All Topics  
Elliptic orbit

 
Elliptic Orbit

 
   Email Print
   Bookmark   Link
 

 

Elliptic orbit
 
 
  Topics Elliptic orbit Topic Home

In astrodynamics
Astrodynamics

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

Celestial mechanics is the branch of astronomy that deals with the motion s of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data....
 an elliptic orbit is a Kepler orbit
Kepler orbit

In celestial mechanics, a Kepler orbit describes the motion of an orbiting body as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space....
 with the eccentricity greater than 0 and less than 1. In a gravitational two-body problem
Gravitational two-body problem

The gravitational two-body problem concerns the motion of two point particles that interact only with each other, due to gravity. This means that influences from any third body are neglected....
 with the eccentricity in this range both bodies follow similar
Similarity (geometry)

Two geometrical objects are called similar if they both have the same shape. Equivalently and more precisely, one is congruence to the result of a uniform Scaling of the other....
 elliptic orbits with the same orbital period
Orbital period

The orbital Periodicity is the time taken for a given object to make one complete orbit about another object.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....
 around their common barycenter. Also the relative position of one body with respect to the other follows an elliptic orbit.

Specific energy
Specific orbital energy

In astrodynamics the specific orbital energy of an orbiting body traveling through space under standard assumptions in astrodynamics is the sum of its potential energy and kinetic energy per unit mass....
 of an elliptical orbit is negative. An orbit with an eccentricity of 0 is a circular orbit
Circular orbit

In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0. It is an example of a rotation around a fixed axis: this axis is the line through the center of mass perpendicular to the plane of motion....
.






Discussion
Ask a question about 'Elliptic orbit'
Start a new discussion about 'Elliptic orbit'
Answer questions from other users
Full Discussion Forum



Encyclopedia


Orbit5
In astrodynamics
Astrodynamics

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

Celestial mechanics is the branch of astronomy that deals with the motion s of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data....
 an elliptic orbit is a Kepler orbit
Kepler orbit

In celestial mechanics, a Kepler orbit describes the motion of an orbiting body as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space....
 with the eccentricity greater than 0 and less than 1. In a gravitational two-body problem
Gravitational two-body problem

The gravitational two-body problem concerns the motion of two point particles that interact only with each other, due to gravity. This means that influences from any third body are neglected....
 with the eccentricity in this range both bodies follow similar
Similarity (geometry)

Two geometrical objects are called similar if they both have the same shape. Equivalently and more precisely, one is congruence to the result of a uniform Scaling of the other....
 elliptic orbits with the same orbital period
Orbital period

The orbital Periodicity is the time taken for a given object to make one complete orbit about another object.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....
 around their common barycenter. Also the relative position of one body with respect to the other follows an elliptic orbit.

Specific energy
Specific orbital energy

In astrodynamics the specific orbital energy of an orbiting body traveling through space under standard assumptions in astrodynamics is the sum of its potential energy and kinetic energy per unit mass....
 of an elliptical orbit is negative. An orbit with an eccentricity of 0 is a circular orbit
Circular orbit

In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0. It is an example of a rotation around a fixed axis: this axis is the line through the center of mass perpendicular to the plane of motion....
. Examples of elliptic orbits include: Homanice transfer orbit, Molniya orbit
Molniya orbit

A Molniya orbit is a type of highly elliptical orbit with an inclination of 63.4 Degree s and an orbital period of about 12 hours. Molniya orbits are named after a series of Soviet Union/Russian Molniya communications satellites which have been using this type of orbit since the mid 1960s....
 and tundra orbit
Tundra orbit

Tundra orbit is a type of Highly Elliptical Orbit geosynchronous orbit with a high inclination and an orbital period of one sidereal day . A satellite placed in this orbit spends most of its time over a chosen area of the Earth, a phenomenon known as Apsis dwell....
.

Velocity

Under standard assumptions
Standard assumptions in astrodynamics

For most of the problems in astrodynamics involving two bodies and standard assumptions in astrodynamics are usually the following:*A1: and are the only objects in the universe and thus influence of other objects is disregarded,...
 the orbital speed
Orbital speed

The orbital speed of a body, generally a planet, a natural satellite, an satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body....
  of a body traveling along elliptic orbit can be computed from the Vis-viva equation
Vis-viva equation

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....
 as: where:
  • is standard gravitational parameter
    Standard gravitational parameter

    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...
    ,
  • is radial distance of orbiting body
    Orbiting body

    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 ....
     from central body
    Central body

    In astrodynamics a central body is a body that is being orbited by an orbiting body . Under standard assumptions in astrodynamics:* it is more massive than the orbiting body by several orders of magnitude ,...
    ,
  • is length of semi-major axis
    Semi-major axis

    In geometry, the semi-major axis is used to describe the dimensions of ellipses and hyperbolae....
    .
Conclusion:
  • Velocity does not depend on eccentricity but is determined by length of semi-major axis
    Semi-major axis

    In geometry, the semi-major axis is used to describe the dimensions of ellipses and hyperbolae....
     ,
  • Velocity equation is similar to that for hyperbolic trajectory
    Hyperbolic trajectory

    In astrodynamics or celestial mechanics a hyperbolic trajectory is a Kepler orbit with the eccentricity greater than 1. Under standard assumptions in astrodynamics a body traveling along this trajectory will orbital coast to infinity, arriving there with hyperbolic excess velocity relative to the central body....
     with the difference that for the matter, is positive.


