BIGpedia - Eccentricity vector - Encyclopedia and Dictionary Online

In astrodynamics the eccentricity vector of a conic section orbit is the vector pointing towards the periapsis and with length equal to the orbit's scalar eccentricity.

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 velocity vector of the orbital state vectors,
$\mathbf{r} \,$ is 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.

Eccentricity vector

Calculation

See also