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The mean anomaly at epoch, M 0, is defined as the instantaneous mean anomaly at a given epoch, t 0. This value is sometimes provided with other orbital elements to enable calculations of the object's past and future positions along the orbit. The epoch for which M 0 is defined is
where the epoch is expressed in terms of Terrestrial Time, with an equivalent Julian date. Four of the elements are independent of any particular coordinate system: M is mean anomaly (deg), n: mean daily motion (deg/d), a: size of semi-major axis (AU), e: eccentricity (dimensionless).
Either the longitude at epoch, L 0, the mean anomaly at epoch, M 0, or the time of perihelion passage, T 0, are used to specify a known point in the orbit. The choices made depend whether the vernal equinox or the node are used as the primary reference. The semi-major axis is known if the mean motion and the gravitational mass are known. [2] [3]
where M 1 and M 0 are the mean anomalies at particular points in time, and Δt (≡ t 1-t 0) is the time elapsed between the two. M 0 is referred to as the mean anomaly at epoch t 0, and Δt is the time since epoch.
Then mean longitude is also [1] L = ϖ + M. Another form often seen is the mean longitude at epoch, ε. This is simply the mean longitude at a reference time t 0, known as the epoch. Mean longitude can then be expressed, [2] L = ε + n(t − t 0), or L = ε + nt, since t = 0 at the epoch t 0. where n is the mean angular motion and t is any ...
M - Mean anomaly; M o - Mean anomaly at epoch; Radius comparison. Radius comparison: R E, R ...
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.
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.