## 3 Results
### Variation Analysis of the Angular Combination Distribution  
The angular combination distribution refers to the coverage of the three observational angles. For an Earth observation platform, the angular combination distribution characterizes the capability of its angular sampling. For a Moon-based platform, the angular combination distribution differs at different observation points because of the orbital characteristics of the Moon and Sun. The orbits of the Moon and Sun can be parameterized as the distance from the Earth and the position of nadirs. It can be inferred from Equations (21)-(27) that the distance does not significantly influence the zenith angles and relative azimuth angle. Hence, the movement of lunar and solar nadirs are the primary factors affecting the angular combination distribution. Actually, neither the Sun nor the Moon has a fixed orbital inclination. As the Earth's rotational axis is inclined about 23\({}^{\circ}\)27\({}^{\prime}\) with respect to the ecliptic plane, the Sun's nadir varies between the 23\({}^{\circ}\)27\({}^{\prime}\)N and 23\({}^{\circ}\)27\({}^{\prime}\)S over one year. The Moon's inclination also changes. As the Moon is orbiting the Earth, the plane of the Moon's orbit is tilted (around 5\({}^{\circ}\)9\({}^{\prime}\)) with respect to the ecliptic plane. Thus, the lunar nadir moves between the southern and northern hemispheres for one orbital period. It is clear that the Moon's maximum and minimum declination vary because the mean ecliptic longitude of the ascending node continuously recedes westward along the ecliptic. It recedes about 19\({}^{\circ}\) westward every year over an 18.6-year period. Consequently, when the mean ecliptic longitude of the ascending node is 0\({}^{\circ}\), the ascending node coincides with the vernal equinox, and thus the obliquity of the ecliptic reaches a maximum. Figure 2: Observational angles, that is, the (**a**) viewing zenith angle, (**b**) solar zenith angle, (**c**) relative azimuth angle, obtained based on the method proposed in this paper and DE430. In contrast, when the mean ecliptic longitude of the ascending node is 180\({}^{\circ}\), the descending node and vernal equinox coincide, and the obliquity of the ecliptic reaches a minimum. Therefore, the extreme value of the Moon's nadir varies roughly from about 18\({}^{\circ}\) to 28\({}^{\circ}\) over an 18.6-year period. Variations in the Moon's and Sun's nadirs lead to differences in the angular combination distribution for different observed points. In general, as the Moon's and Sun's nadirs mainly move within the mid-low latitude zone, the viewing and solar zenith angle of observed points in this region can reach a maximum of 90\({}^{\circ}\) and thus range from 0\({}^{\circ}\) to 90\({}^{\circ}\). For the solar zenith angle, its minimum varies with the seasons because of the movement regularity of the Sun's nadir, and the maximum difference is around 23\({}^{\circ}\). For the viewing zenith angle, the difference of its maximum can reach 10\({}^{\circ}\) under the two extreme cases of 0\({}^{\circ}\) and 180\({}^{\circ}\) for mean ecliptic longitude of ascending node. The relative azimuth angle is defined only when the observed points can be visible by the Moon and Sun simultaneously. Thus, it is mainly affected by the Moon phase angle. The moon phase refers to the part of the Moon that is illuminated by the Sun and can also be seen on the Earth. It represents the relative position of the Moon, Sun, and Earth. Specifically, it mainly affects the difference between the longitude of the Sun's and Moon's nadir, and the period of the moon phase angle is a synodic month. To reveal differences in the distribution of the angular combination for different observed points, we compared the latitudinal and longitudinal variations for selected points. As shown in Figure 3, ten observed points were selected at different latitudes and longitudes for experiments.