No abstract

No abstract

The increasing number of anthropogenic space objects (ASOs) in low Earth orbit (LEO) poses a threat to the safety and sustainability of the space environment. Multiple companies are planning to launch large constellations of hundreds to thousands of satellites in the near future, increasing the probability of collisions and debris generation. This paper analyzes the long-term evolution of the LEO ASO population with the goal of estimating LEO orbital capacity. This is carried out by introducing a new probabilistic source–sink model. The developed source–sink model is a multishell multispecies model, which includes different object species, such as active and derelict satellites, and debris. Furthermore, debris are divided into the following two subgroups: trackable and nontrackable debris, the last ones representing a significant hazard for active satellites. In addition, the proposed model accounts for collision events and atmospheric drag effects, which include the influence of solar activity. Indeed, the Jacchia–Bowman 2008 thermospheric density model is exploited. The results prove that considering untracked debris within the model produces more collisions, and therefore a smaller population of active satellites affecting the safety of LEO and its orbital capacity.

No abstract

This paper investigates the application of theKoopman Operator theory to the motion of a satellite about a libration point in the Circular Restricted Three-Body Problem. Recently, the Koopman Operator has emerged as a promising alternative to the geometric perspective for dynamical systems, where the Koopman Operator formulates the analysis and dynamical systems in terms of observables. This paper explores the use of the Koopman Operator for computing both 2D and 3D periodic orbits near libration points. Further, simulation results show that the Koopman Operator provides analytical solutions with high accuracy for both Lyapunov and Halo orbits, which are then applied to a station-keeping application.Periodic orbits in the circular Restricted Three-Body Problem (RTBP), such as Lissajous and Halo type trajectories, are of high interest for space mission design applications. In particular, many missions, such as the cislunar space gateway concept, have been proposed that utilize these orbits. The proposed orbit for the gateway is a Near-Rectilinear Halo Orbit (NRHO), which is a non-Keplerian trajectory with the favorable properties of a continuous line of sight coverage for communications with Earth and fuel-efficient access to the lunar surface [1]. Although operating in the RTBP region while utilizing non-Keplerian trajectories has its benefits, it remains challenging to develop, analyze, and perform guidance, navigation, and control for these missions due to the nonlinearities of the RTBP region. Therefore, new approaches for the analytical analysis of these missions are needed.Analytical approaches exist for analyzing the RTBP and developing solutions for their trajectories. In particular, Richardson [2] developed a Lindstedt-Poincaré procedure for computing the Halo orbits through matching the 𝑥-𝑦 periodic frequency with that of the 𝑧 direction motion. Lindstedt-Poincaré methods are powerful perturbation approaches, but they require extensive algebraic computation and can be difficult to derive for higher-order solutions. In addition