Simulation of the space debris environment in LEO using a simplified approach

At the Institute of Space Systems (IRAS) a model capable of describing the evolution of the space debris environment has been developed and implemented. The model is based on source and sink mechanisms, where yearly launches as well as collisions and explosions are considered as sources. The natural decay and post mission disposal measures are the only sink mechanisms. This method reduces the computational costs tremendously. In order to achieve this benefit a few simplifications have been applied. The approach of the model partitions the Low Earth Orbit (LEO) region into altitude shells. Only two kinds of objects are considered, intact bodies and fragments, which are also divided into diameter bins. As an extension to a previously presented model the eccentricity has additionally been taken into account with 67 eccentricity bins. While a set of differential equations has been implemented in a generic manner, the Euler method was chosen to integrate the equations for a given time span. For this paper parameters have been derived so that the model is able to reflect the results of the numerical MC-based simulation Long-term Utility for Collision Analysis (LUCA), which is also being developed at the IRAS. The evolution of the population in LEO for a 200 years time span is shown and compared for both approaches using step sizes of 1 year. For selected objects in LEO the collision flux values are shown. Additionally a value called environmental criticality (EC) is derived. It describes the effect an object can have on the space debris environment. In conclusion the field of application for such a fast model is shown.