Orbital state vectors

In astrodynamics or celestial dynamics orbital state vectors are vectors of position ($\mathbf {r}$) and velocity ($\mathbf {v}$)that uniquely determine the state of orbiting body.

Frame of reference

The state vectors must be considered in a particular inertial frame of reference setting. For most practical applications in astrodynamics this is usually assumed to have the following properties:

• cartesian frame of reference
• with x-axis pointing to
• with z-axis pointing to
• with y-axis pointing to

Position vector

Orbital position vector $\mathbf {r}$ is a cartesian vector describing position of the orbiting body in #Frame of reference. Orbital position vector together with orbital velocity vector describe uniquely state of the orbiting body and thus are called Orbital state vectors

Velocity vector

Orbital velocity vector $\mathbf {v}$ is a cartesian vector describing velocity of the orbiting body in #Frame of reference. Orbital velocity vector together with orbital position vector describe uniquely state of the orbiting body and thus are called Orbital state vectors

Derivatives

In astrodynamics Orbital state vectors are used with the help of following auxiliary vectors:

• orbital momentum vector $\mathbf {h} =\mathbf {r} \times \mathbf {v}$

Orbital state vectors $\mathbf {r}$ and $\mathbf {v}$ can be used to calculate following orbital elements:

• Inclination
• Eccentricity
• Longitude of ascending node
• Argument of periapsis
• Mean anomaly
• Orbital period

and other parameters:

• True anomaly
• Semi-major axis
• Semi-minor axis
• Linear eccentricity
• Periapsis distance
• Apoapsis distance
• Eccentric anomaly
• Mean longitude
• True longitude