Long-term configuration stability is essential for an interferometric detection constellation (IDC), which is closely related to initial uncertainty. Therefore, it is vital to evaluate the uncertainty and characterize the configuration stability. In this study, an analytical method was developed for the configuration uncertainty propagation of a geocentric triangular IDC. The angular momentum and the argument latitude were found to be significantly affected by the initial uncertainty and were selected as the core variables. By averaging the perturbation in one revolution, an analytical solution was proposed for propagating the core orbital elements in one revolution. Subsequently, the analytical solution of the orbit elements during the mission period is obtained by multiplying the solutions in iterative revolutions. The relationship between the selected orbital elements and the configuration stability parameters was established using an analytical solution. The effects of the initial uncertainty in different directions on the configuration and stable domains were studied. Simulations show that the developed method is highly efficient and accurate in predicting the configuration stability. The relative error with respect to the Monte Carlo simulations was less than 3% with a time consumption of 0.1%. The proposed method can potentially be useful for constellation design and stability analysis.

Asteroid 469219 Kamo'oalewa, also named 2016 HO3, is a small-size fast-rotating near-Earth asteroid, which is a potential target for future explorations. Owing to its weak gravity and fast spin rate, the dynamics on the surface or in the vicinity of 2016 HO3 are significantly different from those of planets or other small bodies explored in previous missions. In this study, the geophysical and orbital environments of 2016 HO3 were investigated to facilitate a potential mission design. First, the geometric and geopotential topographies of 2016 HO3 were examined using different shape models. The lift-off and escape conditions on its fast-rotating surface were investigated. Then, the periodic orbits around 2016 HO3 were studied in the asteroid-fixed frame and the Sun–asteroid frame considering the solar radiation pressure. The stable regions of the terminator orbits were discussed using different parameters. Finally, the influence of the nonspherical shape on the terminator orbits was examined. The precise terminator orbits around a real shape model of 2016 HO3 were obtained and verified in the high-fidelity model. This study shows that the polar region of 2016 HO3 is the primary region for landing or sampling, and the terminator orbits are well suited for global mapping and measurements of 2016 HO3. The analysis and methods can also serve as references for the exploration of other small fast-rotating bodies.

Satellite encounters during close operations, such as rendezvous, formation, and cluster flights, are typical long-term encounters. The collision probability in such an encounter is a primary safety concern. In this study, a parametric method is proposed to compute the long-term collision probability for close satellite operations with initial state uncertainty. Random relative state errors resulting from system uncertainty lead to possible deviated trajectories with respect to the nominal one. To describe such a random event meaningfully, each deviated trajectory sample should be mapped to a unique and time-independent element in a random variable (RV) space. In this study, the RV space was identified as the transformed state space at a fixed initial time. The physical dimensions of both satellites were characterized by a combined hard-body sphere. Transforming the combined hard-body sphere into the RV space yielded a derived ellipsoid, which evolved over time and swept out a derived collision volume. The derived collision volume was solved using the reachable domain method. Finally, the collision probability was computed by integrating a probability density function over the derived collision volume. The results of the proposed method were compared with those of a nonparametric computation-intensive Monte Carlo method. The relative difference between the two results was found to be < 0.6%, verifying the accuracy of the proposed method.

In this paper, we investigate the orbital behavior of the transition between the quasi-satellite (QS) and horseshoe (HS) motions of 2016 HO ${}_3$. Based on the phase space structure in the Sun–Earth circular restricted three-body problem, we find that the surface of 2016 HO ${}_3$ in the torus space is a compound surface formed by QS and HS portions. Its co-orbital motion is therefore a QS–HS transition. 2016 HO ${}_3$ is currently located in a QS state, and its locus clings to the QS portion in the isosurface in agreement with the semi-analytical results. We provide a criterion to separate the QS and HS stages in the transition and obtain accurate incoming and outgoing epochs of the QS motion. We then propose an approximate curve to describe the locus of 2016 HO ${}_3$ in the $\omega -e$ projection. Virtual asteroids (VAs) near 2016 HO ${}_3$ in the isosurface were created to study the influence of the initial state of the QS–HS transition. We find that the duration of the QS state is mainly influenced by the loci in the $\omega -e$ projection. The VAs with large QS durations usually have longer loci across the QS region than those with shorter durations. In addition, although some VAs are close to 2016 HO ${}_3$ in the $\omega -e$ projection, their co-orbital behaviors are significantly different from that of the latter. This indicates that the QS–HS transition of 2016 HO ${}_3$ is sensitive to the $(\omega ,e)$ position.

In this paper, the optimal interplanetary transfer including planetary escape and capture phases is investigated in the heliocentric frame. Based on primer vector theory, a modified cost function with variable coefficients is developed to reflect the gravitational effect more precisely. The necessary conditions as well as the transversality conditions of the new cost function are derived to search the optimal solution in fixed-time. By introducing the initial and final coasts, the optimal interplanetary transfer is extended to the time-free situation. Finally, the proposed method is applied to the Earth-Mars and Earth-Asteroid transfer. Comparisons with existing methods show that the proposed method can provide better transfer performances with high efficiency. The proposed method extends the application of primer vector theory and provides a fast and accurate reference for preliminary mission design in spacecraft planetary exploration.

This paper investigates the equilibria and their stabilities in the doubly synchronous binary asteroid systems, which are modelled as the two tri-axial ellipsoids with various shape and system parameters. Particularly, the influences of shape and system parameters on equilibria are discussed analytically. Firstly, the geometrical models of doubly synchronous binary asteroid systems are established. The dual second degree and order gravity field is employed to approximate the gravitational potential of the system. Six shape and system parameters are defined. Then, based on the linearized perturbation equations, the explicit expressions of the offsets of equilibria in doubly synchronous systems are derived, which clearly illustrate the relationship between the distribution of equilibria and the variations of shape parameters. Further, the approximate expressions are applied to estimate the offsets of equilibria due to parameter errors, respectively. Finally, in order to have a better insight into the equilibriaum structure, the stabilities of equilibria under different system parameters are investigated. In particular, critical regions of triangular equilibria are calculated and the role of the relative distance on the stability is discussed in detail. This study could provide a preliminary analysis of equilibria for the mission design in doubly synchronous binary asteroid systems.