We focus on a type of circular restricted five-body problem in which four primaries with equal masses form a regular tetrahedron configuration and circulate uniformly around the center of mass of the system. The fifth particle, which can be regarded as a small celestial body or probe, obeys the law of gravity determined by the four primaries. The geometric configuration of zero-velocity surfaces of the fifth particle in the three-dimensional space is numerically simulated and addressed. Furthermore, a transfer trajectory of the fifth particle skimming over four primaries then is designed.

From the statistical point of view, this paper mainly emphasizes the orbital distribution laws of Jupiter's irregular moons, most of which are located in Ananke group, Carme group and Pasiphae group. By comparing 19 known continuous distributions, it is verified that there are suitable distribution functions to describe the distribution of these natural satellites. For each distribution type, interval estimation is used to estimate the corresponding parameter values. At a given significant level, one-sample Kolmogorov-Smirnov nonparametric test is applied to verify the specified distribution, and we often select the one with the largest p-value. The resultsshow that all the semi-major axis, mean inclination and the orbital period of the moons in Ananke group and Carme group obey the Stable distribution. In addition, according to Kepler's third planetary motion law, and by comparing the theoretically calculated best-fit cumulative distribution function (CDF) with the observed CDF, we demonstrate that the theoretical distribution is in good agreement with the empirical distribution. Therefore, these characteristics of Jupiter's irregular moons are indeed very likely to follow some specific distribution laws, and it will be possible to use these laws to help study certain features of poorly investigated moons or even predict undiscovered ones.