Using normal forms to study Oterma's transition in the Planar RTBP

Abstract

<p style='text-indent:20px;'>Comet 39P/Oterma is known to make fast transitions between heliocentric orbits outside and inside the orbit of Jupiter. In this note the dynamics of Oterma is quantitatively studied via an explicit computation of high order Birkhoff normal forms at the points <inline-formula><tex-math id="M1">\begin{document}$ L_1 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ L_2 $\end{document}</tex-math></inline-formula> of the Planar Restricted Three-Body Problem. A previous work [<xref ref-type="bibr" rid="b14">14</xref>] has shown the existence of heteroclinic connections between the neigbourhood of <inline-formula><tex-math id="M3">\begin{document}$ L_1 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ L_2 $\end{document}</tex-math></inline-formula> which provide paths for this transition. Here we combine real data on the motion of Oterma with normal forms to compute the invariant objects that are responsible for this transition.</p>