Part II — New Observations on Cosmos 1408 Breakup

In trying to make sense of the debris counts from Cosmos 1408 over the last few days, a few characteristics have been difficult to reconcile. For instance, on the day of the ASAT test Jonathan McDowell noted the potential posigrade tendency of the resulting debris fragments and associated implications.

In the Medium post we released just yesterday (now dubbed “Part I”) with our initial analysis on current and potential debris object counts and distributions, the Gabbard diagram that we released showed a definite skewness toward objects ejected to higher altitudes. This aligns well with the theorized posigrade observations described above.

Gabbard diagram of LeoLabs debris fragments from Cosmos 1408

However, it has been difficult to grapple with the low debris count number observed by our LeoLabs data relative to the large mass of the Cosmos 1408 satellite (~2,200 kg). Frankly, we expected to see many more fragments by now. As we have watched our own identification and characterization rate start to level off (currently at 250–300 unique fragments from Cosmos 1408), it struck us that there was a simple explanation for all of these quandaries.

Time to do a deep dive into the characteristics of hypervelocity vs. non-hypervelocity impacts, and compare these traits to our observations.

Hypervelocity Space Impacts 101

First, we need to define “hypervelocity.” Hypervelocity for this application is when the impact velocity exceeds the speed of sound in the materials involved. This is typically around 6 km/s for the aluminum and steel structures for aerospace structures (especially from the Cold War era). The table below summarizes the key differences between the results from a hypervelocity collision and a non-hypervelocity collision.

Properties of hypervelocity vs. non-hypervelocity collisions in space

So, in general when objects collide cleanly (i.e., center-of-mass on center-of-mass) at hypervelocity speeds with a sufficiently high projectile energy to mass of target ratio*, the two objects fragment completely, creating a high number of fragments. The Chinese Fengyun 1C ASAT test of 2007 was a classic case of such an event; the satellite basically fragmented isotropically providing very few clues as to the direction of the impactor.

However, when the impact velocity is well below 6 km/s, the resulting debris cloud looks much more like a high-speed terrestrial traffic accident, where investigators can recreate the velocity and direction of the two vehicles by their masses, skid marks, and where they ended up.

Unfortunately, we often just assume that an on-orbit event is hypervelocity because it is far less common to actually have an encounter in low Earth orbit (LEO) at non-hypervelocity speeds. Since the orbital velocity in LEO is around 7.5 km/s:

  • A head-on collision would result in a ~15 km/s impact.
  • Getting “T-boned” (e.g., impact angle of 90 degrees) the relative impact velocity would be on the order of 10 km/s.
  • Even a collision where the two objects travel in generally similar directions at orbital velocities can still result in hypervelocity impact.

As a matter of fact, in examining over one million conjunction events observed by LeoLabs in the last year, the median relative velocity for these events was ~11 km/s. It is no wonder that we assumed this was a hypervelocity encounter.

New Assessment for Cosmos 1408 Fragmentation Counts

If the Russian ASAT impactor approached Cosmos 1408 generally from behind to “rear end” Cosmos 1408 at a relative velocity well below 6 km/s, this would explain both the distribution of posigrade debris and the lower debris count currently observed by LeoLabs. This would also explain the Russian government’s comment this week that debris from the test “would not pose any threat to orbital stations”. What Russia apparently did not know, that breakup modelers are quite aware of, is that non-hypervelocity breakup modeling is very difficult.

Our updated assessment at LeoLabs, based on our observation data and these new insights is that:

The Cosmos 1408 breakup event likely createdmoredebris than Russia anticipated, yetlessdebris than the rest of the world thought, since we initially assumed a hypervelocity impact, as was the case in previous catastrophic collisions.

If (and only if) it is correct that this was a non-hypervelocity impact, we believe the total large debris fragment count is likely to not grow significantly beyond our current count. In addition, estimates for lethal non-trackable (LNT) debris would also be much smaller. This would of course be welcome news, all things considered.

As stated in Part I of this analysis, the one obvious ramification of the good news of fewer pieces of debris is also the bad news that the resulting debris will be larger and more long-lived than typical smaller fragments.

The key takeaways from yesterday’s post remain unchanged: the new debris still poses a threat to the LEO operating environment, and will for years and decades to come. We will continue to monitor this evolution; to identify and characterize the new debris; and report to the community on our findings to focus on space safety for all.

It would demonstrate some level of responsibility for Russia to share the initial conditions of their ASAT test with the international community, to help us characterize the likely debris cloud better and contribute to reducing the potential collision risks to the 95 countries that strive to peacefully share the use of the limited LEO environment.

