About the equation of center

[Anselmo P�rez Serrada]

Hi dialists,   Maybe this is an off-topic, but I found it in some gnomonics books and I'd like to know more about it:   It is well known that due to Kepler's Second Law the Earth (and any satellite) does not follow a circular uniform movement but an elliptical non-uniform one. So the longitude of the Earth across the ecliptic is not exactly proportional to time: the difference (True Longitude minus Mean Longitude) is called equation of center 'c' and can be derived either solving Kepler's equation ( M = E - e*sin(E) ) or using an approximate formula, something like     c = (2e- 1/4*e^3)*sin(M) + 5/4*sin(2*M) + 13/12*e^3*sin(3*M)+ ... where M, the mean anomaly, is the fraction of area swept by the Earth and e is the eccentricity of the orbit (Yes, it's pre-copernican, but it works!).   OK, but which is the general _expression_ of this formula (for the n-th term) and where does it come from? Is it a Fourier series or a Taylor series?  I've tried both and wasn't able to reach to any result like this.   Could anyone point me at some website where this series is derived?   Anselmo Perez Serrada