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Encyclopedia > 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. Astrodynamics is the study of the motion of rockets, missiles, and space vehicles, as determined from Sir Isaac Newtons laws of motion and his law of universal gravitation. ... This article or section should include material from Celestial Mechanics This article or section should be merged with Astrodynamics Celestial mechanics is a term for the application of physics, historically Newtonian mechanics, to astronomical objects such as stars and planets. ... Look up position in Wiktionary, the free dictionary. ... The velocity of an object is simply its speed in a particular direction. ... In astronomy, an epoch is a moment in time for which celestial coordinates or orbital elements are specified. ...

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. In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ...

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

Image File history File links Download high resolution version (1024x768, 78 KB)State vectors and other orbit elements Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1. ... Image File history File links Download high resolution version (1024x768, 78 KB)State vectors and other orbit elements Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1. ... In astrodynamics or celestial dynamics orbital state vectors (sometimes State Vectors) are vectors of position () and velocity () that together with their time () ( epoch) uniquely determine the state of an orbiting body. ... In astrodynamics or celestial dynamics orbital state vectors (sometimes State Vectors) are vectors of position () and velocity () that together with their time () ( epoch) uniquely determine the state of an orbiting body. ...

## Contents

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: An inertial frame is a coordinate system in which Newtons First Law of Motion is valid. ...

Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ... Illumination of Earth by Sun on the day of equinox The vernal equinox (or spring equinox) marks the beginning of astronomical spring. ...

## 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. Cartesian means of or relating to the French philosopher and mathematician René Descartes. ... In astrodynamics or celestial dynamics orbital state vectors (sometimes State Vectors) are vectors of position () and velocity () that together with their time () ( epoch) uniquely determine the state of an orbiting body. ...

## 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. Cartesian means of or relating to the French philosopher and mathematician René Descartes. ... In astrodynamics or celestial dynamics orbital state vectors (sometimes State Vectors) are vectors of position () and velocity () that together with their time () ( epoch) uniquely determine the state of an orbiting body. ...

For any object moving through space, the velocity vector is tangent to the trajectory. If $hatmathbf{u}_t$ is the unit vector tangent to the trajectory, then This article is about the mathematical concept of tangent. For other meanings, see tangent (disambiguation). ... In mathematics, a unit vector in a normed vector space is a vector (most commonly a spatial vector) whose length is 1. ...

$mathbf{v} = vhatmathbf{u}_t$

### Derivation

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

$mathbf{v} = {dmathbf{r}over{dt}}$

## Relation to orbital elements

Orbital state vectors are equivalent to orbital elements (Keplerian elements) and each can be computed with each other (and used to derive other parameters of the orbit). The elements of an orbit are the parameters needed to specify that orbit uniquely, given a model of two ideal masses obeying the Newtonian laws of motion and the inverse-square law of gravitational attraction. ... In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ...

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: Astrodynamics is the study of the motion of rockets, missiles, and space vehicles, as determined from Sir Isaac Newtons laws of motion and his law of universal gravitation. ...

Orbital state vectors can than be used to calculate following orbital elements (Keplerian elements) (see their definitions for directions): In astrodynamics specific relative angular momentum () of orbiting body () relative to central body () is the relative angular momentum of per unit mass. ... The elements of an orbit are the parameters needed to specify that orbit uniquely, given a model of two ideal masses obeying the Newtonian laws of motion and the inverse-square law of gravitational attraction. ... The elements of an orbit are the parameters needed to specify that orbit uniquely, given a model of two ideal masses obeying the Newtonian laws of motion and the inverse-square law of gravitational attraction. ...

together with time ($t,$) ( epoch) those can be used to compute other orbit's parameters: Inclination in general is the angle between a reference plane and another plane or axis of direction. ... In astrodynamics, under standard assumptions any orbit must be of conic section shape. ... The Longitude of the ascending node () is one of the orbital elements used to specify the orbit of an object in space. ... In an orbit, the argument of periapsis () is the angle between the ascending node (the point where the orbiting body passes from the southern to the northern hemisphere) and the periapsis (the point of closest approach to the central body). ... In the study of orbital dynamics the mean anomaly is a measure of time, specific to the orbiting body p, which is a multiple of 2π radians at and only at periapsis. ... The orbital period is the time it takes a planet (or another object) to make one full orbit. ... In astronomy, an epoch is a moment in time for which celestial coordinates or orbital elements are specified. ...

• True anomaly ($v,$)
• Semi-major axis ($a,$)
• Semi-minor axis ($b,$)
• Linear eccentricity ($epsilon,$)
• Periapsis distance ($d_p,$)
• Apoapsis distance ($d_a,$)
• Eccentric anomaly ($E,$)
• Mean longitude ($L,$)
• True longitude ($l,$)

Results from FactBites:

 What is a State Vector? (564 words) A state vector is a set of data telling exactly where the shuttle is in its orbit in space. State vectors are as important to the ground support personnel as they are to the shuttle itself. The form of a state vector is just a way of identifying which set of orbit parameters is being used to define the orbit.
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