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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.
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time.Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular ...
When the scalar field is the real numbers, the vector space is called a real vector space, and when the scalar field is the complex numbers, the vector space is called a complex vector space. [4] These two cases are the most common ones, but vector spaces with scalars in an arbitrary field F are also commonly considered.
The matrix and the vector can be represented with respect to a right-handed or left-handed coordinate system. Throughout the article, we assumed a right-handed orientation, unless otherwise specified. Vectors or forms The vector space has a dual space of linear forms, and the matrix can act on either vectors or forms.
The initial derivation begins with vector addition to determine the orbiting body's position vector. Then based on the conservation of angular momentum and Keplerian orbit principles (which states that an orbit lies in a two dimensional plane in three dimensional space), a linear combination of said position vectors is established.
Position space (also real space or coordinate space) is the set of all position vectors r in Euclidean space, and has dimensions of length; a position vector defines a point in space. (If the position vector of a point particle varies with time, it will trace out a path, the trajectory of a particle.)
The range, R, is the greatest distance the object travels along the x-axis in the I sector. The initial velocity, v i, is the speed at which said object is launched from the point of origin. The initial angle, θ i, is the angle at which said object is released. The g is the respective gravitational pull on the object within a null-medium.
and are the masses of objects 1 and 2, and is the specific angular momentum of object 2 with respect to object 1. The parameter θ {\displaystyle \theta } is known as the true anomaly , p {\displaystyle p} is the semi-latus rectum , while e {\displaystyle e} is the orbital eccentricity , all obtainable from the various forms of the six ...