State vectors

Updated July 13, 2026

An orbital state vector describes a body with two 3-D vectors at a single instant (the epoch): its position r = (x, y, z) and its velocity v = (v_x, v_y, v_z), in an Earth-centered inertial frame. Those six numbers fix the entire orbit — they carry exactly the same information as the six classical elements.

Position and velocity at an epoch

Where the classical elements describe an orbit geometrically (an ellipse, oriented, with the body somewhere on it), a state vector describes it kinematically: this is exactly where the body is and how fast it is going, right now. Position is typically in kilometres and velocity in kilometres per second. A state vector is only meaningful together with its epoch and its reference frame — the same r and v mean different orbits at different times or in different frames.

Why six numbers equal six elements

An orbit has six degrees of freedom, so any complete description needs exactly six independent numbers. A state vector supplies them as three position and three velocity components; the classical elements supply them as a, e, i, Ω, ω, and ν. Because both describe the same orbit, you can convert either way — and the Orbit Visualizer does exactly that internally, translating between a state vector, classical elements, and (for supported cases) a TLE. See classical orbital elements for the geometric side.

When to prefer a state vector

• You already have r and v. Numerical propagators, GPS/GNSS solutions, and many ephemerides emit position and velocity directly — no need to fit elements first.
• Near-singular orbits. A near-circular orbit has an ill-defined argument of periapsis, and a near-equatorial orbit has an ill-defined ascending node; the state vector has no such singularities, so it stays well-behaved where the angles do not.
• Snapshots and hand-offs. A single (r, v, epoch) triple is a compact, unambiguous way to hand one instant of an orbit to another tool.

Classical elements, by contrast, are better when you want to reason about the orbit's shape and orientation, or design a maneuver in terms of period, inclination, or apogee.

In the Orbit Visualizer

Choose State Vector (r, v) as the data format and enter an Epoch (UTC), the three position components r₁x, r₁y, r₁z (km), and the three velocity components v₁x, v₁y, v₁z (km/s). The app interprets these in its inertial scene frame (J2000/EME2000) — it does not ask which frame your vector is in, so supply an Earth-centered inertial state. Switching the input type re-expresses the same orbit as classical elements or a TLE.

State vectors are entered in that form rather than through the URL: the deep-link API covers classical elements and TLEs, so the example below loads an equivalent orbit as elements, which you can then switch to State Vector (r, v) in the app to read off r and v.

▶ Open a LEO orbit, then switch to State Vector (r, v)

Related

• Classical orbital elements — the geometric description of the same orbit.
• Propagation models — how a state is moved forward in time.
• Export formats — the app writes time-stamped r and v as CSV/OEM.

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