Dynamics of “jumping” Trojans: a perturbative treatment

Abstract

The term "jumping" Trojan was introduced by Tsiganis et al. (2000) in their studies of long-term dynamics exhibited by the asteroid (1868) Thersites, which had been observed to jump from librations around L 4 to librations around L 5 . Another example of a "jumping" Trojan was found by Connors et al. (2011): librations of the asteroid 2010 TK7 around the Earth's libration point L 4 preceded by its librations around L 5 . We explore the dynamics of "jumping" Trojans under the scope of the restricted planar elliptical three-body problem. Via double numerical averaging we construct evolutionary equations, which allow analyzing transitions between the orbital motion regimes.

Dynamics in first-order mean motion resonances: analytical study of a simple model with stochastic behaviour

“…Presence of MMR may lead to the so-called adiabatic chaos (Wisdom 1985), which is caused, roughly speaking, by small quasi-random jumps between regular phase trajectories in certain parts of the phase space, where adiabatic approximation is violated. Applying systematically Wisdom's ideas to study of MMRs (Sidorenko 2006;Sidorenko et al 2014;Sidorenko 2018), we found that adiabatic chaos often coexists with the quasi-probabilistic transitions between specific phase regions. Both phenomena occur in that part of the phase space, where the "pendulum" or first-order Second Fundamental Model for Resonance (Henrard and Lamaitre 1983) approximations fail, because the first harmonic in the disturbing function Fourier series is not dominant.…”

Using Mars co-orbitals to estimate the importance of rotation-induced YORP break-up events in Earth co-orbital space

“…Trojans can jump from librating around L 4 to librating around L 5 and vice versa (see e.g. Tsiganis, Dvorak & Pilat-Lohinger 2000;Connors et al 2011;Sidorenko 2018). If λ r does not oscillate around a certain value, we have a passing object whose position relative to the host planet is not controlled by the 1:1 mean-motion resonance .…”

Long-term orbital dynamics of trans-Neptunian objects

“…This kind of semianalytical procedure is now widely used for resonant problems in celestial mechanics involving high eccentricities and/or high inclinations (see e.g. Milani and Baccili 1998;Gallardo 2006aGallardo ,b, 2019bSidorenko 2006Sidorenko , 2018Saillenfest et al 2016;Saillenfest and Lari 2017;Pichierri et al 2017;Batygin and Morbidelli 2017). We note that the evolution of the pair (U, u) is secular by nature (frequency ∝ ε P ), whereas the evolution of the pair (Σ, σ) is semi-secular (frequency ∝ √ ε P ).…”

“…We will recall here the method proposed by Henrard (1990Henrard ( , 1993 and applied to the trans-Neptunian region by Saillenfest et al (2016Saillenfest et al ( , 2017b and Saillenfest and Lari (2017). We will also discuss its variant introduced independently by Wisdom (1985) and used for instance by Sidorenko (2006Sidorenko ( , 2018. Section 5.1 presents the change of coordinates used to isolate the resonant angle and compute a semiaveraged Hamiltonian.…”