A space debris model is a representation of the space environment that focuses on accurately replicating the generation and depletion of the in-orbit space debris population and its relationship with existing spacecraft, in order to provide short- and long-term forecasts analyses. In this latter case, it is a core tool for space sustainability, used to assess the impact of past and current practices in the space economy through the development of sensitivity studies by the main space agencies (such as ASI, CNES, DLR, ESA, JAXA and NASA).
History
The problem of the space debris
The number of human-originated objects in space has grown significantly and persistently since the beginning of the space era. Besides the actual payload (the spacecraft intended to serve scientific, commercial, governmental or military purposes), several other objects used during the deployment phase are produced and left in orbit: these include rocket bodies, leaked fluids and other elements generally referred to as mission-related objects.
In addition to these elements, internal failures have led to several instances of satellite explosions that resulted in the production of space debris fragments (a fragmentation event). Together with other uncontrollable and uncontrolled objects (made by mission-related objects, rocket bodies and spacecraft that have reached the end of their operative lives), these events have contributed to creating a population of different sized objects that can exhibit significant orbital lifetimes due to the very low effect of atmospheric drag at high altitudes.
The problem of space debris has been recognised since the early years of the development of the human spaceflight programs; however, given the limited detection capabilities of small particles in space, the issue required multiple strategies:
on one hand, the actual improvement of detection capabilities, both in terms of detectable size and timing in case of possible conjunction events. This strategy is linked with advances in collision avoidance solutions such as the development of just-in-time collision avoidance (JCA); on the other hand, the development of numerical simulations that can provide a forecast of the evolution of the space population, to study the short-term effects (e.g., to characterise the evolution of a fragmentation event to possibly develop collision avoidance schemes) or the long-term effects (e.g., to estimate the possible number of collision events and the size of the population on the long-term).
Modelling developments
Initial studies beginning from 1976 on the phenomena of space debris focused on describing the evolution of an orbiting debris cloud following a debris generation event. These early models are generally short-term only and assume that perturbations can largely be neglected, hence they are based on analytical equations that describe the cloud volume time variation.
Following the explosion of an upper stage of Ariane in 1986, the European Space Agency started the development of MASTER (meteoroid and space debris terrestrial environment reference), a flux-based model used to estimate the flux of particles for a satellite mission. The model, used on IADC level, reached version 8 (MASTER-8) in March 2019.
In the same period, NASA initiated the ORDEM programme, initially based on analytical solutions and later converted to computer-based version in 1996 with ORDEM96. Further progress and modelling features were introduced with ORDEM 3.0 and ORDEM 4.0 respectively.
In parallel with the development of more complex models, which are too computationally expensive to produce long-term estimations, a new series of simpler models was developed starting from 1990 with Talent's particle-in-a-box. These models, characterised by a limited number of ordinary differential equations, provide a trend evolution that links certain practices (such as launch traffic, ASAT or disposal adherence to the 25 years rule) to the outcomes of the evolution.
Overview
A space debris model is a mathematical or numerical description of a series of physical phenomena that replicates (partly or completely) the underlying effects of debris on the near-Earth space region. As any other physical model, it must be used within the predefined validity ranges that are derived from the combination of the founding assumptions of the mathematical descriptions of the model.
Depending on the scope of the model, there are several possible representations that can be employed: the selection is generally based on the desired degree of accuracy within a time frame, taking into account the significant trade-off between accuracy and numerical cost of the analysis.
Types of models Several classification methods can be defined with respect to the available models. Three main types of models are generally recognised, based on the available knowledge, resources and scope:
Engineering models, used to assess the flux of debris particles in specific regions to estimate the risk that an existing or planned mission may encounter during its lifetime. Differential models, used for fast (but generally low accuracy) forecasts of the long-term environment. Evolutionary models, which are instead long-term and generally high-precision models that simulate the behaviour of single objects with more complex representations of physical, economical and heuristic processes.
Engineering models Engineering models are used to estimate the flux of particles registered in a region or encountered by a mission in order to possibly estimate the risk and the mitigations to adopt. They are generally used by spacecraft designer/planners, operators and debris researchers.
Models in this category usually employ reference debris populations computed by simulating all (or most) known debris-generating events in space and ground-based tests, therefore require frequent updates of the available population. They are generally used for limited, short-time, simulations as they are generally computationally intensive and are used to study the impact on specific missions, accounting for small-size debris (down to 1 μm). General outputs provided by these models include:
Spatial density at given locations and times; Cross-sectional area flux ; Angular distribution of fluxes.
