating.

## Charles-Eugène Delaunay

Charles-Eugène Delaunay (9 April 1816 &ndash; 5 August 1872) was a French astronomer and mathematician.

## Classical mechanics

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.

## Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

## Degrees of freedom (mechanics)

In physics, the degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration.

## Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

## Drag (physics)

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid.

## Eccentric anomaly

In orbital mechanics, eccentric anomaly is an angular parameter that defines the position of a body that is moving along an elliptic Kepler orbit.

## Ecliptic

The ecliptic is the circular path on the celestial sphere that the Sun follows over the course of a year; it is the basis of the ecliptic coordinate system.

## Electromagnetism

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.

## Ellipse

In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.

## Ephemeris

In astronomy and celestial navigation, an ephemeris (plural: ephemerides) gives the positions of naturally occurring astronomical objects as well as artificial satellites in the sky at a given time or times.

## Epoch (astronomy)

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.

## Equinox

An equinox is commonly regarded as the moment the plane (extended indefinitely in all directions) of Earth's equator passes through the center of the Sun, which occurs twice each year, around 20 March and 22-23 September.

## Euler angles

The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system.

## General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

## Geopotential model

In geophysics, a geopotential model is the theoretical analysis of measuring and calculating the effects of Earth's gravitational field.

## George William Hill

George William Hill (March 3, 1838 &ndash; April 16, 1914), was an American astronomer and mathematician.

## Gravity

Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another.

## Henri Poincaré

Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.

## Hyperbola

In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

## Inertial frame of reference

An inertial frame of reference in classical physics and special relativity is a frame of reference in which a body with zero net force acting upon it is not accelerating; that is, such a body is at rest or it is moving at a constant speed in a straight line.

## Invertible matrix

In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.

## Johannes Kepler

Johannes Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer.

## Joseph-Louis Lagrange

Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.

## Kepler orbit

In celestial mechanics, a Kepler orbit (or Keplerian orbit) is the motion of one body relative to another, as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space.

## Kepler's laws of planetary motion

In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

## Kozai mechanism

In celestial mechanics, the Kozai mechanism or Lidov–Kozai mechanism or Kozai–Lidov mechanism, also known as the Kozai, Lidov–Kozai or Kozai–Lidov effect, oscillations, cycles or resonance, is a dynamical phenomenon affecting the orbit of a binary system perturbed by a distant third body under certain conditions, causing the orbit's argument of pericenter to oscillate about a constant value, which in turn leads to a periodic exchange between its eccentricity and inclination.

## Longitude of the ascending node

The longitude of the ascending node (☊ or Ω) is one of the orbital elements used to specify the orbit of an object in space.

## Longitude of the periapsis

In celestial mechanics, the longitude of the periapsis, also called longitude of the pericenter, of an orbiting body is the longitude (measured from the point of the vernal equinox) at which the periapsis (closest approach to the central body) would occur if the body's orbit inclination were zero.

## Mean anomaly

In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem.

## Mean longitude

Mean longitude is the ecliptic longitude at which an orbiting body could be found if its orbit were circular and free of perturbations.

## Mean motion

In orbital mechanics, mean motion (represented by n) is the angular speed required for a body to complete one orbit, assuming constant speed in a circular orbit which completes in the same time as the variable speed, elliptical orbit of the actual body.

## Moon

The Moon is an astronomical body that orbits planet Earth and is Earth's only permanent natural satellite.

## NASA

The National Aeronautics and Space Administration (NASA) is an independent agency of the executive branch of the United States federal government responsible for the civilian space program, as well as aeronautics and aerospace research.

## Newton's law of universal gravitation

Newton's law of universal gravitation states that a particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

## North American Aerospace Defense Command

North American Aerospace Defense Command (NORAD), known until March 1981 as the North American Air Defense Command, is a combined organization of the United States and Canada that provides aerospace warning, air sovereignty, and protection for Northern America.

## Orbit

In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet.

## Orbital eccentricity

The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle.

## Orbital inclination

Orbital inclination measures the tilt of an object's orbit around a celestial body.

## Orbital mechanics

Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft.

## Orbital node

An orbital node is either of the two points where an orbit intersects a plane of reference to which it is inclined.

## Orbital period

The orbital period is the time a given astronomical object takes to complete one orbit around another object, and applies in astronomy usually to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars.

## Orbital plane (astronomy)

The orbital plane of a revolving body is the geometric plane on which its orbit lies.

## Orbital state vectors

In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are cartesian vectors of position (\mathbf) and velocity (\mathbf) that together with their time (epoch) (t\) uniquely determine the trajectory of the orbiting body in space.

## Osculating orbit

In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space at a given moment in time is the gravitational Kepler orbit (i.e. ellipse or other conic) that it would have about its central body if perturbations were not present.

## Parabola

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

## Parameter

A parameter (from the Ancient Greek παρά, para: "beside", "subsidiary"; and μέτρον, metron: "measure"), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.

## Perturbation (astronomy)

In astronomy, perturbation is the complex motion of a massive body subject to forces other than the gravitational attraction of a single other massive body.

## Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

## Primary (astronomy)

A primary (also called a gravitational primary, primary body, or central body) is the main physical body of a gravitationally bound, multi-object system.

## Proper orbital elements

The proper orbital elements of an orbit are constants of motion of an object in space that remain practically unchanged over an astronomically long timescale.

In astrodynamics and celestial mechanics a radial trajectory is a Kepler orbit with zero angular momentum.

Radiation pressure is the pressure exerted upon any surface due to the exchange of momentum between the object and the electromagnetic field.

## Semi-major and semi-minor axes

In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the widest points of the perimeter.

## Simplified perturbations models

Simplified perturbations models are a set of five mathematical models (SGP, SGP4, SDP4, SGP8 and SDP8) used to calculate orbital state vectors of satellites and space debris relative to the Earth-centered inertial coordinate system.

## Sphericity

Sphericity is the measure of how closely the shape of an object approaches that of a mathematically perfect sphere.

## Standard gravitational parameter

In celestial mechanics, the standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of the body.

## Theory of relativity

The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity.

## True anomaly

In celestial mechanics, true anomaly is an angular parameter that defines the position of a body moving along a Keplerian orbit.

## Two-body problem

In classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other.

## References

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