Calculating Method of Series for the True Anomaly of a Spacecraft Elliptic Orbit

The transcendental equation of a true anomaly was written in a power series instead of a differential form.When the sufficient condition of the iterative convergence is satisfied,the relationship between the true anomaly and the time was gotten by the iterative method.And for the others,the transcendental equation of an eccentric anomaly was solved by the iterative method.After the eccentric anomaly had been calculated,the relationship between the true anomaly and the time was gotten with the numerical integral method.The approximate equation,which included the first five terms in general expansion,was written for the spacecraft quasi-circular orbit.And the true anomaly as the function of the time was also gotten by the iterative method.The numerical simulation results show that these methods are efficient.