View source for Earth:State vector (navigation)

In navigation, a '''state vector''' is a set of data describing exactly where an object is located in space, and how it is moving.

==Mathematical representation==
A state vector typically will contain seven elements: three [[Position (vector)|position]] coordinates, three [[Physics:Velocity|velocity]] terms, and the [[Time|time]] at which these values were valid.{{Citation needed|date=August 2012}} Mathematically, in order to describe positions in a N-dimensional space (<math> \mathbb{R}^N </math>) then a state vector <math> \textbf{x} </math> belongs to <math> \mathbb{R}^{2N}</math>:

<math display="block"> \mathbf{x}(t) = \begin{bmatrix} x_1(t)\\ x_2 (t)\\ x_3(t) \\ v_1(t) \\ v_2 (t) \\ v_3 (t) \end{bmatrix} </math>

or simply

<math display="block"> \mathbf{x}(t) = \begin{bmatrix} \mathbf{r}(t) \\ \mathbf{v}(t)\end{bmatrix}</math>

where <math> \mathbf{r} = \begin{bmatrix} x_1 & x_2 & x_3 \end{bmatrix}^\mathsf{T}</math> is the position vector and <math> \mathbf{v} = \dot{\mathbf{r}} = \begin{bmatrix} v_1 & v_2 & v_3 \end{bmatrix}^\mathsf{T}</math> is the velocity vector.

Since there is freedom to choose coordinate systems for position, a state vector may also be expressed in a variety of [[Coordinate system|coordinate system]]s (e.g. the [[North east down]] coordinate system).

==See also==
*[[Orbital state vectors]]

[[Category:Navigation]]

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