## 1 Introduction  
Occultation is a well-proven remote sensing method that requires at least one electromagnetic signal transmitting satellite (Tx) and one receiving satellite (Rx) to observe the Earth's atmospheric thermodynamic state variables (e.g., pressure, temperature, and humidity) [1; 2; 3; 4; 5; 6], chemical composition (e.g., the greenhouse gases H\({}_{2}\)O, CO\({}_{2}\), CH\({}_{4}\), N\({}_{2}\)O, O\({}_{3}\), and CO) [7; 8; 9; 10; 11], dynamics (e.g., line-of-sight wind speed) [12], and ionospheric electron density profiles by using particular frequency signals [13]. Occultation events happen when the Tx and Rx see each other through the atmosphere just before (a setting occultation event) or after (a rising occultation event) they are occulted by the Earth during the relative orbital motion [14]. The amount of occultation data depends on the odds of occultation events, so satellite orbit and constellation design is significant to occultation Earth observation missions to optimize the performances and reduce the costs. In recent years, Global Navigation Satellite System (GNSS) radio occultation (RO) has become a major method by which to observe the Earth's atmospheric thermodynamic state variables, but it has a temperature and humidity ambiguity problem in the troposphere [15; 16; 17; 18]. Fortunately, as an advanced technique, low Earth orbit intersatellite link (LEO-LEO) microwave occultation (LMO), using various X/K band and M band frequencies around the 22 GHz and 183 GHz water absorption lines, can exploit both the refraction and absorption of the signals to solve the temperature-humidity ambiguity problem; thus, LMO enables us to retrieve pressure, temperature, and humidity profiles without background information [5; 15]. Liquid water and rain rate profiles as well as turbulence and complementary 3D cloud information can be co-observed [18; 19]. Additionally, the LEO-LEO infrared laser occultation (LIO), using laser signals in the short-wave infrared band (2-2.5 \(\upmu\)m) between LEO satellites, has been designed to accurately observe key trace gas species for chemistry and the climate (e.g., the greenhouse gases H\({}_{2}\)O, CO\({}_{2}\), CH\({}_{4}\), N\({}_{2}\)O, O\({}_{3}\), and CO), line-of-sight wind speed, and profiles of cloud layers and aerosols as by-products [7; 8; 9; 18; 20; 21]. LIO measures the absorption of the signals to retrieve volume mixing ratio (VMR) profiles of the greenhouse gases, in which the differential transmission principle between carefully selected pairs of absorption signals and reference signals is commonly used. The feasibility of the LMO and LIO techniques has been proven by ground-based demonstration experiments [10; 11; 17; 18; 22; 23]. Nowadays, the development of small satellites and remote sensing instrument miniaturization technologies allows LEO-LEO occultation to provide observations with global coverage and acceptable mission costs. Moreover, the increase in the in-orbit and planned LEO constellations provides more signal and instrument onboard opportunities to realize space-borne LEO-LEO occultation observations in combination with other spacecraft, such as communication, navigation, and meteorological satellites. Therefore, the impacts of the Rx and Tx orbital parameters on the number and spatial-temporal distribution of LEO-LEO occultation events and the exploration capability of LEO-LEO occultation constellations need to be deeply investigated and assessed as they are significant to LEO-LEO mission design and optimization. In this study, the impacts of the Rx and Tx orbital parameters on the LEO-LEO occultation event numbers and distribution were investigated and assessed using a two-satellite constellation with one LEO Rx and one LEO Tx based on simulation datasets by the variable separation approach. Then, 2 Rx/2 Tx, 6 Rx/6 Tx, and 12 Rx/12 Tx dual-orbit constellations and 6 Rx/6 Tx multiple-orbit constellations were designed and their occultation event numbers and spatial-temporal distributions were evaluated and analyzed.