The orbital dynamics in the gravitational environment of irregular asteroids is an important issue for space missions and a quite complex problem. In this paper we propose a methodological approach for computing periodic orbits around rotating, irregular-shaped asteroids. Our study starts from the families of periodic orbits of a triaxial ellipsoid model that can approximate the gravitational field of an irregular body. The families of periodic orbits of the triaxial ellipsoid have particular structures and symmetries. By using a particular periodic orbit, which belongs in a family of the ellipsoid model, we introduce and apply the method of shape continuation in order to obtain a corresponding periodic orbit in the gravitational field of an irregular body, which in our study is approximated with a sufficient number of mascons. Then, by applying analytic continuation to this orbit, we can compute a family of periodic orbits in the asymmetric gravitational field. This family can be assumed as a perturbed family, with respect to that of the ellipsoid, with the strength of the perturbation being dependent on the irregular shape of the asteroid and the distance of the orbits from its surface. We apply our methodology to the asteroid 433 Eros and present results on particular planar and 3D orbits. Similarities and differences between families of the ellipsoid and the asteroid model are indicated and discussed.

不规则小行星引力环境中的轨道动力学是空间任务的一个重要问题，也是一个相当复杂的问题。在本文中，我们提出了一种计算围绕旋转的不规则形状小行星的周期轨道的方法论方法。我们的研究从可以近似不规则体引力场的三轴椭球模型的周期轨道族开始。三轴椭球的周期轨道族具有特定的结构和对称性。通过使用属于椭球模型族的特定周期轨道，我们引入并应用形状延续的方法，以获得不规则体引力场中相应的周期轨道，在我们的研究中近似为足够数量的 mascon。然后，通过对该轨道应用解析延拓，我们可以计算非对称引力场中的一系列周期轨道。相对于椭球体，该族可以被假定为扰动族，扰动的强度取决于小行星的不规则形状和轨道与其表面的距离。我们将我们的方法应用于小行星 433 Eros，并在特定的平面和 3D 轨道上展示结果。指出并讨论了椭球族和小行星模型之间的异同。扰动的强度取决于小行星的不规则形状和轨道与其表面的距离。我们将我们的方法应用于小行星 433 Eros，并在特定的平面和 3D 轨道上展示结果。指出并讨论了椭球族和小行星模型之间的异同。扰动的强度取决于小行星的不规则形状和轨道与其表面的距离。我们将我们的方法应用于小行星 433 Eros，并在特定的平面和 3D 轨道上展示结果。指出并讨论了椭球族和小行星模型之间的异同。