Space Invaders for a New Space Age: Using ODE’s to Model the Trajectory of Low Earth Orbit with an Increasing Debris Field

Abstract

As we enter a New Space Age categorized by the influence of private entities on the space sector, we are facing a corresponding increase in launches and a growing space debris field that continues to threaten the longevity of current and future active satellites. As we look at the spike in new satellite constellations launches per year, we see that we sit at an amount a staggering 20 times higher than in 2002 [22]. Alongside an increasing launch rate, the number of satellites in orbit has increased seven times in the past decade [34]. These numbers are only projected to grow, as we continue to see an increasing number of ventures into the global space economy through asteroid mining, space tourism, manufacturing, and scientific research [33]. From these statistics, we see clear motivation to explore the e↵ect that varying parameters have on active satellites and the Low Earth Orbit (LEO) environment. In this research, we create an extension to Farinella and Cordelli’s 1991 simple mathematical orbital debris model [15] where we make a distinction between active and defunct satellites. With the addition of removal parameters and collision probabilities for three distinct collision scenarios, we conclude that based on our analysis of dominant terms, defunct satellites are not the leading cause in active satellite depletion and that collision avoidance is essential to maintain the mission lifetimes of active satellites. Within our discussion we acknowledge these two results and recommend mitigation strategies and broad policy implications to aid in the continued protection of a stable and working LEO environment.