  • *35–45 J/gm determined empirically in 1992. Source: McKnight, D. and Hoyle, S., “Investigation of ANOVA Techniques Applied to Breakup Modeling,” Presented at the 18th International Symposium on Space Technology and Science, Kagoshima, Japan, 17–23 May 1992

Analysis of the Cosmos 1408 Breakup

By now we’ve all heard the news that none of us wanted to hear — a significant breakup occurred in space, and was intentionally performed by Russia via direct-ascent anti-satellite (DA-ASAT) missile strike against one of their own defunct satellites. LeoLabs unequivocally condemns this irresponsible act that now harms all spacefaring nations and the entire space economy for years to come.

Frustrated as we all are, we now must turn to the aftermath to start understanding the ramifications of this event on the low Earth orbit (LEO) operating environment. This post will share preliminary data from LeoLabs collected so far on newly tracked debris, along with insights and predictions based on decades of research and conclusions drawn from past similar events.

At the time of this writing, it’s been three days since the breakup of the Cosmos 1408 satellite. The debris created from the fragmentation of Cosmos 1408 has not been fully cataloged or characterized yet, and will likely not be for some time. However, from early measurements and a knowledge of previous relevant breakup events, several observations can be made. It should be noted that much of the information required to re-create accurate simulations of this event will likely never be available, so the community will have to rely on empirical observations of the fragments and “rules of thumb” developed analyzing past similar events. One thing is for certain:

There will be some potential collision risk to most satellites in LEO from the fragmentation of Cosmos 1408 over the next few years to decades.

The first question we’re all wondering is…how many new pieces of space debris resulted from this new event, and where are they? We can start by examining the extent of previous highly energetic collision events in LEO, namely the Iridium 33 / Cosmos 2251 collision of 2009 and Chinese ASAT destruction of Fengyun 1C in 2007. Then we can compare this to early information gathered on newly detected objects to glean some insights.

First, some observations about Cosmos 1408 and its orbit. While any ASAT test is a terrible idea, this one occurred in one of the worst possible orbits. This satellite was in a high inclination orbit, at an altitude that put it right in the middle of many other operational assets; notably, it was less than 100km above the International Space Station, and less than 100km below multiple commercial constellations including SpaceX’s Starlink fleet.

Orbit path of Cosmos 1408 satellite prior to breakup

Cosmos 1408 was also a very large satellite, with a reported mass of ~2,200 kg. LeoLabs reported radar cross-section (RCS) was 8.63 meters squared.

LeoLabs high level information on Cosmos 1408

As LeoLabs is first and foremost a space safety company, this breakup was an “all hands on deck” event for us. Upon first hearing the reports of a possible ASAT test on the morning of November 15, we immediately began checking our data on Cosmos 1408. We saw that we had been regularly tracking this satellite roughly three times per day without issue.

LeoLabs tracking data on Cosmos 1408 for 30 days prior to the breakup event

Over the past 30 days prior to the ASAT impact, we had collected 1,796 radar measurements and generated 69 state vectors with position uncertainties regularly under 100 meters. In short — the Cosmos 1408 satellite was well tracked by our system prior to this event.

As we checked our tracking data for Cosmos 1408 on the morning the ASAT test was reported to have occurred, we noted that our last few planned tracking passes did not return expected data. This was a troubling sign that indicated something was off-nominal, but we needed additional information to confirm. So we tasked Cosmos 1408 to the highest level of prioritization on our space radar network, and scheduled extended observation windows on the next pass to collect additional information.

The next pass occurred at 16:20 UTC, at our Kiwi Space Radar in New Zealand. Our Data Science team was standing by as the data rolled in, and upon review, we quickly noted a “multiple headcount” scenario; that is, we detected multiple individual objects where we would nominally only expect one object. This was a clear confirmation from us that a breakup had occurred, sadly supporting the reports of the successful ASAT test.

Subsequent radar passes over the next two days increased the number of detected fragments significantly. As of this writing, we’ve detected nearly 300 unique fragments and continue to analyze the data.

LeoLabs data collected on new Cosmos 1408 debris taken from Costa Rica Space Radar

Within a day of the Russian ASAT test, the 18th Space Control Squadron notified the general public that they had initially detected around 1500 possible associated objects from this impact.

An initial look at the orbits of some of the new fragments is shown in the Gabbard diagram below. A Gabbard diagram plots the apogee and perigee of breakup fragments against each of the fragments’ orbital period. They are a convenient way to get a quick visual representation of the “landscape” of space fragmentation events, and have been used for decades in the space industry to analyze such events.

Here, blue dots denote the apogee while the “partner” orange dots denote perigee for the same object. The apogee / perigee points for one sample object have been circled in red for ease of interpretation.

