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Critical inclinations in planetary problems

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Abstract

The general conception of the critical inclinations and eccentricities for theN-planet problem is introduced. The connection of this conception with the existence and stability of particular solutions is established. In the restricted circular problem of three bodies the existence of the critical inclinations is proved for any values of the ratio of semiaxes α. The asymptotic behaviour of the critical inclinations as α→1 is investigated.

Резюме

В ⦕адаче о двишенииг дланет вводится понятие критических наклонностей и эксцентриситетов. Устанавливается связя этого понятия с существованием и устойчивостью некоторьИх гастньИш решений. Для огра↭игенной круговой задаги трех тел доказано существование критигеских наклонностей полуосей α. Изугено асимптотигеское поведние критигеских наклонностей при α→1.

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  1. Institute for Theoretical Astronomy, Leningrad, U.S.S.R.

    G. A. Krasinsky

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  1. G. A. Krasinsky
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Krasinsky, G.A. Critical inclinations in planetary problems. Celestial Mechanics 6, 60–83 (1972). https://doi.org/10.1007/BF01237448

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