## Abstract

Recently, the first treatment of the space population as a multi-layer temporal network was introduced. This model has allowed the application of network theory techniques for a holistic treatment of the space environment. In this work, we go one step further by focusing on the physical layer of the network, investigating its structure, dynamics, and stability.

The interactions among resident space objects are modeled through their collision rates: each node represents a population of satellites in a given orbital class, and each link represents their time-varying collision rates with other nodes. Satellites can flow in between these classes and populations, depending on several sink and source phenomena, including explosions, collisions, natural decay due to atmospheric drag, post-mission disposal strategies, operational lifetime duration, and new launches. The underlying dynamics on the network is modeled as a stochastic contact process, in which nodes can assume two possible states: operational and non-operational. The network, therefore, presents a time-varying structure where the number of active and inactive objects, their distribution, their time-varying collision rates, and many other key variables can be studied. The conceptual simplicity and versatility of the network allow to study various topologies and dynamics, and therefore investigate interactions among space objects under different levels.

In this framework, several aspects are studied: first of all, two network topologies are introduced. Then, the concept of global stability of the network is introduced and discussed, and a stochastic evolutionary network model is built to simulate the sink and source phenomena in the space environment and evolve the overall population of objects in low Earth orbit for long periods of time. Finally, we perform experiments using a lattice network structure to show how this model can be used to probabilistically study the evolution of space objects and all the key variables involved, such as the number of collisions, the fragments generated, the collision rates evolution, and many others.

The interactions among resident space objects are modeled through their collision rates: each node represents a population of satellites in a given orbital class, and each link represents their time-varying collision rates with other nodes. Satellites can flow in between these classes and populations, depending on several sink and source phenomena, including explosions, collisions, natural decay due to atmospheric drag, post-mission disposal strategies, operational lifetime duration, and new launches. The underlying dynamics on the network is modeled as a stochastic contact process, in which nodes can assume two possible states: operational and non-operational. The network, therefore, presents a time-varying structure where the number of active and inactive objects, their distribution, their time-varying collision rates, and many other key variables can be studied. The conceptual simplicity and versatility of the network allow to study various topologies and dynamics, and therefore investigate interactions among space objects under different levels.

In this framework, several aspects are studied: first of all, two network topologies are introduced. Then, the concept of global stability of the network is introduced and discussed, and a stochastic evolutionary network model is built to simulate the sink and source phenomena in the space environment and evolve the overall population of objects in low Earth orbit for long periods of time. Finally, we perform experiments using a lattice network structure to show how this model can be used to probabilistically study the evolution of space objects and all the key variables involved, such as the number of collisions, the fragments generated, the collision rates evolution, and many others.

Original language | English |
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Pages | 1-9 |

Number of pages | 9 |

Publication status | Published - 23 Apr 2021 |

Event | 8th European Conference on Space Debris - ESA/ESOC, Darmstadt, Germany Duration: 20 Apr 2021 → 23 Apr 2021 https://space-debris-conference.sdo.esoc.esa.int/ |

### Conference

Conference | 8th European Conference on Space Debris |
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Country | Germany |

City | Darmstadt |

Period | 20/04/21 → 23/04/21 |

Internet address |

## Keywords

- space environment
- space debris
- network theory
- evolutionary model
- spacecraft conjunction assessment