State vector (geographical)

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A geographical state vector is a set of data describing exactly where an object is located in space, and how it is moving. From a state vector, and sufficient mathematical conditions (e.g. the Picard-Lindelöf theorem), the object's past and future position can be determined.[citation needed]

A geographical state vector typically will contain seven elements: three position coordinates, three velocity terms, and the time at which these values were valid.[citation needed] Mathematically, if we are to describe positions in a N-dimensional space () then a state vector belongs to :

or simply

where is the position vector and is the velocity vector.

Due to the freedom one has in choosing coordinate systems for position, a state vector may also be expressed in a variety of coordinate systems (e.g. the North east down coordinate system).