This paper answers how multiple satellites are seen from the ground. This question is inspired by space-advertising, a public exhibition in the night sky using a dot matrix of satellites that are bright enough to be seen by the naked eye. Thus, it is important for space advertisement that the specific dot matrix is seen. Moreover, the stability of the dot matrix during a visible span is very valuable. To stabilize the dot matrix, this study formulates an apparent position of a dot from a representative dot seen from the ground. The formulation, linear functions of a set of relative orbital elements, reveals the appearance of the dot matrix. The proposed relative variable in the formulation drives the instability of the dot matrix, thereby revealing an initial stable configuration of deputies from a chief. The arbitrary dot matrix designed using the configuration is stable even at low elevations without orbital control during the visible span.

For deep-space mission design, the gravity of the Sun and the Moon can be first considered and utilized. Their gravity can provide the energy change for launching spacecraft and retrieving spacecraft as well as asteroids. Regarding an asteroid retrieval mission, it can lead to the mitigation of asteroid hazards and an easy exploration and exploitation of the asteroid. This paper discusses the application of the Sun-driven lunar swingby sequence for asteroid missions. Characterizing the capacity of this technique is not only interesting in terms of the dynamic insights but also non-trivial for trajectory design. The capacity of a Sun-driven lunar swingby sequence is elucidated in this paper with the help of the “Swingby-Jacobi” graph. The capacity can be represented by a range of the Jacobi integral that encloses around 660 asteroids currently cataloged. To facilitate trajectory design, a database of Sun-perturbed Moon-to-Moon transfers, including multi-revolution cases, is generated and employed. Massive trajectory options for spacecraft launch and asteroid capture can then be explored and optimized. Finally, a number of asteroid flyby, rendezvous, sample-return, and retrieval mission options enabled by the proposed technique are obtained.