Algebraic function

In celestial mechanics, the eccentricity vector of a Kepler orbit is the vector that points towards the periapsis and has a magnitude equal to the orbit's scalar eccentricity. The magnitude is unitless. 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. For the eccentricity and argument of periapsis parameters, eccentricity zero (circular orbit) corresponds to a singularity.

Calculation

The eccentricity vector $\mathbf {e} \,$ can be calculated

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

where:

• $\mathbf {v} \,\!$ is velocity vector
• $\mathbf {h} \,\!$ is specific angular momentum vector (equal to $\mathbf {r} \times \mathbf {v}$)
• $\mathbf {r} \,\!$ is position vector
• $\mu \,\!$ is standard gravitational parameter

or equivalently:

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

See also

• Kepler orbit
• Orbit
• Eccentricity
• Laplace–Runge–Lenz vector

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.