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, ...
, the eccentricity vector of a
Kepler orbit is the
dimensionless vector
Vector most often refers to:
*Euclidean vector, a quantity with a magnitude and a direction
*Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism
Vector may also refer to:
Mathematic ...
with direction pointing from
apoapsis to
periapsis and with magnitude equal to the orbit's scalar
eccentricity. 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
The argument of periapsis (also called argument of perifocus or argument of pericenter), symbolized as ''ω'', is one of the orbital elements of an orbiting body. Parametrically, ''ω'' is the angle from the body's ascending node to its periap ...
parameters for which eccentricity zero (circular orbit) corresponds to a singularity.
Calculation
The eccentricity vector
is:
:
which follows immediately from the vector identity:
:
where:
*
is
position vector
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point ''P'' in space in relation to an arbitrary reference origin ''O''. Usually denoted x, r, or ...
*
is
velocity vector
*
is
specific angular momentum vector (equal to
)
*
is
standard gravitational parameter
In celestial mechanics, the standard gravitational parameter ''μ'' of a celestial body is the product of the gravitational constant ''G'' and the mass ''M'' of the bodies. For two bodies the parameter may be expressed as G(m1+m2), or as GM whe ...
See also
*
Kepler orbit
*
Orbit
In celestial mechanics, an orbit 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 object or position in space such as ...
*
Eccentricity
*
Laplace–Runge–Lenz vector
References
{{DEFAULTSORT:Eccentricity Vector
Orbits
Vectors (mathematics and physics)