Thi
s paper i
s aimed to addre
ss the
study of technique
s focu
sed on the u
se of a family of anomalie
s ba
sed on a family of geometric tran
sformation
s that include
s the true anomaly <
span id="mml
si5" cla
ss="mathml
src"><
span cla
ss="formulatext
stixSupport mathImg" data-mathURL="/
science?_ob=MathURL&_method=retrieve&_eid=1-
s2.0-S037
7042716300978&_mathId=
si5.gif&_u
ser=111111111&_pii=S037
7042716300978&_rdoc=1&_i
ssn=037
70427&md5=3b5cb5e8666577a31ad45dd6a8df0391" title="Click to view the MathML
source">f
span><
span cla
ss="mathContainer hidden"><
span cla
ss="mathCode">
span>
span>
span>, the eccentric anomaly <
span id="mml
si4" cla
ss="mathml
src"><
span cla
ss="formulatext
stixSupport mathImg" data-mathURL="/
science?_ob=MathURL&_method=retrieve&_eid=1-
s2.0-S037
7042716300978&_mathId=
si4.gif&_u
ser=111111111&_pii=S037
7042716300978&_rdoc=1&_i
ssn=037
70427&md5=8b
24f86ea65f653bf0d4ef5132e106bd" title="Click to view the MathML
source">g
span><
span cla
ss="mathContainer hidden"><
span cla
ss="mathCode">
span>
span>
span> and the
secondary anomaly <
span id="mml
si3" cla
ss="mathml
src"><
span cla
ss="formulatext
stixSupport mathImg" data-mathURL="/
science?_ob=MathURL&_method=retrieve&_eid=1-
s2.0-S037
7042716300978&_mathId=
si3.gif&_u
ser=111111111&_pii=S037
7042716300978&_rdoc=1&_i
ssn=037
70427&md5=a7c6918f994c192ae2a8fa2b73c9e0ad" title="Click to view the MathML
source">f<
sup>′
sup>
span><
span cla
ss="mathContainer hidden"><
span cla
ss="mathCode">
span>
span>
span> defined a
s the polar angle with re
spect to the
secondary focu
s of the ellip
se.
sp000155">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.
sp000160">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.