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Such EC orbits have a value of the Jacobi constant of the form $$C=3\\mu +Ln^{2\/3}(1-\\mu )^{2\/3}$$<\/jats:tex-math>\n \n C<\/mml:mi>\n =<\/mml:mo>\n 3<\/mml:mn>\n \u03bc<\/mml:mi>\n +<\/mml:mo>\n L<\/mml:mi>\n \n n<\/mml:mi>\n \n 2<\/mml:mn>\n \/<\/mml:mo>\n 3<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n \n \n (<\/mml:mo>\n 1<\/mml:mn>\n -<\/mml:mo>\n \u03bc<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n \n 2<\/mml:mn>\n \/<\/mml:mo>\n 3<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, where $$L>0$$<\/jats:tex-math>\n \n L<\/mml:mi>\n ><\/mml:mo>\n 0<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is big enough but independent of $$\\mu $$<\/jats:tex-math>\n \u03bc<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and n<\/jats:italic>. In order to prove this optimal result, we consider Levi-Civita\u2019s transformation to regularize the collision with one primary and a perturbative approach using an ad hoc small parameter once a suitable scale in the configuration plane and time has previously been applied. This result improves a previous work where the existence of the n<\/jats:italic>-EC orbits was stated when the mass parameter $$\\mu >0$$<\/jats:tex-math>\n \n \u03bc<\/mml:mi>\n ><\/mml:mo>\n 0<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> was small enough. Moreover, for decreasing values of C<\/jats:italic>, there appear some bifurcations which are first numerically investigated and afterward explicit expressions for the approximation of the bifurcation values of C<\/jats:italic> are discussed. Finally, a detailed analysis of the existence of n<\/jats:italic>-EC orbits when $$\\mu \\rightarrow 1$$<\/jats:tex-math>\n \n \u03bc<\/mml:mi>\n \u2192<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is also described. In a natural way, Hill\u2019s problem shows up. For this problem, we prove an analytical result on the existence of four families of n<\/jats:italic>-EC orbits, and numerically, we describe them as well as the appearing bifurcations.<\/jats:p>","DOI":"10.1007\/s00332-022-09873-y","type":"journal-article","created":{"date-parts":[[2022,11,30]],"date-time":"2022-11-30T18:21:02Z","timestamp":1669832462000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Generalized Analytical Results on n-Ejection\u2013Collision Orbits in the RTBP. 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