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^(2n): x(t) = r(t) taken v(t) where r is the position vector and v 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