 in astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are cartesian vectors of position (\mathbf{r}) and velocity (\mathbf{v}) that together with their time (epoch) (t\,) uniquely determine the trajectory of the orbiting body in space.  ==frame of reference== state vectors are defined with respect to some frame of reference, usually but not always an inertial reference frame. one of the more popular reference frames for the state vectors of bodies moving near the earth is the earth-centered equatorial system defined as follows: *the origin is the earth's center of mass; *the z axis is coincident with the earth's rotational axis, positive northward; *the x/y plane coincides with the earth's equatorial plane, with the +x axis pointing toward the vernal equinox and the y axis completing a right-handed set. this reference frame is not truly inertial because of the slow, 26,000 year precession of the earth's axis, so the reference frames defined by the earth's orientation at a standard astronomical epoch such as b1950 or j2000 are also commonly used. many other reference frames can be used to meet various application requirements, including those centered on the sun or on other planets or moons, the one defined by the barycenter and total angular momentum of the solar system, or even a spacecraft's own orbital plane and angular momentum. ==position vector== the position vector \mathbf{r} describes the position of the body in the chosen frame of reference, while the velocity vector \mathbf{v} describes its velocity in the same frame at the same time. together, these two vectors and the time at which they are valid uniquely describe the body's trajectory. the body does not actually have to be in orbit for its state vector to determine its trajectory; it only has to move ballistically, i.e., solely under the effects of its own inertia and gravity. for example, it could be a spacecraft or missile in a suborbital trajectory. if other forces such as drag or thrust are significant, they must be added vectorially to those of gravity when performing the integration to determine future position and velocity. for any object moving through space, the velocity vector is tangent to the trajectory. if \hat{\mathbf{u}}_t is the unit vector tangent to the trajectory, then :\mathbf{v} = v\hat{\mathbf{u}}_t ===derivation=== the velocity vector \mathbf{v}\, can be derived from position vector \mathbf{r}\, by differentiation with respect to time: :\mathbf{v} = {d\mathbf{r}\over{dt}} an objec
Orbits Vectors