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), 508–513, 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 ⩾10 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), 508–513, 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 ⩾10 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.