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# Appendices

## A The Transformation Matrix $Σ(t)$

This appendix presents the elements of the transformation matrix $Σ(t)=[A(t)+A2B(t)]$, where $A2=3J2Re2$. All the orbital elements are the elements of the chief; for brevity, the subscript “0” has been dropped. The following quantities will be needed:

$r=p/\left(1+{q}_{1}cos\theta +{q}_{2}sin\theta \right)$

(A.1)

$p=a\left(1-{q}_{1}^{2}-{q}_{2}^{2}\right)$

${v}_{t}=\sqrt{\frac{\mu }{p}}\left(1+{q}_{1}cos\theta +{q}_{2}sin ...$

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