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A Stochastic Dynamic Network Model of the Space Environment

Yirui Wang, Pietro De Marchi, Massimiliano Vasile

TL;DR

The paper presents NESSY, a stochastic dynamic network framework for modeling the space environment where nodes group objects by class and orbit site, and links encode collision, fragmentation, and decay flows. It derives a compact evolution equation $oldsymbol{X}_{k+1} = oldsymbol{X}_{k} + oldsymbol{Y}(oldsymbol{X}_k) + oldsymbol{g}(t_k)$ and develops 1D and 2D carrying-capacity analyses using $\\dot{x} = -a x + b x^2$ and a two-species system $\\dot{x}=b x^2- a x + c y^2 + d x y$, $\\dot{y}=-e y^2 - f x y + \\lambda - \\gamma y$. Validation against MOCAT-MC shows comparable long-term trends with some differences in collision treatment, and sensitivity analyses confirm robustness to discretization and network size. Case studies explore the impact of future launch traffic and debris-mitigation actions, revealing that high launch growth and reduced collision avoidance raise debris while centrality analyses identify critical sinks and spreaders for targeted management. The framework offers a pathway to evaluate space-traffic policies and ADR needs, with extensions to additional object types, different orbits, and fragmentation dynamics planned for future work.

Abstract

This work proposes to model the space environment as a stochastic dynamic network where each node is a group of objects of a given class, or species, and their relationship is represented by stochastic links. A set of stochastic dynamic equations, governing the evolution of the network, are derived from the network structure and topology. It will be shown that the proposed system of stochastic dynamic equations well reproduces existing results on the evolution of the space environment. The analysis of the structure of the network and relationships among node can help to understand which species of objects and orbit regimes are more critical and affect the most the future evolution of the space environment. In analogy with ecological networks, we develop a theory of the carrying capacity of space based on the stability of equilibria of the network dynamics. Some examples are presented starting from the current population of resident objects and different launch traffic forecast models. It will be shown how the proposed network model can be used to study the effect of the adoption of different policies on the execution of collision avoidance and post mission disposal manoeuvres.

A Stochastic Dynamic Network Model of the Space Environment

TL;DR

The paper presents NESSY, a stochastic dynamic network framework for modeling the space environment where nodes group objects by class and orbit site, and links encode collision, fragmentation, and decay flows. It derives a compact evolution equation and develops 1D and 2D carrying-capacity analyses using and a two-species system , . Validation against MOCAT-MC shows comparable long-term trends with some differences in collision treatment, and sensitivity analyses confirm robustness to discretization and network size. Case studies explore the impact of future launch traffic and debris-mitigation actions, revealing that high launch growth and reduced collision avoidance raise debris while centrality analyses identify critical sinks and spreaders for targeted management. The framework offers a pathway to evaluate space-traffic policies and ADR needs, with extensions to additional object types, different orbits, and fragmentation dynamics planned for future work.

Abstract

This work proposes to model the space environment as a stochastic dynamic network where each node is a group of objects of a given class, or species, and their relationship is represented by stochastic links. A set of stochastic dynamic equations, governing the evolution of the network, are derived from the network structure and topology. It will be shown that the proposed system of stochastic dynamic equations well reproduces existing results on the evolution of the space environment. The analysis of the structure of the network and relationships among node can help to understand which species of objects and orbit regimes are more critical and affect the most the future evolution of the space environment. In analogy with ecological networks, we develop a theory of the carrying capacity of space based on the stability of equilibria of the network dynamics. Some examples are presented starting from the current population of resident objects and different launch traffic forecast models. It will be shown how the proposed network model can be used to study the effect of the adoption of different policies on the execution of collision avoidance and post mission disposal manoeuvres.

Paper Structure

This paper contains 20 sections, 55 equations, 28 figures, 7 tables.

Table of Contents

  1. Introduction
  2. A Network Model of the Space Environment
  3. Network Dynamics
  4. Launch Traffic Model
  5. Collision Rate
  6. Decay Model
  7. Treatment of Elliptical Orbits
  8. Comparison of NESSY Against MOCAT-MC.
  9. Long Term Evolution Results
  10. Sensitivity Analysis
  11. Case Studies
  12. Impacts of Future Launch Traffic
  13. Impacts of Debris Mitigation Actions
  14. Topological and Dynamical Properties of the Network
  15. Definition of the Network Links
  16. ...and 5 more sections

Figures (28)

  • Figure 1: Illustration of the network model of the space environment proposed in this paper.
  • Figure 2: List of modelled interactions among the nodes due to collisions.
  • Figure 3: Three launch traffic forecasts of objects launched into LEO.
  • Figure 4: Average relative velocity for different combinations of inclinations at an altitude of 800 km
  • Figure 5: Cross-collision test case between two test nodes $S_i$ and $S_j$: a) distribution of the radii in each node and b) probability matrix used to select the colliding objects.
  • ...and 23 more figures