Periodic orbits of the retrograde coorbital problem
Periodic orbits of the retrograde coorbital problem
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DOI：
10.1093/mnras/stz2868
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发表时间：
2019-10
影响因子：
4.8
通讯作者：
M. Morais;F. Namouni
中科院分区：
文献类型：
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作者：
M. Morais;F. Namouni
小行星（514107）Ka 'epaoka 'awela是第一个与木星在1/1平均运动共振中逆行绕太阳运动的物体。它的轨道在整个太阳系的年龄中都是稳定的，这意味着它一定是在太阳还在其诞生星团中时从另一颗恒星那里捕获的。Ka 'epaoka 'awela轨道也位于共轨道共振捕获概率的峰值。确定Ka 'epaoka 'awela和类似小行星在其演化过程中遵循的周期性轨道是精确理解其捕获机制的重要一步。在此，我们找到了二维逆行共轨道问题中的周期轨道族，并分析了它们在三维周期轨道上的稳定性和分叉性。我们的结果解释了在二维和三维共轨道捕获模拟中观察到的根本差异。特别地，我们发现平面运动的解析和数值结果在与平面的极小偏差处并不总是有效的。
Asteroid (514107) Ka‘epaoka‘awela is the first example of an object in the 1/1 mean motion resonance with Jupiter with retrograde motion around the Sun. Its orbit was shown to be stable over the age of the Solar system, which implies that it must have been captured from another star when the Sun was still in its birth cluster. Ka‘epaoka‘awela orbit is also located at the peak of the capture probability in the coorbital resonance. Identifying the periodic orbits that Ka‘epaoka‘awela and similar asteroids followed during their evolution is an important step towards precisely understanding their capture mechanism. Here, we find the families of periodic orbits in the two-dimensional retrograde coorbital problem and analyse their stability and bifurcations into three-dimensional periodic orbits. Our results explain the radical differences observed in 2D and 3D coorbital capture simulations. In particular, we find that analytical and numerical results obtained for planar motion are not always valid at infinitesimal deviations from the plane.