State vector (geographical)

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.

A geographical state vector typically will contain seven elements: three position coordinates, three velocity terms, and the time at which these values were valid. Mathematically, if we are to describe positions in a N-dimensional space ( R N ) then a state vector x belongs to R 2 N :

x ( t ) = ( x 1 ( t ) x 2 ( t ) x 3 ( t ) v 1 ( t ) v 2 ( t ) v 3 ( t ) ) T

or simply

x ( t ) = ( r ( t ) v ( t ) )

where r = ( x 1 x 2 x 3 ) T is the position vector and v = r ˙ = ( v 1 v 2 v 3 ) T 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).