This paper focuses on the opportunity to use multiple star trackers to help space situational awareness and space surveillance. Catalogs of space debris around Earth are usually based on ground-based measurements, which rely on data provided by ground-based radar observations and ground-based optical observations. However, space-based observations offer new opportunities because they are independent of the weather and the circadian rhythms to which the ground system is subjected. Consequently, space-based optical observations improve the possibility of space debris detection and cataloging. This work deals with a feasibility study of an innovative strategy, which consists of the use of a star sensor with a dedicated algorithm to run directly on board. This approach minimizes the impact on the original mission of the satellite, and on this basis, it has also the function of space debris monitoring. Therefore, theoretically, every satellite with a star tracker can be used as a space surveillance observer. In this paper, we propose a multi-star space debris detecting and positioning method with constant geocentric observation. Using the multi-star tracker joint positioning method, the angle measurement data of the star tracker is converted into the spatial coordinates of the target. In addition, the Gaussian MMSE difference correction algorithm is used to realize the target positioning of multiple optical observations, and the spatial target position information of the multi-frame images is fused, thus completing the solution of the orbit equation. The simulation results show that the proposed method is sufficient to detect and position space debris. It also demonstrates the necessity and feasibility of cooperative network observation by multiple star trackers.