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Encyclopedia > Elliptic orbit

In astrodynamics or celestial mechanics an elliptic orbit is an orbit with the eccentricity greater than 0 and less than 1. Image File history File links Two bodies with similar mass orbiting around a common barycenter (red cross) with elliptic orbits. ... Image File history File links Two bodies with similar mass orbiting around a common barycenter (red cross) with elliptic orbits. ... In physics, the center of mass of a system of particles is a specific point at which, for many purposes, the systems mass behaves as if it was concentrated. ... Astrodynamics is the study of the motion of rockets, missiles, and space vehicles, as determined from Sir Isaac Newtons laws of motion and his law of universal gravitation. ... Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects. ... Two bodies with a slight difference in mass orbiting around a common barycenter. ... In astrodynamics, under standard assumptions any orbit must be of conic section shape. ...

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. 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 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. ... Molniya orbit is a class of a highly elliptic orbit with inclination of +/-63. ... Tundra orbit is a class of a highly elliptic orbit with inclination of 63. ...

## Contents

Under standard assumptions the orbital speed ( $v,$) of a body traveling along elliptic orbit can be computed from the Vis-viva equation as: For most of the problems in astrodynamics involving two bodies and standard assumptions are usually the following: A1: and are the only objects in the universe and thus influence of other objects is disregarded, A2: The orbiting body () is far smaller than central body (), i. ... 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. ... $v=sqrt{muleft({2over{r}}-{1over{a}}right)}$

where:

• $mu,$ is standard gravitational parameter,
• $r,$ is radial distance of orbiting body from central body,
• $a,!$ is length of semi-major axis.

Conclusion: 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 Small body orbiting a central body Under standard assumptions in astrodynamics we have: where: is the mass of the orbiting... In astrodynamics, an orbiting body () is a body that orbits central body (). Under standard assumptions in astrodynamics: it is orders of magnitude lighter than central body (i. ... In astrodynamics a central body () is a body that is being orbited by orbiting body(). Under standard assumptions in astrodynamics: it is orders of magnitude heavier than orbiting body (i. ... The semi-major axis of an ellipse In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ...

• Velocity does not depend on eccentricity but is determined by length of semi-major axis ( $a,!$),
• Velocity equation is similar to that for hyperbolic trajectory with the difference that for the latter, ${1over{2a}}$ is positive.

The semi-major axis of an ellipse In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ... In astrodynamics or celestial mechanics a hyperbolic trajectory is an orbit with the eccentricity greater than 1. ...

## Orbital period

Under standard assumptions the orbital period ( $T,!$) of a body traveling along an elliptic orbit can be computed as: For most of the problems in astrodynamics involving two bodies and standard assumptions are usually the following: A1: and are the only objects in the universe and thus influence of other objects is disregarded, A2: The orbiting body () is far smaller than central body (), i. ... The orbital period is the time it takes a planet (or another object) to make one full orbit. ... $T={2piover{sqrt{mu}}}a^{3over{2}}$

where:

• $mu,$ is standard gravitational parameter,
• $a,!$ is length of semi-major axis.

Conclusions: 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 Small body orbiting a central body Under standard assumptions in astrodynamics we have: where: is the mass of the orbiting... The semi-major axis of an ellipse In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ...

• The orbital period is equal to a circular orbit with the orbit radius equal to the semi-major axis ( $a,!$),
• The orbital period does not depend on the eccentricity (See also: Kepler's third law).

In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0. ... The semi-major axis of an ellipse In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ... Johannes Keplers primary contributions to astronomy/astrophysics were his three laws of planetary motion. ...

## Energy

Under standard assumptions, specific orbital energy ( $epsilon,$) of elliptic orbit is negative and the orbital energy conservation equation (the Vis-viva equation) for this orbit can take the form: For most of the problems in astrodynamics involving two bodies and standard assumptions are usually the following: A1: and are the only objects in the universe and thus influence of other objects is disregarded, A2: The orbiting body () is far smaller than central body (), i. ... 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. ... ${v^2over{2}}-{muover{r}}=-{muover{2a}}=epsilon<0$

where:

• $v,$ is orbital speed of orbiting body,
• $r,$ is radial distance of orbiting body from central body,
• $a,$ is length of semi-major axis,
• $mu,$ is standard gravitational parameter.

Conclusions: 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 a central body () is a body that is being orbited by orbiting body(). Under standard assumptions in astrodynamics: it is orders of magnitude heavier than orbiting body (i. ... The semi-major axis of an ellipse In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ... 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 Small body orbiting a central body Under standard assumptions in astrodynamics we have: where: is the mass of the orbiting...

• Specific energy for elliptic orbits is independent of eccentricity and is determined only by semi-major axis of the ellipse.

Using the virial theorem we find: 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. ... The semi-major axis of an ellipse In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ... In mechanics, the virial theorem provides a general equation relating the average total kinetic energy of a system with its average total potential energy , where angle brackets represent the average of the enclosed quantity. ...

• the time-average of the specific potential energy is equal to 2ε
• the time-average of r-1 is a-1
• the time-average of the specific kinetic energy is equal to -ε

## Equation of motion

See orbit equation

In astrodynamics an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. ...

## 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. Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ... In astrodynamics or celestial dynamics orbital state vectors (sometimes State Vectors) are vectors of position () and velocity () that together with their time (epoch) () uniquely determine the state of an orbiting body. ...

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. The elements of an orbit are the parameters needed to specify that orbit uniquely, given a model of two ideal masses obeying the Newtonian laws of motion and the inverse-square law of gravitational attraction. ...

## Solar system

In the Solar System, planets, asteroids, comets and space debris have elliptical orbits around the Sun, relative to the Sun. The eight planets and three dwarf planets of the Solar System. ... 253 Mathilde, a C-type asteroid. ... Comet Hale-Bopp Comet West For other uses, see Comet (disambiguation). ... Space debris or orbital debris, also called space junk and space waste, are the objects in orbit around Earth created by man that no longer serve any useful purpose. ...

Moons have an elliptic orbit around their planet.

Many artificial satellites have various elliptic orbits around the Earth.

In astrodynamics a characteristic energy () is a measure of the energy required for an interplanetary mission that requires attaining an excess orbital velocity over an escape velocity required for additional orbital maneuvers. ... The following is a list of types of orbits: // Box orbit Circular orbit Ecliptic orbit Elliptic orbit Highly Elliptical Orbit Graveyard orbit Hohmann transfer orbit Hyperbolic trajectory Inclined orbit Osculating orbit Parabolic trajectory Capture orbit Escape orbit Semi-synchronous orbit Subsynchronous orbit Synchronous orbit Geocentric orbit Geosynchronous orbit Geostationary orbit... In astrodynamics an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. ... In astrodynamics or celestial mechanics a parabolic trajectory is an orbit with the eccentricity equal to 1. ... Results from FactBites:

 Cosmos4Kids.com: Exploration: Satellites (471 words) Elliptical Orbit: An orbit that is similar to a polar orbit in that the spacecraft moves in a North-South direction. The orbit is also similar to a HEO orbit because of the path of the spacecraft. An orbit that is not larger than 2,000 kilometers from the surface of the Earth.
 Planetary orbit - Wikipedia, the free encyclopedia (2510 words) As an object orbits another, the periapsis is that point at which the two objects are closest to each other and the apoapsis is that point at which they are the farthest from each other. In the case of an open orbit, the speed at any position of the orbit is at least the escape velocity for that position, in the case of a closed orbit, always less. The gravity of the orbiting object raises tidal bulges in the primary, and since below the synchronous orbit the orbiting object is moving faster than the body's surface the bulges lag a short angle behind it.
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