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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.
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 ...
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 argument of periapsis (also called argument of perifocus or argument of pericenter), symbolized as ω , is one of the orbital elements of an orbiting body. Parametrically, ω is the angle from the body's ascending node to its periapsis , measured in the direction of motion.
The longitude of the ascending node, also known as the right ascension of the ascending node, is one of the orbital elements used to specify the orbit of an object in space. Denoted with the symbol Ω , it is the angle from a specified reference direction, called the origin of longitude , to the direction of the ascending node (☊), as ...
Corresponding orbital elements are semi-major axis = 23001 km; eccentricity = 0.566613; true anomaly at time t 1 = −7.577° true anomaly at time t 2 = 92.423° This y-value corresponds to Figure 3. With r 1 = 10000 km; r 2 = 16000 km; α = 260° one gets the same ellipse with the opposite direction of motion, i.e. true anomaly at time t 1 = 7 ...
The classical method of finding the position of an object in an elliptical orbit from a set of orbital elements is to calculate the mean anomaly by this equation, and then to solve Kepler's equation for the eccentric anomaly. Define ϖ as the longitude of the pericenter, the angular distance of the pericenter from a reference direction.
A two-line element set (TLE, or more rarely 2LE) or three-line element set (3LE) is a data format encoding a list of orbital elements of an Earth-orbiting object for a given point in time, the epoch. Using a suitable prediction formula, the state (position and velocity) at any point in the past or future can be estimated to some accuracy.