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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.
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit . There are many different ways to mathematically describe the same orbit, but certain schemes, each consisting of a set of six parameters, are commonly used in ...
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2] The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of ...
The orbital state vectors have now been found, the position (r 2) and velocity (v 2) vector for the second observation of the orbiting body. With these two vectors, the orbital elements can be found and the orbit determined.
In orbital mechanics, Kepler's equation relates various geometric properties of the orbit of a body subject to a central force.. It was derived by Johannes Kepler in 1609 in Chapter 60 of his Astronomia nova, [1] [2] and in book V of his Epitome of Copernican Astronomy (1621) Kepler proposed an iterative solution to the equation.
The basic orbit determination task is to determine the classical orbital elements or Keplerian elements, ,,,,, from the orbital state vectors [,], of an orbiting body with respect to the reference frame of its central body. The central bodies are the sources of the gravitational forces, like the Sun, Earth, Moon and other planets.
The TLE format is a de facto standard for distribution of an Earth-orbiting object's orbital elements. A TLE set may include a title line preceding the element data, so each listing may take up three lines in the file, in which case the TLE is referred to as a three-line element set (3LE), instead of a two-line element set (2LE). The title is ...
The formula is dimensionless, describing a ratio true for all units of measure applied uniformly across the formula. If the numerical value a {\displaystyle \mathbf {a} } is measured in meters per second squared, then the numerical values v {\displaystyle v\,} will be in meters per second, r {\displaystyle r\,} in meters, and ω {\displaystyle ...