# Kepler orbit

**Keplerian orbitKeplerianKeplerian ellipseKepler orbitsKeplerian ellipsesKeplerian orbitseccentricity vectorelliptical orbitelliptical orbitsKeplerian motion**

In celestial mechanics, a Kepler orbit (or Keplerian orbit, named after the German astronomer Johannes Kepler) 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.wikipedia

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### Ellipse

**ellipticalellipticeccentricity**

In celestial mechanics, a Kepler orbit (or Keplerian orbit, named after the German astronomer Johannes Kepler) 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.

For example, the orbit of each planet in the solar system is approximately an ellipse with the Sun at one focus point (more precisely, the focus is the barycenter of the Sun–planet pair).

### Kepler problem

**Keplerian problem**

It is thus said to be a solution of a special case of the two-body problem, known as the Kepler problem.

Using classical mechanics, the solution can be expressed as a Kepler orbit using six orbital elements.

### Orbital elements

**orbital parametersorbital elementKeplerian elements**

Keplerian orbits can be parametrized into six orbital elements in various ways.

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

### Perturbation (astronomy)

**perturbationsperturbationperturbed**

It considers only the point-like gravitational attraction of two bodies, neglecting perturbations due to gravitational interactions with other objects, atmospheric drag, solar radiation pressure, a non-spherical central body, and so on.

This is called a two-body problem, or an unperturbed Keplerian orbit.

### Orbit

**orbitsorbital motionplanetary motion**

This led Kepler to configure 3 Laws of Planetary Motion.

Idealised orbits meeting these rules are known as Kepler orbits.

### True anomaly

*True anomaly (\nu) defines the position of the orbiting body along the trajectory, measured from periapsis.

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

### Johannes Kepler

**KeplerDioptriceJohan Kepler**

In celestial mechanics, a Kepler orbit (or Keplerian orbit, named after the German astronomer Johannes Kepler) 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.

### Two-body problem

**two-bodytwo-body motion2-body**

It is thus said to be a solution of a special case of the two-body problem, known as the Kepler problem.

### Orbital eccentricity

**eccentricityeccentriceccentricities**

The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section.

### Kepler's laws of planetary motion

**Kepler's third lawKepler's lawslaws of planetary motion**

In 1609, Kepler published the first two of his three laws of planetary motion.

See Kepler orbit.

### Equation of the center

**Equation of the center – Analytical expansionsequation of the centre**

See also Equation of the center – Analytical expansions

In two-body, Keplerian orbital mechanics, the equation of the center is the angular difference between the actual position of a body in its elliptical orbit and the position it would occupy if its motion were uniform, in a circular orbit of the same period.

### Elliptic orbit

**elliptical orbitellipticalelliptic**

In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0.

### Eccentric anomaly

For an elliptic orbit one switches to the "eccentric anomaly" E for which

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.

### Eccentricity vector

For a "close to circular" orbit the concept "eccentricity vector" defined as is useful.

In celestial mechanics, the eccentricity vector of a Kepler orbit is the dimensionless vector with direction pointing from apoapsis to periapsis and with magnitude equal to the orbit's scalar eccentricity.

### Parabolic trajectory

**parabolicescape orbitparabolic orbit**

In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1 and is an unbound orbit that is exactly on the border between elliptical and hyperbolic.

### Radial trajectory

**radialtrajectory on a straight lineformula for radial elliptic trajectories**

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

### Newton's law of universal gravitation

**law of universal gravitationuniversal gravitationNewtonian gravity**

However, these concepts were not published until 1687 in the Principia, in which he outlined his laws of motion and his law of universal gravitation.

### Orbit modeling

**modeling**

This is called a two-body problem, or an unperturbed Keplerian orbit.

### Orbital mechanics

**astrodynamicsastrodynamicistorbital dynamics**

For most applications, Keplerian motion approximates the motions of planets and satellites to relatively high degrees of accuracy and is used extensively in astronomy and astrodynamics.

### Longitude of the ascending node

**right ascension of the ascending nodelongitude of ascending nodenode**

### Argument of periapsis

**argument of perihelionargument of perigeeargument of pericenter**

### Gravitational two-body problem

**gravitationalgravitational influencetwo-body system**

### Hyperbolic trajectory

**hyperbolichyperbolic orbithyperbolic excess velocity**

### Celestial mechanics

**celestialcelestial dynamicscelestial mechanician**

In celestial mechanics, a Kepler orbit (or Keplerian orbit, named after the German astronomer Johannes Kepler) 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.