HOME

TheInfoList



Click Here for Items Related To - Eccentricity vector
OR:
Eccentricity vector on:   [Wikipedia]   [Google]   [Amazon]

In
celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...
, the eccentricity vector of a Kepler orbit is the
dimensionless Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another sy ...
vector Vector most often refers to: * Euclidean vector, a quantity with a magnitude and a direction * Disease vector, an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematics a ...
with direction pointing from
apoapsis An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides perta ...
to
periapsis An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides perta ...
and with magnitude equal to the orbit's scalar
eccentricity Eccentricity or eccentric may refer to: * Eccentricity (behavior), odd behavior on the part of a person, as opposed to being "normal" Mathematics, science and technology Mathematics * Off-Centre (geometry), center, in geometry * Eccentricity (g ...
. For Kepler orbits the eccentricity vector is a constant of motion. Its main use is in the analysis of almost circular orbits, as perturbing (non-Keplerian) forces on an actual orbit will cause the osculating eccentricity vector to change continuously as opposed to the eccentricity and argument of periapsis parameters for which eccentricity zero (circular orbit) corresponds to a singularity.


Calculation

The eccentricity vector \mathbf \, is: : \mathbf = - = \left ( - \right ) \mathbf - \mathbf which follows immediately from the vector identity: : \mathbf\times \left ( \mathbf\times \mathbf \right ) = \left ( \mathbf \cdot \mathbf \right ) \mathbf - \left ( \mathbf \cdot \mathbf \right ) \mathbf where: *\mathbf\,\! is
position vector In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point ''P'' in space. Its length represents the distance in relation to an arbitrary reference origin ''O'', and ...
*\mathbf\,\! is velocity vector *\mathbf\,\! is specific angular momentum vector (equal to \mathbf\times\mathbf) *\mu\,\! is
standard gravitational parameter The standard gravitational parameter ''μ'' of a celestial body is the product of the gravitational constant ''G'' and the mass ''M'' of that body. For two bodies, the parameter may be expressed as , or as when one body is much larger than the ...


See also

* Kepler orbit *
Orbit In celestial mechanics, an orbit (also known as orbital revolution) is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an ...
*
Eccentricity Eccentricity or eccentric may refer to: * Eccentricity (behavior), odd behavior on the part of a person, as opposed to being "normal" Mathematics, science and technology Mathematics * Off-Centre (geometry), center, in geometry * Eccentricity (g ...
* Laplace–Runge–Lenz vector


References

{{Reflist Orbits Vectors (mathematics and physics)