Dynamics of "jumping" Trojans: a perturbative treatment

The term “jumping” Trojan was introduced by Tsiganis et al. (Astron Astrophys 354:1091–1100, 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. (Nature 475:481–483, 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 different regimes of orbital motion.