Time scales for Co-orbital Cycles of Venus Trojans Asteroids

Co-orbital asteroids are asteroids locked in a 1:1 mean-motion resonance with a planet. The mechanism of capture of these objects into their current resonant configuration can shed light on the origin and evolution of asteroids and the whole Solar System. Terrestrial planets’ co-orbital configurations include retrograde satellite orbits (RS), tadpole orbits (T) around the Lagrangian equilibrium points L4 or L5, and horseshoe orbits around both L4 and L5 (H). At high eccentricity or inclination, co-orbital configurations may include compounds of T and RS (T-RS, T-RS-T), H and RS (H-RS) orbits, or transitions between distinct co-orbital modes. These instantaneous configurations may change into one another in short time scales, and Venus Trojans may alternate between several of these configurations before being lost to a passing orbit. We define the time between long periods of staying in a passing orbit as a co-orbital cycle. Here, we use digital filtering of the resonant arguments and rolling averages, a calculation used to analyze data points by creating averages of different subsets of the full data set, of the number of close encounters with Venus of a large population of clones of the currently known co-orbitals of Venus to estimate the times of permanence in one or several cycles. The typical duration of a single cycle is $12000\pm 6000$ yrs. Some asteroids may experience two or more cycles before finally escaping co-orbital status, remaining in circulating orbits in between cycles. We call these orbital configurations “dormant orbit”. Six of the Venus’ Trojan may become Potentially Hazardous Asteroid (PHA) with Earth in a few thousand of years, and three asteroids, 2020 SB, 524522, and 2020 CL1, have a severe risk of collision.