## 1 Introduction
In order to use a Moon-based platform, the first step is to model its observation geometry. The most fundamental method is to unify the Moon-based sensor, Sun, and observed point in the same coordinate system based on the planetary ephemerides. Planetary ephemerides mainly provide the positions and attitudes of the Moon and Sun for Moon-based Earth observations. Many types of planetary ephemerides have been published by different organizations [22; 23; 24]. The development ephemeris (DE) established by the Jet Propulsion Laboratory is one of the most widely used ephemeris in previous studies, and there are many versions of this ephemeris (e.g., DE405, DE410, DE421, and DE430) [24]. Based on the DE, the lunar and solar positions and attitudes at any time can be calculated using the Chebyshev interpolation, as demonstrated in various pioneering studies. [PERSON] et al. [21] constructed an observation geometry based on DE 421 and discussed the characteristics and scientific objectives of Moon-based Earth observation. [PERSON] et al. [25] analyzed the geometrical characteristics of Moon-based Earth observations using an ellipsoid model based on DE430. [PERSON] et al. [26] used DE 405 and DE 421 data and systems tool kit numerical analysis data to simulate the observation geometry. [PERSON] et al. [27] analyzed the geometric characteristics and coverage of Moon-based Earth observations in the electro-optical region based on DE430. [PERSON] et al. [28] constructed a geometric Moon-based platform model based on DE430 and analyzed the observation scope and spatial coverage. [PERSON] et al. [29] simulated the spatiotemporal coverage of Moon-based synthetic aperture radar (SAR) based on DE 430 and provided guidelines for the optimal site selection for Moon-based SAR. [PERSON] et al. [30] analyzed the spatiotemporal characteristics of Moon-based Earth observation based on DE430. [PERSON] et al. [31] compared the observation duration of the two polar regions of Earth from four specific sites on the Moon-based DE 430. [PERSON] et al. [32] analyzed the global spatiotemporal sampling characteristics of Moon-based Earth observation based on DE430. Apart from very high-precision planetary ephemerides, analytical models are available for constructing the observation geometry. [PERSON] et al. [33] developed an observational geometry SAR model based on the simplified Keplerian orbital model. [PERSON] and [PERSON] [34] constructed dynamic models for a Moon-based SAR based on the Ephemerides Lunaires Parisiennes theory (ELP 2000), which is a lunar semi-analytic theory. The results of these studies have provided valuable insights into the construction of observation geometries for observational angles based on an analytic model. In addition, because the analysis of angular combination characteristics does not require very high-precision solar and lunar positions, the introduction of simple analytic models will make preliminary studies more affordable. Thus, it is of interest to model the observation geometry based on analytical expressions of the Moon's and Sun's orbits. Some scholars have initially carried out pioneering research on the characteristics of angular sampling for a Moon-based platform. [PERSON] et al. [35] and [PERSON] et al. [36] adopted four types of observation angular parameters, that is, the viewing zenith angle, solar zenith angle, viewing azimuth angle, and solar azimuth angle, to describe light incident from the Sun and reflected from surface features. In contrast, [PERSON] et al. [37] reduced the four angular parameters to three parameters by introducing the relative azimuth angle, which is the difference between the viewing and solar azimuth angles. Compared with the four parameters, the relative azimuth angles of the three parameters can be used to directly describe the relative positions of a Moon-based sensor, the Sun, and the observed point. However, few studies have focused on the effect of time sampling interval on the angular combination richness.