+Engineering debris modelsModelOrganisationReleasedMeteoroid and space debris terrestrial environment reference (MASTER) ESA1987Orbital debris engineering model (ORDEM) NASA1996Space debris environment engineering model (SDEEM) CNSA2015Space debris prediction and analysis - engineering (SDPA-E) ROSCOSMOS2001
Differential models Differential models use a set of numerically integrated differential equations (that discretise the space into regions or bins) to model the dynamical system as a whole. These are generally fast and computationally inexpensive models that are used to obtain quick and rough estimations of the long-term trends of the population.
A subset of these models are usually defined as particle-in-a-box (PIB) models due to the underneath assumption of (partially) neglecting the orbital motion and treating the debris as gas particles subjected to gas kinetics in a Lagrangian estimation.
It is common to classify different elements into species. Each species undergoes different dynamics or may present different physical properties. Examples of species include:
Operative satellites, which can be launched and can explode, collide or undergo a collision, but due to station keeping cannot decay. Rocket bodies, which are produced with a launch and can explode, collide, decay and be involved in a collision. Mission-related objects, which are produced with a launch and can collide, decay and be involved in a collision. Debris, which are produced by fragmentation events and can collide and decay.
In general, using a state-space representation, the rate of change of debris in orbit is represented through the combination of different sources and sinks:
where is the number of objects belonging to a species and represents a modelled aspect of the population, which generally includes all or some of those presented in more detail below (launches, atmospheric re-entries, collisions, explosions, etc.). It must be noticed that the complexity of the model can vary significantly, going from a single equation that models the total number of objects in orbit to hundreds of coupled equations that study each bin and species (e.g., operative satellites, inactive satellites, debris and possibly others).
Given their simplicity, general speed and predisposition to sensitivity studies, as well as the use of state-space representations, differential and PIB models have also been used to study the implementation of control theories in order to study the best mitigations and corrective measures, allowing the discussions of policies and regulations in space operations. +Differential debris modelsModelOrganisationReleasedTalent Lockheed Engineering and Sciences1990Farinella and Cordelli University of Pisa1991Stochastic analog tool (STAT) CNUCE/CNR1994Kessler NASA2001Stochastic impressionistic low Earth (SIMPLE) Indian Institute of Science2006Fast debris evolution model (FADE) University of Southampton2009Computational adaptive strategy to control accurately the debris environment (CASCADE) University of Southampton2014MIT orbital capacity assessment tool-sources sinks evolutionary model (MOCAT-SSEM) MIT2024Network model for space sustainability (NESSY) University of Strathclyde2024
Evolutionary models Contrary to engineering models, that simulate the debris motion, and differential models, that significantly simplify the dynamics of the involved objects, the goal of evolutionary models is to achieve a high degree of precision and fidelity. This is generally achieved by simulating each object and its behaviour individually (across all possible phases, including high-precision orbital propagation and collision probability estimation).
Despite the high precision involved, stochastic processes are still inherently present in the models due to the many uncertainties in the interactions; therefore, a single execution of the model is generally not enough, and multiple Monte Carlo runs are necessary to obtain reliable data. +Evolutionary debris modelsModelOrganisationReleasedEVOLVE NASA1991Space debris mitigation long-term analysis program (SDM) ASI1995Long term utility for collision analysis (LUCA) TU Branuschweig/DLR1998Space debris prediction and analysis (SDPA) ROSCOSMOS2000Debris environment long term analysis (DELTA) ESA2001Debris analysis and monitoring architecture to the geosynchronous environment (DAMAGE) University of Southampton2001LEO-to-GEO environment debris model (LEGEND) NASA2003Near Earth orbit debris environment evolutionary model (NEODEEM) Kyushu University/JAXA2009Aerospace debris environment projection tool (ADEPT) Aerospace Corporation2009Modelling the evolution of debris on Earth's environment (MEDEE) CNES2012Space objects long-term evolution model (SOLEM) CNSA2019MOCAT-Monte Carlo (MOCAT-MC) MIT2023
Components of a debris model A space debris model generally decomposes the modelling of all the complex physical interactions and processes into independent "blocks" or components, each of which performs a specific task. Depending on the complexity and the scope of the model, some or all the following components are included in different complexity shapes. The components, from an implementation point of view, can vary from being plug-ins of the main program, such as in the case of LUCA2, to being simple equation terms, such as in the case of most PIBs.
Initial population The initial or background population is constituted by all the existing objects that are already in orbit by the select initial date of the simulation. Depending on the goal of the simulation and of the model, the initial date may be one of the following: