Motivated by some problems in Celestial Mechanics that combines quasihomogeneous potential in the anisotropic space, we investigate the existence of several families of first kind symmetric periodic solutions for a family of planar perturbed Kepler problem. In addition, we give sufficient conditions for the existence of first kind periodic solutions and also we characterize its type of stability. As an application of this general situation, we discuss the existence of symmetric periodic solutions for the anisotropic Kepler problem plus a generalized anisotropic perturbation, (shortly, p-AKPQ problem) and for the Kepler problem plus a generalized anisotropic perturbation (shortly, p-KPQ problem), as continuation of circular orbits of the two-dimensional Kepler problem. To get this objective, we consider different types of perturbations and then we apply our main result.

受天体力学中结合各向异性空间中准齐次势的一些问题的启发，我们研究了一类平面扰动开普勒问题族的几类第一类对称周期解的存在。此外，我们为第一类周期解的存在提供了充分的条件，并刻画了其稳定性的类型。作为这种一般情况的应用，我们讨论了各向异性开普勒问题加广义各向异性摄动（简称p-AKPQ问题）和开普勒问题加广义各向异性摄动（简称p- KPQ问题），作为二维开普勒问题的圆形轨道的延续。为了达到这个目标，