This paper is aimed to address
the study of techniques focused on
the use of a family of anomalies based on a family of geometric transformations that includes
the true anomaly
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the eccentric anomaly
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the secondary anomaly
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the polar angle with respect to
the secondary focus of
the ellipse.
This family is constructed using a natural generalization of the eccentric anomaly. The use of this family allows closed equations for the classical quantities of the two body problem that extends the classic, which are referred to eccentric, true and secondary anomalies.
In this paper we obtain the exact analytical development of the basic quantities of the two body problem in order to be used in the analytical theories of the planetary motion. In addition, this paper includes the study of the minimization of the errors in the numerical integration by an appropriate choice of parameters in our selected family of anomalies for each value of the eccentricity.