Orbital state vectors

In astrodynamics or celestial dynamics orbital state vectors (sometimes state vectors) are vectors of position (\mathbf{r}) and velocity (\mathbf{v}) that together with their time (epoch) (t\,) uniquely determine the state of an orbiting body.

State vectors are excellent for pre-launch orbital predictions when combined with time (epoch) expressed as an offset to the launch time. This makes the state vectors time-independent and good general prediction for orbit.

Orbital position vector and orbital velocity vector and other orbit's elements


Frame of reference

The state vectors must be considered in a particular inertial frame of reference setting. For most practical applications in astrodynamics this is usually assumed to have the following properties:

Position vector

The orbital position vector \mathbf{r} is a cartesian vector describing the position of the orbiting body in Frame of reference. Together, the orbital position vector and orbital velocity vector describe uniquely the state of an orbiting body and thus are called Orbital state vectors.

Velocity vector

Orbital velocity vector \mathbf{v} is a cartesian vector describing velocity of the orbiting body in frame of reference. Orbital velocity vector together with orbital position vector describe uniquely state of the orbiting body and thus are called Orbital state vectors.

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


Orbital velocity vector \mathbf{v}\, can be derived from orbital position vector \mathbf{r}\, by differentiation with respect to time:

\mathbf{v} = {d\mathbf{r}\over{dt}}

Orbital position is when a planet rotates another planet.

Both state vectors and orbital elements have unique advantages over the other. Computed in advance state vectors are more useful for orbital prediction. A time-independent state vector can be combined with the launch time using xxx method in order to arrive at a valid set of orbital elements whereas computed in advance orbital elements are valid only when launch occurs without the slip.

In astrodynamics orbital state vectors (\mathbf{r} and \mathbf{v}) are used with the help of following auxiliary vector:

Orbital state vectors can then be used to calculate following orbital elements (Keplerian elements) (see their definitions for directions):

together with time (t\,) (epoch) those can be used to compute other orbit's parameters:

Keplerian elements typically define an osculating orbit because of perturbations in the orbital path. The osculating orbit is valid only at the epoch of the original Cartesian elements.

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Orbital elements — are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are generally considered in classical two body systems, where a Kepler orbit is used (derived from Newton s laws of motion and Newton s law… …   Wikipedia

  • Orbital inclination change — is an orbital maneuver aimed at changing the inclination of an orbiting body s orbit. This maneuver is also known as an orbital plane change as the plane of the orbit is tipped. This maneuver requires a change in the orbital velocity vector… …   Wikipedia

  • Orbital eccentricity — This article is about eccentricity in astrodynamics. For other uses, see Eccentricity (disambiguation). An elliptic Kepler orbit with an eccentricity of 0.7 (red), a parabolic Kepler orbit (green) and a hyperbolic Kepler orbit with an… …   Wikipedia

  • Orbital mechanics — A satellite orbiting the earth has a tangential velocity and an inward acceleration. Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other… …   Wikipedia

  • Orbital maneuver — In spaceflight, an orbital maneuver is the use of propulsion systems to change the orbit of a spacecraft. For spacecraft far from Earth for example those in orbits around the Sun an orbital maneuver is called a deep space maneuver (DSM).[not… …   Wikipedia

  • Orbital period — For the music album, see Orbital Period (album). The orbital period is the time taken for a given object to make one complete orbit about another object. When mentioned without further qualification in astronomy this refers to the sidereal period …   Wikipedia

  • Orbital speed — Not to be confused with Escape Velocity. The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more… …   Wikipedia

  • Orbital station-keeping — In astrodynamics orbital station keeping is a term used to describe the orbital maneuvers made by thruster burns that are needed to keep a spacecraft in a particular assigned orbit. For many Earth satellites the effects of the non Keplerian… …   Wikipedia

  • Orbital inclination — For the science fiction novella by William Shunn, see Inclination (novella). Fig. 1: One view of inclination i (green) and other orbital parameters Inclination in general is the angle between a reference plane and another plane or axis of… …   Wikipedia

  • Specific orbital energy — In the gravitational two body problem, the specific orbital energy (or vis viva energy) of two orbiting bodies is the constant sum of their mutual potential energy ( ) and their total kinetic energy ( ), divided by the reduced mass. According to… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.