Orbital state vectors

In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position () and velocity () that together with their time (epoch) () uniquely determine the trajectory of the orbiting body in space. 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 Earth is the Earth-centered equatorial system defined as follows: The origin is Earth's center of mass; The Z axis is coincident with Earth's rotational axis, positive northward; The X/Y plane coincides with 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 Earth's axis, so the reference frames defined by 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 (in particular the ICRF), or even a spacecraft's own orbital plane and angular momentum. The position vector describes the position of the body in the chosen frame of reference, while the velocity vector 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 as detailed in Orbit determination. The principal reasoning is that Newton's law of gravitation yields an acceleration ; if the product of gravitational constant and attractive mass at the center of the orbit are known, position and velocity are the initial values for that second order differential equation for which has a unique solution. The body does not actually have to be in orbit for its state vectors to determine its trajectory; it only has to move ballistically, i.