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Shown are mean anomaly and true anomaly for two units of time. (Note that for visual simplicity, a non-overlapping circular orbit is diagrammed, thus this circular orbit with same orbital period is not shown in true scale with this elliptical orbit: for scale to be true for the two orbits of equal period, these orbits must intersect.)
The true anomaly is usually denoted by the Greek letters ν or θ, or the Latin letter f, and is usually restricted to the range 0–360° (0–2π rad). The true anomaly f is one of three angular parameters (anomalies) that defines a position along an orbit, the other two being the eccentric anomaly and the mean anomaly.
An orbiting body's mean longitude is calculated L = Ω + ω + M, where Ω is the longitude of the ascending node, ω is the argument of the pericenter and M is the mean anomaly, the body's angular distance from the pericenter as if it moved with constant speed rather than with the variable speed of an elliptical orbit.
Because it increases uniformly with time, expressing any other variable as a series in mean anomaly is essentially the same as expressing it in terms of time. Although the true anomaly is an analytic function of M, it is not an entire function so a power series in M will have a limited range of convergence.
Solving for is more or less equivalent to solving for the true anomaly, or the difference between the true anomaly and the mean anomaly, which is called the "Equation of the center". One can write an infinite series expression for the solution to Kepler's equation using Lagrange inversion , but the series does not converge for all combinations ...
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Instead of the mean anomaly at epoch, the mean anomaly M, mean longitude, true anomaly ν 0, or (rarely) the eccentric anomaly might be used. Using, for example, the "mean anomaly" instead of "mean anomaly at epoch" means that time t must be specified as a seventh orbital element. Sometimes it is assumed that mean anomaly is zero at the epoch ...