Asteroids in retrograde resonance with Jupiter and Saturn
M.H.M. Morais, F. Namouni

TL;DR
This paper identifies the first known Solar System objects in retrograde resonance with Jupiter and Saturn, revealing their orbital characteristics and transient resonant states over thousands of years.
Contribution
It reports the discovery of the first known asteroids in retrograde resonance with Jupiter and Saturn, expanding understanding of orbital dynamics in the Solar System.
Findings
Two asteroids in current retrograde resonance with Jupiter.
One asteroid in retrograde resonance with Saturn.
Resonant configurations last for several thousand years.
Abstract
We identify a set of asteroids among Centaurs and Damocloids, that orbit contrary to the common direction of motion in the Solar System and that enter into resonance with Jupiter and Saturn. Their orbits have inclinations I >= 140 deg and semi-major axes a < 15 AU. Two objects are currently in retrograde resonance with Jupiter: 2006 BZ8 in the 2/-5 resonance and 2008 SO218 in the 1/-2 resonance. One object, 2009 QY6, is currently in the 2/-3 retrograde resonance with Saturn. These are the first examples of Solar System objects in retrograde resonance. The present resonant configurations last for several thousand years. Brief captures in retrograde resonance with Saturn are also possible during the 20,000 years integration timespan, particularly in the 1/-1 resonance (2006 BZ8) and the 9/-7 resonance (1999 LE31).
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