The fast debris evolution model

Abstract

The 'particles-in-a-box' (PIB) model introduced by Talent [Talent, D.L. Analytic model for orbital debris environmental management. J. Spacecraft Rocket, 29 (4), [508][509][510][511][512][513] 1992.] removed the need for computer-intensive Monte Carlo simulation to predict the gross characteristics of an evolving debris environment. The PIB model was described using a differential equation that allows the stability of the low Earth orbit (LEO) environment to be tested by a straightforward analysis of the equation's coefficients. As part of an ongoing research effort to investigate more efficient approaches to evolutionary modelling and to develop a suite of educational tools, a new PIB model has been developed. The model, entitled Fast Debris Evolution (FADE), employs a first-order differential equation to describe the rate at which new objects P10 cm are added and removed from the environment. Whilst Talent [Talent, D.L. Analytic model for orbital debris environmental management. J. Spacecraft Rocket, 29 (4), [508][509][510][511][512][513] 1992.] based the collision theory for the PIB approach on collisions between gas particles and adopted specific values for the parameters of the model from a number of references, the form and coefficients of the FADE model equations can be inferred from the outputs of future projections produced by high-fidelity models, such as the DAMAGE model.The FADE model has been implemented as a client-side, web-based service using JavaScript embedded within a HTML document. Due to the simple nature of the algorithm, FADE can deliver the results of future projections immediately in a graphical format, with complete user-control over key simulation parameters. Historical and future projections for the P10 cm LEO debris environment under a variety of different scenarios are possible, including business as usual, no future launches, post-mission disposal and remediation. A selection of results is presented with comparisons with predictions made using the DAMAGE environment model. The results demonstrate that the FADE model is able to capture comparable time-series of collisions and number of objects as predicted by DAMAGE in several scenarios. Further, and perhaps more importantly, its speed and flexibility allows the user to explore and understand the evolution of the space debris environment.

Sensitivity analysis of launch activities in Low Earth Orbit

“…where each component can be cross-dependent on the population of other species, as illustrated in Figure 1. The model uses an explicit Euler model [13] to compute the future states with…”

Engineering and technology challenges for active debris removal

“…Hence, the mass, M , and the collision probability, Pc, of each object can be used as a target selection criterion for the removal [8,9]. Numerical simulations have shown that, indeed, [M × Pc] is an e¨ective ADR selection criterion for environment remediation in LEO [4,8,10,11]. Figure 6 shows the e¨ectiveness of debris population control of ADR based on the mass and collision probability criterion [12].…”

Statistical analysis of the inherent variability in the results of evolutionary debris models

“…White & Lewis (2014). From the uncertainty sources, which depend on the assumptions of the evolutionary debris model in use, orbital collisions have been found to be the source of the largest variability between different Monte Carlo runs (Liou & Johnson, 2008;Lewis et al, 2009). Both sets of uncertain parameters mean that the predictions of the future debris environment generate a distribution of the possible number of objects in orbit.…”

“…Most importantly, only such models were used in the IADC comparison study (Liou et al, 2013). These simulation tools are used to probe plausible future scenarios and enable additional data, e.g the relative effectiveness of various mitigation measures, to be extracted from the simulations (DoladoPerez et al, 2015;Lewis et al, 2009). The use of random numbers creates a need for large Monte Carlo samples that have to be generated in order to establish statistics about the expected number of collisions, their severities and the total numbers of objects in orbit (Liou & Johnson, 2006).…”

“…The purpose of the remainder of this section is not to review the history of the debris modelling but to give the Reader an overview of how the models function. The PIB models, for example by Farinella & Cordelli (1991), Talent (1992), Kebschull et al (2014) or Lewis et al (2009), describe the evolution of the number of objects on-orbit (N ) with differential equations. This set of equations expresses the rate of change of N as a function with coefficients corresponding to deposition (A), decay (B), and collisions (C) of objects (Talent, 1992):…”