关于太阳系外系统Laplace-Lagrange久期理论的二阶质量扩展
On the extension of the Laplace-Lagrange secular theory to order two in the masses for extrasolar systems
摘要：
我们研究了几个系外行星系统的长期演化扩展的拉普拉斯-拉格朗日理论，以二阶的质量。使用的庞加莱正则变量的哈密顿展开，我们确定的基频的运动和计算分析的开普勒元素的长期演变。我们的研究清楚地表明，对于接近平均运动共振的系统，二阶近似比通常采用的一阶近似更准确地描述了它们的长期演化。此外，该方法考虑了平均距平对长期动态的影响。最后，我们建立了一个简单的标准，这是有用的区别三类不同的行星系统：（i）{ \it长期}系统（HD 11964、HD 74156、HD 134987、HD 163607、HD 12661和HD 147018）;（ii）系统{ \it接近平均运动共振}（HD 11506、HD 177830、HD 9446、HD 169830和$\upsilon$仙女座）;（iii）系统{ \it非常接近}或{ \it处于平均运动共振}（HD 108874、HD 128311和HD 183263）。
英文摘要：
We study the secular evolution of several exoplanetary systems by extending the Laplace-Lagrange theory to order two in the masses. Using an expansion of the Hamiltonian in the Poincaré canonical variables, we determine the fundamental frequencies of the motion and compute analytically the long-term evolution of the keplerian elements. Our study clearly shows that, for systems close to a mean-motion resonance, the second order approximation describes their secular evolution more accurately than the usually adopted first order one. Moreover, this approach takes into account the influence of the mean anomalies on the secular dynamics. Finally, we set up a simple criterion that is useful to discriminate between three different categories of planetary systems: (i) {\it secular} systems (HD 11964, HD 74156, HD 134987, HD 163607, HD 12661 and HD 147018); (ii) systems {\it near a mean-motion resonance} (HD 11506, HD 177830, HD 9446, HD 169830 and $\upsilon$ Andromedae); (iii) systems {\it really close to} or {\it in a mean-motion resonance} (HD 108874, HD 128311 and HD 183263).
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