Eccentricity Vector
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
(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
.
See also
Eccentricity
Orbit
Laplace-Runge-Lenz vector
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