We present a GPU-accelerated numerical integrator specifically optimized for stability calculations of small bodies in planetary systems. Specifically, the integrator is designed for cases when large numbers of test particles (tens or hundreds of thousands) need to be followed for long durations (millions of orbits) to assess the orbital stability of their initially “close-encounter free” orbits. The GLISSE (Gpu Long-term Integrator for Solar System Evolution) code implements several optimizations to achieve a roughly factor of 100 speed increase over running the same code on a CPU. We explain how various hardware speed bottlenecks can be avoided by the careful code design, although some of the choices restrict the usage to specific types of application.

As a first application, we study the long-term stability of small bodies initially on orbits between Uranus and Neptune. We map out in detail the small portion of the phase space in which small bodies can survive for 4.5 billion years of evolution; the ability to integrate large numbers of particles allow us to identify for the first time how instability-inducing mean-motion resonance overlaps sharply define the stable regions. As a second application, we map the boundaries of 4 Gyr stability for transneptunian objects in the 5:2 and 3:1 mean-motion resonances, demonstrating that long-term perturbations remove the initially stable Neptune-crossing members.

我们提出了一个 GPU 加速的数值积分器，专门针对行星系统中小天体的稳定性计算进行了优化。具体而言，积分器专为需要长时间（数百万轨道）跟踪大量测试粒子（数万或数十万）以评估其最初“无近距离接触”轨道的轨道稳定性的情况而设计。GLISSE（Gpu Long-term Integrator for Solar System Evolution）代码实施了多项优化，与在 CPU 上运行相同代码相比，速度大约提高了 100 倍。我们解释了如何通过仔细的代码设计来避免各种硬件速度瓶颈，尽管一些选择将使用限制为特定类型的应用程序。

作为第一个应用，我们研究最初在天王星和海王星之间轨道上的小天体的长期稳定性。我们详细绘制了小物体可以在其中存活 45 亿年进化的一小部分相空间；整合大量粒子的能力使我们第一次确定了引起不稳定的平均运动共振重叠如何清晰地定义稳定区域。作为第二个应用，我们在 5:2 和 3:1 平均运动共振中绘制了跨海王星物体的 4 Gyr 稳定性边界，证明长期扰动消除了最初稳定的海王星交叉成员。