Eccentricity vector

In astrodynamics the eccentricity vector of a conic section orbit is the Vector (spatial) pointing towards the periapsis and with length equal to the orbit's scalar eccentricity (orbit). ==Calculation== The eccentricity vector

\mathbf{e} \,

can be calculated from the orbital state vectors

\mathbf{v} \,

and

\mathbf{r} \,

at any time (the result is constant): :

\mathbf{e} = {1 \over {\mu}} \left [\left (v^2 - {\mu \over {\mathbf{\left |r \right |}}}\right)
\mathbf{r} - (\mathbf{r} \cdot \mathbf{v} ) \mathbf{v} \right ]

where: *

\mathbf{v} \,

is orbital state vectors#velocity vector of the orbital state vectors, *

\mathbf{r} \,

is orbital state vectors#position vector of the orbital state vectors, *

\mu \,

is standard gravitational parameter. Alternatively it can also be computed from orbital angular momentum vector h: :

\mathbf{e} = {\mathbf{v}\times\mathbf{h}\over{\mu}} - {\mathbf{r}\over{\left|\mathbf{r}\right|}}

where: *

\mathbf{v}\,\!

is orbital velocity vector, *

\mathbf{h}\,\!

is orbital angular momentum vector, *

\mathbf{r}\,\!

is orbital position vector, *

\mu\,\!

is standard gravitational parameter. ==See also== *Eccentricity (orbit) *Orbit *Laplace-Runge-Lenz vector Astrodynamics Celestial mechanics

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Words begining with Eccentricity_vector:

Eccentricity_vector