* Speaker.* Andrew Clarke

*Date.*06.12.22 at 3:30 pm

*Consider the 4-body problem with arbitrary masses in the regime where 3 bodies revolve around the other. We assume that the semimajor axes of theĀ orbital ellipses are of different orders and that there is non-negligible mutual inclination between the orbital planes of bodies 1 and 2. We prove that, given any finite itinerary of the angular momentum vector of body 2, there exist orbits of the 4-body problem shadowing this itinerary with arbitrary precision. From a geometric point of view, this implies that the eccentricity of the orbit of body 2 and the mutual inclination of the orbital planes of bodies 2 and 3 can be made to follow any finite itinerary. For example, the second planet can flip from prograde to retrograde nearly horizontal revolutions and back again arbitrarily many times.*

*Abstract*.