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In astrodynamics or celestial dynamics orbital state vectors (sometimes State Vectors) are vectors of position ( ) and velocity ( ) that together with their time ( ) ( epoch) uniquely determine the state of an orbiting body.
State vectors are excellent for pre-launch orbital predictions when combined with time (epoch) expressed as an offset to the launch time. This makes the state vectors time-independent and good general prediction for orbit.
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:
Position vector The orbital position vector' is a cartesian vector describing the position of the orbiting body in Frame of reference. Together, the orbital position vector and orbital velocity vector describe uniquely the state of an orbiting body and thus are called Orbital state vectors
Velocity vector Orbital velocity vector 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.
For any object moving through space, the velocity vector is tangent to the trajectory. If  is the unit vector tangent to the trajectory, then
Derivation Orbital velocity vector  can be derived from orbital position vector  by differentiation with respect to time: 
Relation to orbital elements Orbital state vectors are equivalent to orbital elements (Keplerian elements) and each can be computed with each other (and used to derive other parameters of the orbit).
Both state vectors and orbital elements have unique adventages over the other. Computed in advance state vectors are more useful for orbital prediction. A time-independent state vector can be combined with the launch time using xxx method in order to arrive at a valid set of orbital elements whereas computed in advance orbital elements are valid only when launch occurs without the slip.
In astrodynamics Orbital state vectors ( and ) are used with the help of following auxiliary vectors:
Orbital state vectors can than be used to calculate following orbital elements (Keplerian elements) (see their definitions for directions):
together with time () ( epoch) those can be used to compute other orbit's parameters:
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