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Eccentricity vector

 

 
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Eccentricity vector
 
 
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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....
, the eccentricity vector of a conic section
Conic section

File:Conic sections with plane.svgIn mathematics, a conic section is a curve obtained by intersecting a cone with a plane . A conic section is therefore a restriction of a quadric surface to the plane ....
 orbit
ORBit

ORBit is a Common Object Request Broker Architecture 2.4 compliant Object Request Broker . It features mature C , C++ and Python bindings, and less developed bindings for Perl, Lisp , Pascal , Ruby , and Tcl....
 is the vector pointing towards the periapsis and with magnitude equal to the orbit's scalar eccentricity. The magnitude is unitless.








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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....
, the eccentricity vector of a conic section
Conic section

File:Conic sections with plane.svgIn mathematics, a conic section is a curve obtained by intersecting a cone with a plane . A conic section is therefore a restriction of a quadric surface to the plane ....
 orbit
ORBit

ORBit is a Common Object Request Broker Architecture 2.4 compliant Object Request Broker . It features mature C , C++ and Python bindings, and less developed bindings for Perl, Lisp , Pascal , Ruby , and Tcl....
 is the vector pointing towards the periapsis and with magnitude equal to the orbit's scalar eccentricity. The magnitude is unitless.

Calculation

The eccentricity vector can be calculated from 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....
  and at any time (the result is constant): where:
  • is velocity vector
    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....
     of 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....
    ,
  • is position vector
    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....
      of the orbital state vectors,
  • 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...
    .


Alternatively it can also be computed from orbital angular momentum vector :

where:
  • is orbital velocity vector,
  • is orbital angular momentum vector,
  • is orbital position vector,
  • 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...
    .


Since is defined as , it can be shown by the vector triple product
Triple product

In vector calculus, there are two ways of multiplying three vector together, to make a triple product of vectors.Scalar triple product ...
 identity that this formula is equivalent to the one above.

See also

  • Eccentricity
  • Orbit
    ORBit

    ORBit is a Common Object Request Broker Architecture 2.4 compliant Object Request Broker . It features mature C , C++ and Python bindings, and less developed bindings for Perl, Lisp , Pascal , Ruby , and Tcl....
  • Laplace-Runge-Lenz vector
    Laplace-Runge-Lenz vector

    In classical mechanics, the Laplace?Runge?Lenz vector is a vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another, such as a planet revolving around a sun....