On the orbits of the outer satellites of Jupiter

Abstract

Abstract. In this work we study the basic aspects concerning the stability of the outer satellites of Jupiter. Including the effects of the four giant planets and the Sun we study a large grid of initial conditions. Some important regions where satellites cannot survive are found. Basically these regions are due to Kozai and other resonances. We give an analytical explanation for the libration of the pericenters − J . Another different center is also found. The period and amplitude of these librations are quite sensitive to initial conditions, so that precise observational data are needed for Pasiphae and Sinope. The effect of Jupiter's mass variation is briefly presented. This effect can be responsible for satellite capture and also for locking − J in temporary libration.

About the dynamics of the evection resonance

“…For distant orbits such those of the irregular satellites of the giant planets, this correction is crucial, as shown by recent analytic models (Yokoyama et al 2003;Ćuk & Burns 2004;Beaugé & Nesvorný 2007). The dynamics of the resonance itself was studied for the first time by Hénon in his numerical study of the restricted three-body problem (Hénon 1969(Hénon , 1970 where he shows that in the Hill's approximation, this resonance appears as a bifurcation of a family of simple periodic orbits (named "g" in his papers) at a value of semi-major axis of a = 0.45r h where r h is the Hill's radius of the planet.…”

The long-term dynamics of the Jovian irregular satellites

“…Special care has been taken in the study of (i) the secular resonance ν =˙ −˙ (Saha & Tremaine 1993;Whipple & Shelus 1993;Beaugé & Nesvorný 2007;Nesvorný et al 2003;Yokoyama et al 2003;Ćuk & Burns 2004;Correa Otto et al 2009), which is one of the most important secular resonances acting on the satellites; (ii) the Lidov-Kozaï resonance for distant satellites (Beaugé et al 2006;Beaugé & Nesvorný 2007;Carruba et al 2002;Ćuk & Burns 2004;Nesvorný et al 2003); and (iii) the evection resonancė − n (Yokoyama et al 2008;Frouard et al 2010;Nesvorný et al 2003). In most of these works, the important need for the development of high-order perturbation methods or numerical ones is clearly stressed.…”

“…Later works have shown that at least the totality of the satellites known in 2003 with a precisely determined orbit (30 objects) do not escape over a very long time (Nesvorný et al 2003; see also Yokoyama et al 2003), and averaged elements were found for these satellites that show their organization in families (Nesvorný et al 2003(Nesvorný et al , 2004, an important fact that was confirmed analytically (Beaugé & Nesvorný 2007). Concerning stability studies of the phase space structure of the satellite region, numerical integrations of fictitious satellites (Carruba et al 2002;Yokoyama et al 2003;Nesvorný et al 2003;Hinse et al 2010) confirm the different dynamical portraits obtained between prograde and retrograde regions (Hénon 1969(Hénon , 1970. The study of the overall dynamical structure of the Jovian satellite region with the determination of the various important mean motion resonances for the three-body problem has been done by Hinse et al (2010).…”

Artificial satellites: resonance effects produced by terrestrial tide

“…The Lidov-Kozai's mechanism has been studied for asteroids as in Kozai (1962), for Uranus's satellites as Nakai (1999, 2007), for Jupiter's satellites as in Yokoyama et. al.…”