## 4 Discussion
However, the introduction of halo motion, depending on its amplitude, engenders a more intricate nadir point variation pattern and a broader latitude range within specific time windows, constituting the primary source of differences in viewing angle distribution and spatiotemporal ground coverage when compared to Moon-based platforms. Although halo motion slightly increases the range of nadir point latitudes (spanning over 28\({}^{\circ}\)S to 28\({}^{\circ}\)N) and widens the distribution range of viewing angles, it does not confer a decisive advantage in complementing Earth observation. Furthermore, over the course of a year, halo motion exerts a slight averaging effect on global coverage along latitudes. While it enhances observation time in Polar Regions, it does not distinctly improve observation frequency. The hallmark advantage of Lagrange points within the Earth-Moon system lies in their unique spatial location and dynamical properties in cislunar space. They can function as observatories for space observations encompassing the entirety of cislunar space, as well as transit stations for low-energy interplanetary transmissions [39; 40]. In comparison to geostationary Earth orbit (GEO), access to Lagrange points is cost-competitive, if not more economical, due to low-energy transfer orbits, and the maintenance costs are significantly lower than those associated with sustaining the north-south position of GEO orbits. This makes Lagrange points a viable option for Earth observation. It should be noted that when designing the halo orbit, the amplitude outside and inside the plane of the halo orbit, orbital period, and phase relative to the lunar orbit need to be considered to ensure the coverage of the polar region. Nevertheless, in contrast to Moon-based platforms, the L1 point exhibits remarkably similar geometric characteristics for Earth observation. Yet, considering the unique advantages of the Moon--such as its extensive lunar surface, marked by exceptional geological stability and protracted life cycles--the L1 point does not demonstrate a distinctive advantage. Consequently, lunar surfaces remain the preferred choice for Earth observation within the cislunar space. Nonetheless, it is essential to acknowledge that there are limitations and avenues for future improvements in this field. In fact, the actual orbital data cannot be accurately predicted due to the interference of various perturbations such as the solar gravitational force, the Earth's aspherical gravity, and the solar photopressure. Enhancing the determination of halo orbits is necessary for in-depth research. One potential avenue for achieving greater precision lies in adopting a realistic force model of the solar system to more accurately determine orbits, such as the doubly synchronous binary asteroid model [41] and the numerical continuation method [42]. However, it is crucial to balance precision with practicality, as overly precise orbit determination is often unnecessary. Additionally, the exploration of other periodic and quasi-periodic orbits, such as Lissajous orbits, which have found utility in space observation, warrants consideration for future research.