Abstract: Orbital perturbation theory is broadly used for the prediction and evolution analysis of perturbed two-body problem, as well as the design of control strategies for orbit corrections. Then, orbital perturbation is a core topic in orbital mechanics courses. During the research work, we find a paradox related to the concept of orbital perturbation and provided a reasonable explanation after some analyses. This paradox involves the definition of orbital elements and their conversion with the position and velocity vectors. The author introduced this paradox into the course instruction, guiding students to engage in critical thinking from unconventional perspectives. This pedagogical approach significantly enhanced their comprehensive grasp of fundamental concepts while cultivating independent thinking capabilities. By elevating the course's challenge level, the implementation yields substantial improvements in teaching efficacy and student learning outcomes.