In this paper we propose a notion of stability, which we call \(\varepsilon -N\)-stability, for systems of particles interacting via Newton’s gravitational potential, and orbiting a much bigger object. For these systems the usual thermodynamical stability condition, ensuring the possibility to perform the thermodynamical limit, fails, but one can use as relevant parameter the maximum number of particles N that guarantees the \(\varepsilon -N\)-stability. With some judicious but not particularly optimized estimates, borrowed from the classical theory of equilibrium statistical mechanics, we show that our model has a good fit with the data observed in the Solar System, and it gives a reasonable interpretation of some of its global properties.

在本文中，我们提出了稳定性的概念，我们称之为\(\varepsilon -N\) -稳定性，用于通过牛顿引力势相互作用的粒子系统，并围绕一个更大的物体运行。对于这些系统，通常的热力学稳定性条件（确保执行热力学极限的可能性）失败了，但可以使用保证\(\varepsilon -N\)稳定性的最大粒子数N作为相关参数。通过一些明智但不是特别优化的估计，借鉴了平衡统计力学的经典理论，我们表明我们的模型与太阳系中观测到的数据有很好的拟合，并且它对它的一些全局特性给出了合理的解释。