论文标题
共轨稳定区域的结构随质量比的函数
The structure of the co-orbital stable regions as a function of the mass ratio
论文作者
论文摘要
尽管到目前为止，寻找明显的外轨道机构尚未成功，但人们认为它们必须像太阳系中一样普遍。共轨道系统已被广泛研究，并且有几项有关稳定性甚至编队的作品。但是，对于稳定区域的大小和位置，作者通常描述其结果，但没有提供在没有数值模拟的情况下找到它们的方法，在大多数情况下，质量比值范围很小。在当前的工作中，我们研究了多种质量比系统的共轨稳定区域的结构，并建立了经验方程来描述它们。它允许从几个系统的参数估算共轨稳定区域的大小和位置。成千上万的无质量颗粒分布在大型次要身体的共轨道区域中，并以数值模拟，以采用平面圆形限制的三体问题的广泛质量比（$μ$）。结果表明，马蹄形区域的上限在$ 9.539 \ times 10^{ - 4} <μ<1.192 \ times 10^{ - 3} $之间，对应于从中学到分隔的最小角度距离，到sameatrix到$ 27.239^{O}^{O} $} $} $ 27.802^{o} $} $} $。我们还发现，在共占区域中存在稳定性的极限约为$μ= 2.3313 \ times 10^{ - 2} $，远小于线性理论预测的值。发现了多项式函数以描述稳定区域参数，并表示任何系统的估计值估计，以估计为$ 9.547 \ times 10^{ - 5} \ leqleqμ\ leqμ\ leq 2.331 \ leq 2.331 \ times 10^times 10^{ - 2} $。
Although the search for extra-solar co-orbital bodies has not had success so far, it is believed that they must be as common as they are in the Solar System. Co-orbital systems have been widely studied, and there are several works on stability and even on formation. However, for the size and location of the stable regions, authors usually describe their results but do not provide a way to find them without numerical simulations, and, in most cases, the mass ratio value range is small. In the current work, we study the structure of co-orbital stable regions for a wide range of mass ratio systems and built empirical equations to describe them. It allows estimating the size and location of co-orbital stable regions from a few system's parameters. Thousands of massless particles were distributed in the co-orbital region of a massive secondary body and numerically simulated for a wide range of mass ratios ($μ$) adopting the planar circular restricted three-body problem. The results show that the horseshoe regions upper limit is between $9.539 \times 10^{-4} < μ< 1.192 \times 10^{-3}$, which correspond to a minimum angular distance from the secondary to the separatrix between $27.239^{o} $ and $27.802^{o} $. We also found that the limit to exist stability in the co-orbital region is about $μ= 2.3313 \times 10^{-2}$, much smaller than the value predicted by the linear theory. Polynomial functions to describe the stable region parameters were found, and they represent estimates of the angular and radial widths of the co-orbital stable regions for any system with $9.547 \times 10^{-5} \leq μ\leq 2.331 \times 10^{-2}$.
