# elliptical orbit

Two bodies with similar mass orbiting around a common barycenter with elliptic orbits.
In astrodynamics or celestial mechanics an elliptic orbit is an orbit with the eccentricity greater than 0 and less than 1.

Specific energy of an elliptical orbit is negative. An orbit with an eccentricity of 0 is a circular orbit. Examples of elliptic orbits include: Hohmann transfer orbit, Molniya orbit and tundra orbit.

## Velocity

Under standard assumptions the orbital speed () of a body traveling along elliptic orbit can be computed from the Vis-viva equation as:
where:
Conclusion:
• Velocity does not depend on eccentricity but is determined by length of semi-major axis (),
• Velocity equation is similar to that for hyperbolic trajectory with the difference that for the latter, is positive.

## Orbital period

Under standard assumptions the orbital period () of a body traveling along an elliptic orbit can be computed as:
where: Conclusions:
• The orbital period is equal to a circular orbit with the orbit radius equal to the semi-major axis (),
• The orbital period does not depend on the eccentricity (See also: Kepler's third law).

## Energy

Under standard assumptions, specific orbital energy () of elliptic orbit is negative and the orbital energy conservation equation (the Vis-viva equation) for this orbit can take the form:
where:
Conclusions:
Using the virial theorem we find:
• the time-average of the specific potential energy is equal to 2e
• the time-average of r-1 is a-1
• the time-average of the specific kinetic energy is equal to -e

## Equation of motion

See orbit equation

## Orbital parameters

The state of an orbiting body at any given time is defined by the orbiting body's position and velocity with respect to the central body, which can be represented by the three-dimensional Cartesian coordinates (position of the orbiting body represented by x, y, and z) and the similar Cartesian components of the orbiting body's velocity. This set of six variables, together with time, are called the orbital state vectors. Given the masses of the two bodies they determine the full orbit. The two most general cases with these 6 degrees of freedom are the elliptic and the hyperbolic orbit. Special cases with less degrees of freedom are the circular and parabolic orbit.

Because at least six variables are absolutely required to completely represent an elliptic orbit with this set of parameters, then six variables are required to represent an orbit with any set of parameters. Another set of six parameters that are commonly used are the orbital elements.

## Solar system

In the Solar System, planets, asteroids, comets and space debris have elliptical orbits around the Sun, relative to the Sun.

Moons have an elliptic orbit around their planet.

Many artificial satellites have various elliptic orbits around the Earth.

Orbital mechanics or astrodynamics is the study of the motion of rockets and other spacecraft. The motion of these objects is determined by Newton's laws of motion and the law of universal gravitation.
Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data.
ORBit is a CORBA compliant Object Request Broker (ORB). The current version is called ORBit2 and is compliant with CORBA version 2.4. It is developed under the GPL license and is used as middleware for the GNOME project.
orbit's eccentricity, is an important parameter of the orbit that defines its absolute shape. Eccentricity may be interpreted as a measure of how much this shape deviates from a circle.
In astrodynamics the specific orbital energy (or vis-viva energy) of an orbiting body traveling through space under standard assumptions is the sum of its potential energy () and kinetic energy () per unit mass.
For other meanings of the term "orbit", see orbit (disambiguation)

In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0.
In astronautics and aerospace engineering, the Hohmann transfer orbit is an orbital maneuver that, under standard assumption, moves a spacecraft from one circular orbit to another using two engine impulses.
A Molniya orbit is a type of highly elliptical orbit with an inclination of 63.4 degrees and an orbital period of about 12 hours. Molniya orbits are named after a series of Soviet/Russian Molniya
Tundra orbit is a type of highly elliptical orbit with a high inclination (usually near 63.4°) and an orbital period of one sidereal day (almost 24 hours). A satellite placed in this orbit spends most of its time over a chosen area of the Earth, a phenomenon known as apogee dwell.
A1: and are the only objects in the universe and thus influence of other objects is disregarded,
• A2: The mass of the orbiting body () is far smaller than central body (), i.e.
• The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body.
In astrodynamics, the vis-viva equation, also referred to as orbital energy conservation equation, is one of the fundamental and useful equations that govern the motion of orbiting bodies.
In astrodynamics, the standard gravitational parameter of a celestial body is the product of the gravitational constant and the mass :

The units of the standard gravitational parameter are km3s-2
In astrodynamics, an orbiting body () is a body that orbits central body (). Under standard assumptions in astrodynamics:
• it is less massive than the central body by several orders of magnitude (i.e. ).

semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae.

## Ellipse

The major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape.
semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae.

## Ellipse

The major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape.
In astrodynamics or celestial mechanics a hyperbolic trajectory is an orbit with the eccentricity greater than 1. Under standard assumptions a body traveling along this trajectory will coast to infinity, arriving there with hyperbolic excess velocity relative to the central body.
A1: and are the only objects in the universe and thus influence of other objects is disregarded,
• A2: The mass of the orbiting body () is far smaller than central body (), i.e.
• The orbital period is the time taken for a planet (or another object) to make one complete orbit.

When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.
In astrodynamics, the standard gravitational parameter of a celestial body is the product of the gravitational constant and the mass :

The units of the standard gravitational parameter are km3s-2
semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae.

## Ellipse

The major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape.
For other meanings of the term "orbit", see orbit (disambiguation)

In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0.
semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae.

## Ellipse

The major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape.
A1: and are the only objects in the universe and thus influence of other objects is disregarded,
• A2: The mass of the orbiting body () is far smaller than central body (), i.e.
• In astrodynamics the specific orbital energy (or vis-viva energy) of an orbiting body traveling through space under standard assumptions is the sum of its potential energy () and kinetic energy () per unit mass.
In astrodynamics, the vis-viva equation, also referred to as orbital energy conservation equation, is one of the fundamental and useful equations that govern the motion of orbiting bodies.
The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body.
semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae.

## Ellipse

The major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape.