It’s tempting to think of a collision or explosion in space the same way you imagine one happening on Earth, as a localized event occurring at a specific area. But when a satellite fragments in space, its pieces don’t stick around. The satellite is in orbit, traveling at kilometers a second; when it breaks apart, each of its pieces will distribute according to the dynamics of the fragmentation and the satellite’s orbit.
That’s what Liam Healy and his fellow researchers Christopher Binz and Scott Kindl are attempting to understand with their ongoing project, begun in 2015. Before you can clean up debris from a fragmentation or collision in space, you have to know where the debris is, and where it’s going. It turns out that’s a complicated problem to solve, especially when you’re dealing with fragments and particles too small to be detected and tracked from Earth.
In his research, Healy is considering the fragmentation of a satellite in terms of an initial velocity distribution, one that results in a spatial density of fragments that changes over time.
Simulated space density of debris at five hours after fragmentation. Illustration by Liam Healy, Christopher Binz, and Scott Kindl.
When an object explodes, the explosion adds velocity, and the velocities of the object’s fragments have direction: forward, backward, left, right, up, or down. The velocities also have a magnitude. Some fragments travel at higher velocities, while others travel at lower velocities. All those fragments’ velocities taken together as a set— that’s a velocity distribution.
What Healy’s team has done is model the fragmentation of an orbiting satellite by computing the evolution of the spatial density directly to simulate its velocity distribution. They’ve done that to study how the varying densities of debris distribute in space over time.
“If we know where those fragments are, we can follow those tracks, but often we can’t, particularly the smaller fragments,” Healy said. “For a long time, people have tried to understand the impact of debris on our orbital operations, and it’s hard to get that understanding when you only have a bunch of tracks. The idea here is that if we simulate a distribution of those fragments, we can get at—basically—what a set of tracks that tell us where the fragments of the spacecraft are going as a whole.”
In February 2016, Healy presented a paper on his team’s work at an American Astronomical Society meeting along with a two-dimensional animated video showing how such a spatial density would look from the fragmentation of an object at 900 kilometers altitude over the course of 36 hours. Since then, his team has produced a series of colorful animations of the fragmentation of a spacecraft over time.
What the videos all show is a debris cloud spreading out from a single point where the fragmentation began (the “pinch point”) and orbiting the Earth—with the brighter colors of the distribution indicating the areas of its highest density of fragments.
“What you see evolving in the simulation is the cloud spreads out from the pinch point, and this was already well known,” Healy said. “But then there's going to be this band structure forming and this intense line of a high-density region opposite the pinch point. No one had ever seen this pattern before.”
The velocity distribution of a fragmentation event in orbit depends on the nature of the event. Is it an explosion? A collision? A disintegration? Each will have different velocity distributions. Regardless of the nature of the initial distribution, however, the line and band structure will look very similar, according to Healy. This is key, because that’s where the distribution’s greatest density of fragments will be.
“This is telling us this is where the hazard is from these kinds of events,” Healy said.
Since the model describes how a distribution of velocities evolve from a single point, it can be applied to more than just the fragmentation of a satellite. The model deals with distributions, and a distribution can be an actual distribution of fragments, or it can be a virtual or probability distribution.
“Sometimes there’s an object in space that’s of interest, but we don't see it often enough to get a good orbit on it—so that is where this would also be applicable,” Healy said. “If we have an uncertain orbit, say something that hasn't been observed very well, this tells us how the uncertainty grows as the orbit moves in time. The math is the same; the orbital physics is the same. And that’s maybe of more interest to what we do, because this is a situation we face quite a bit.”