Dia: Dimecres, 13 de novembre de 2024
Lloc: Aula T2 (segon pis), Facultat de Matemàtiques i Informàtica, UB.A càrrec de: José Lamas (UPC)
Títol: Final motions and ejection-collision orbits in the 3 Body
Resum: We consider the Planar Circular Restricted 3 Body Problem (PCRTBP), which describes the motion of a massless body under the attraction of other two bodies, the primaries, which describe circular orbits around their common center of mass located at the origin. In rotating coordinates, this system is Hamiltonian with two degrees of freedom. The orbits of this system are either defined for all (future or past) time or eventually go to collision with one of the primaries. For orbits defined for all time, Chazy provided a classification of all possible asymptotic behaviors, usually called final motions.
By considering a sufficiently small mass ratio between the primaries, we analyze the interplay between collision orbits and various final motions and construct several types of dynamics.
In particular, we show that orbits corresponding to any combination of past and future final motions can be created to pass arbitrarily close to the massive primary. Furthermore, we construct arbitrarily large ejection-collision orbits (orbits which experience collision in both past and future times) and periodic orbits that are arbitrarily large and get arbitrarily close to the massive primary. Additionally, we also establish oscillatory motions in both position and velocity, meaning that as time tends to infinity, the superior limit of the position or velocity is infinity while the inferior limit remains a real number.
Last updated: Fri Nov 8 20:09:53 2024