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arXiv 1004.0726astro-ph.EP
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两颗行星共轨运动的动力学

Dynamics of two planets in co-orbital motion

C. A. Giuppone, C. Beaugé, T. A. Michtchenko, S. Ferraz-Mello

摘要:

我们研究了两个行星锁定在一个共轨配置的周期轨道的稳定区域和家庭。我们考虑不同的行星质量比和轨道偏心率,我们还假设两颗行星共享同一个轨道平面。最初,我们进行数值模拟密切初始条件的网格映射稳定/混沌运动的区域,并确定平衡的解决方案。这些结果稍后使用半分析模型进行更详细的分析。除了已知的准卫星(QS)轨道和经典的平衡拉格朗日点L4和L5,我们还发现了一个新的制度的非对称周期解。对于低偏心率,这些值位于$(σ,Δω) = (\pm 60°, \mp 120°)$,其中σ是平均偏心距的差值,Δω是近心点偏心距的差值。这些反拉格朗日解的位置随质量比和轨道偏心率而变化,并且发现偏心率高达~ 0.7。最后,我们还对其中一颗行星施加了缓慢的质量变化,并分析了其对初始不对称周期轨道的影响。我们发现,共振的解决方案是保存,只要质量变化是绝热的,几乎没有变化的平衡值的角度。

英文摘要:

We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities, also we assume that both planets share the same orbital plane. Initially we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analyzed in more detail using a semi-analytical model. Apart from the well known quasi-satellite (QS) orbits and the classical equilibrium Lagrangian points L4 and L5, we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at $(σ,Δω) = (\pm 60°, \mp 120°)$, where σis the difference in mean longitudes and Δωis the difference in longitudes of pericenter. The position of these Anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities, and are found for eccentricities as high as ~ 0.7. Finally, we also applied a slow mass variation to one of the planets, and analyzed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.

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