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Orbital position vector, orbital velocity vector, other orbital elements. 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 () uniquely determine the trajectory of the orbiting body in space.
The angular velocity of the particle at P with respect to the origin O is determined by the perpendicular component of the velocity vector v.. In the simplest case of circular motion at radius , with position given by the angular displacement () from the x-axis, the orbital angular velocity is the rate of change of angle with respect to time: =.
The relative velocity of an object B relative to an observer A, denoted (also or ), is the velocity vector of B measured in the rest frame of A. The relative speed v B ∣ A = ‖ v B ∣ A ‖ {\displaystyle v_{B\mid A}=\|\mathbf {v} _{B\mid A}\|} is the vector norm of the relative velocity.
Note: This page uses common physics notation for spherical coordinates, in which is the angle between the z axis and the radius vector connecting the origin to the point in question, while is the angle between the projection of the radius vector onto the x-y plane and the x axis. Several other definitions are in use, and so care must be taken ...
The radial velocity or line-of-sight velocity of a target with respect to an observer is the rate of change of the vector displacement between the two points. It is formulated as the vector projection of the target-observer relative velocity onto the relative direction or line-of-sight (LOS) connecting the two points.
Speed, the scalar magnitude of a velocity vector, denotes only how fast an object is moving, while velocity indicates both an object's speed and direction. [3] [4] [5] To have a constant velocity, an object must have a constant speed in a constant direction. Constant direction constrains the object to motion in a straight path thus, a constant ...
In differential geometry, especially the theory of space curves, the Darboux vector is the angular velocity vector of the Frenet frame of a space curve. [1] It is named after Gaston Darboux who discovered it. [2] It is also called angular momentum vector, because it is directly proportional to angular momentum.
A space curve; the vectors T, N, B; and the osculating plane spanned by T and N. In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space, or the geometric properties of the curve itself irrespective of any motion.