论文标题
共振小体的世俗演变：在共面案例中的任意偏心率的半分析方法
Secular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar case
论文作者
论文摘要
我们研究粒子在深平均运动共振（MMR）中的世俗演变（MMR）与平面椭圆形中的行星限制了三个身体问题。我们不考虑地球的怪异$ e_p $中的任何限制，也不考虑粒子的怪异$ e $。所使用的方法基于半分析模型，该模型包括在数值上计算平均的谐振函数，假设在时间的谐振范围内，粒子的所有轨道元素都是恒定的。为了获得MMR内部的世俗演化，我们使用绝热不变原理，假设零振幅谐振库文布。我们在三维空间$（σ，e，\ varpi）$中构建二维表面（称为$ \ Mathcal {h} $表面），使我们能够预测这三个变量的世俗演化。 2：1 MMR用作显示一些结果的示例。我们发现了四个APSidal Colotation共振（ACR）家族，两个对称和两个不对称。几乎所有$ e_p $ value的对称家庭之一。另一个用于$ e_p> 0.3 $，$ e_p> 0.44 $的不对称$。我们证实了$ e $的世俗变化和$ \ \ varpi $通过数值集成预测的，即使初始条件从这些ACR中移开。为3：1和3：2 mmr提供了一些奇特的例子，显示了偏心率的大偏移。作为应用，将行星9研究为高偏心远处TNO的可能原因。
We study the secular evolution of a particle in deep mean motion resonance (MMR) with a planet in the planar elliptic restricted three body problem. We do not consider any restriction neither in the planet's eccentricity $e_p$ nor in the particle's eccentricity $e$. The methodology used is based on a semi-analytical model that consists on calculating the averaged resonant disturbing function numerically, assuming for this that in the resonant scale of time all the orbital elements of the particle are constant. In order to obtain the secular evolution inside the MMR, we make use of the adiabatic invariance principle, assuming a zero-amplitude resonant libration. We construct two-dimensional surfaces (called $\mathcal{H}$ surfaces) in the three-dimensional space $(σ, e, \varpi)$ that allow us to predict the secular evolution of these three variables. The 2:1 MMR is used as example to show some results. We found four apsidal corotation resonance (ACR) families, two symmetric and two asymmetric. One of the symmetric families exists for almost any $e_p$ value. The other one for $e_p>0.3$ and the asymmetric ones for $e_p>0.44$. We corroborate the secular variations in $e$ and $\varpi$ predicted by the model through numerical integrations even when the initial conditions are displaced from those ACR. Some peculiar examples are presented for the 3:1 and 3:2 MMR showing large excursions in eccentricity. As an application, the Planet 9 is investigated as a possible responsible of high eccentric distant TNOs.
