This study investigates the influence of orbital parameters on the number of satellite visibility events from ground stations, with the aim of optimizing orbit design for space weather monitoring missions. A two-body dynamical model was employed to simulate the satellite trajectory over a 24 hour period, and the number of visibility passes was evaluated with respect to a network of five ground stations located across Iran. The contribution of key orbital elements—including semi-major axis, eccentricity, inclination, RAAN, argument of perigee, and mean anomaly—was quantified using the global Sobol sensitivity analysis method. The first-order Sobol indices revealed that inclination and argument of perigee exert the strongest independent influence on visibility, with maximum values of 0.45 and 0.18, respectively. In contrast, parameters such as RAAN and mean anomaly exhibited minimal first order effects, yet their total indices indicated highly significant interactive contributions, in some cases exceeding 0.9. Furthermore, scenarios corresponding to the maximum number of daily passes were identified. All five stations recorded configurations yielding up to nine passes within 24 hours. The associated orbital parameters exhibited diverse geometrical characteristics, ranging from nearly circular orbits with low eccentricity (0.0028) to more elongated orbits with higher eccentricity (0.0915), and inclinations spanning approximately 40° to 60°. These findings demonstrate the critical role of both independent and interactive effects of orbital elements in determining ground visibility, and they provide valuable insights for the multi-objective design of satellite orbits aimed at enhancing temporal coverage, maximizing pass frequency, and improving the efficiency of space weather monitoring missions.