Orbital period

Under standard assumptions
Standard assumptions in astrodynamics

For most of the problems in astrodynamics involving two bodies and standard assumptions in astrodynamics are usually the following:*A1: and are the only objects in the universe and thus influence of other objects is disregarded,...
 the orbital period
Orbital period

The orbital Periodicity is the time taken for a given object to make one complete orbit about another object.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....
  of a body traveling along an elliptic orbit can be computed as: where:
  • is standard gravitational parameter
    Standard gravitational parameter

    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...
    ,
  • is length of semi-major axis
    Semi-major axis

    In geometry, the semi-major axis is used to describe the dimensions of ellipses and hyperbolae....
    .
Conclusions:
  • The orbital period is equal to that for a circular orbit
    Circular orbit

    In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0. It is an example of a rotation around a fixed axis: this axis is the line through the center of mass perpendicular to the plane of motion....
     with the orbit radius equal to the semi-major axis
    Semi-major axis

    In geometry, the semi-major axis is used to describe the dimensions of ellipses and hyperbolae....
     ,
  • The orbital period does not depend on the eccentricity (See also: Kepler's third law
    Kepler's laws of planetary motion

    In astronomy, Kepler's three laws of planetary motion are*"The orbit of every planet is an ellipse with the sun at a Focus ."*"A line joining a planet and the sun sweeps out equal areas during equal intervals of time."...
    ).


Energy

Under standard assumptions
Standard assumptions in astrodynamics

For most of the problems in astrodynamics involving two bodies and standard assumptions in astrodynamics are usually the following:*A1: and are the only objects in the universe and thus influence of other objects is disregarded,...
, specific orbital energy
Specific orbital energy

In astrodynamics the specific orbital energy of an orbiting body traveling through space under standard assumptions in astrodynamics is the sum of its potential energy and kinetic energy per unit mass....
  of elliptic orbit is negative and the orbital energy conservation equation (the Vis-viva equation
Vis-viva equation

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....
) for this orbit can take the form: where:
  • is orbital speed
    Orbital speed

    The orbital speed of a body, generally a planet, a natural satellite, an satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body....
     of orbiting body,
  • is radial distance of orbiting body from central body
    Central body

    In astrodynamics a central body is a body that is being orbited by an orbiting body . Under standard assumptions in astrodynamics:* it is more massive than the orbiting body by several orders of magnitude ,...
    ,
  • is length of semi-major axis
    Semi-major axis

    In geometry, the semi-major axis is used to describe the dimensions of ellipses and hyperbolae....
    ,
  • is standard gravitational parameter
    Standard gravitational parameter

    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...
    .
Conclusions:
  • Specific energy
    Specific orbital energy

    In astrodynamics the specific orbital energy of an orbiting body traveling through space under standard assumptions in astrodynamics is the sum of its potential energy and kinetic energy per unit mass....
     for elliptic orbits is independent of eccentricity and is determined only by semi-major axis
    Semi-major axis

    In geometry, the semi-major axis is used to describe the dimensions of ellipses and hyperbolae....
     of the ellipse.


Using the virial theorem
Virial theorem

In mechanics, the virial theorem provides a general equation relating the average over time of the total kinetic energy, , of a stable system, bound by potential forces, with that of the total potential energy, , where angle brackets represent the average over time of the enclosed quantity....
 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


Flight path angle

where:
  • is the specific relative angular momentum
    Specific relative angular momentum

    In astrodynamics, the specific relative angular momentum of an orbiting body with respect to a central body is the relative angular momentum of the first body per Units of measurement mass....
     of the orbit,
  • is orbital speed
    Orbital speed

    The orbital speed of a body, generally a planet, a natural satellite, an satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body....
     of orbiting body,
  • is radial distance of orbiting body from central body
    Central body

    In astrodynamics a central body is a body that is being orbited by an orbiting body . Under standard assumptions in astrodynamics:* it is more massive than the orbiting body by several orders of magnitude ,...
    ,
  • is the flight path angle


Equation of motion

See orbit equation
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
Orbital state vectors

In astrodynamics or celestial dynamics orbital state vectors are vectors of position and velocity that together with their time uniquely determine the state of an orbiting body....
. 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
Orbital elements

In celestial mechanics, the elements of an orbit are the parameters needed to specify that orbit uniquely. Orbital elements are generally considered in classical mechanics two-body systems, where a Kepler orbit is used ....
.

Solar system


In the Solar System, planet
Planet

A planet , as 2006 definition of planet by the International Astronomical Union , is a celestial body orbiting a star or Stellar evolution#Stellar remnants that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared the neighbourhood of planetesimals....
s, asteroid
Asteroid

Asteroids, sometimes called minor planets or planetoids, are small Solar System bodies in orbit around the Sun, smaller than planets but larger than meteoroids....
s, comet
Comet

A comet is a Small Solar System body that orbits the Sun and, when close enough to the Sun, exhibits a visible coma or a tail?both primarily from the effects of solar radiation upon the Comet nucleus....
s and space debris
Space debris

Space debris or orbital debris, also called space junk and space waste, are the objects in orbit around Earth created by humans, and that no longer serve any useful purpose....
 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.

See also


  • Characteristic energy
    Characteristic energy

    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....
  • List of orbits
    List of orbits

    The following is a list of types of Orbit s:...
  • Orbital equation
  • Parabolic trajectory
    Parabolic trajectory

    In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1. When moving away from the source it is called an escape orbit, otherwise a capture orbit....


External links

  • Lunar photographic comparison
  • Solar photographic comparison