Eccentricity vector
From Freepedia
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 <math> \mathbf{e} \,</math> can be calculated from the orbital state vectors <math> \mathbf{v} \,</math> and <math> \mathbf{r} \,</math> at any time (the result is constant):
- <math> \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 ]</math> where:
- <math> \mathbf{v} \,</math> is velocity vector of the orbital state vectors,
- <math> \mathbf{r} \,</math> is position vector of the orbital state vectors,
- <math> \mu \,</math> is standard gravitational parameter.
Alternatively it can also be computed from orbital angular momentum vector h:
- <math> \mathbf{e} = {\mathbf{v}\times\mathbf{h}\over{\mu}} - {\mathbf{r}\over{\left|\mathbf{r}\right|}}</math>
where:
- <math> \mathbf{v}\,\!</math> is orbital velocity vector,
- <math>\mathbf{h}\,\!</math> is orbital angular momentum vector,
- <math>\mathbf{r}\,\!</math> is orbital position vector,
- <math>\mu\,\!</math> is standard gravitational parameter.