Gabbard diagram of LeoLabs data on 253 new Cosmos 1408 debris objects

This Gabbard diagram shows 253 objects whose orbits have already been preliminarily characterized by LeoLabs (as of 17 November 2021). These data are being refined as our global network of radars provide more detail of the new objects.

Our initial assessment is that these 253 objects likely represent the largest fragments with the least amount of delta velocity imparted to them, as they are orbiting closest to the original orbit of Cosmos 1408. If this is accurate, rules of thumb would indicate 5–10x more objects than this, putting total notional trackable debris counts in the area of 1,250–2,500 pieces.

Given the precarious altitude where this event occurred, the Gabbard diagram provides us with two key takeaways for this event:

  1. Objects ejected into lower perigees will have their orbits circularize relatively quickly, and the majority will re-enter the atmosphere over the next five years.
  2. Objects ejected into higher orbits will have their orbits circularize more slowly, and the majority will re-enter the atmosphere over much longer timeframes — potentially decades, depending on altitude.

The collision risk from this resulting debris in the short-term is largely dependent on the orientation of an object’s orbit and the expanding cloud of debris. However, within weeks to months of the breakup, the debris will largely be dispersed around the Earth (i.e., global spread of the fragments’ right ascension of the ascending node). Thus, ultimately the statistical collision risk to other LEO satellites will then be predominantly dependent on altitude.

While the Gabbard diagram does a good job of showing the range of altitudes generally affected by this event, the spatial density of resident space objects (RSOs) provides a better way to depict and quantify the statistical collision risk. Statistical collision risk is proportional to the spatial density of the RSO population at that altitude.

The plot below shows our best estimate at the new, current debris distribution. The black spatial density curve provides the number of RSOs per volume as a function of altitude before the breakup of Cosmos 1408. The red line depicts the likely new spatial density values immediately after the breakup event due only to these new fragments.

LeoLabs assessment of the new debris density from Cosmos 1408 breakup

The red line is calculated by taking the preliminary LeoLabs observation data on 253 objects and extrapolating it to corresponding levels for assuming a notional scenario of 1,500 new fragments.

This depiction will be updated as objects become cataloged and exact orbital elements and exact number of fragments are determined. However, since we have seen the evolution of other major breakup events in the past, the trends depicted are helpful in providing a general assessment of the deleterious effects for the LEO regime.

Importantly, this new debris distribution will evolve over the next few years in line with the above observations. Thus, the left half of the red line will diminish more rapidly while the right half of the red line will diminish much more slowly.

The exact longevity of each new debris object will depend greatly on the area and mass properties (usually combined into an area-to-mass ratio), object altitude, and even the construction materials of the objects. The Cosmos 2251 and Iridium-33 collision event at ~788km in 2009 highlighted this difference. For that event, consider the following:

  1. The majority of the fragments created from the Iridium 33 satellite have decayed over the past 12 years, largely due to the lower material density from it being made much more recently.
  2. The majority of the fragments created from the Cosmos 2251 satellite are still in orbit, largely due to their Cold War construction — very similar to the lineage of Cosmos 1408 being built “last century”.

When the Chinese catastrophically destroyed their Fengyun 1C satellite in another ASAT test in 2007, that 950 kg satellite generated over 3,000 trackable debris fragments. This equates to over three fragments per kilogram of mass in the target. On the other hand, Cosmos 1408 was a 2,200 kg satellite, yet the current fragment count preliminarily reported by the 18th Space Control Squadron is ~1,500. Taking this number at face value, if correct, would actually represent a better than expected outcome by comparison for the current event. Using the same ratio of fragments generated per mass for the Fengyun 1C event, this would result in a total of ~8,000 new fragments for Cosmos 1408. (Let’s all hope that’s not the case.)

If it is indeed closer to 1,500 trackable fragments, this would be more consistent with the debris generated from the Iridium 33 collision. That event has been highly speculated as not having been a complete fragmentation event (i.e., there were significant parts of the spacecraft that remained intact after the collision with Cosmos 2251). The number of cataloged debris objects was equal roughly to the mass of the satellite (i.e., one cataloged fragment per kilogram of the target).

Unfortunately, the downside to this observation is that there are likely a large number of fragments from the Cosmos 1408 fragmentation that will thus have relatively high masses (e.g., tens of kilograms) so will linger longer than “typical” smaller fragments.

Some of the new Cosmos 1408 debris fragments may be as large or larger than many cubesats operating in LEO.

As debris from Cosmos 1408 is cataloged and characterized by the 18th Space Control Squadron and LeoLabs over the coming weeks, the figures above will be refined and filled in with actual data for the larger, complete data set. We will also begin routinely tracking the new debris objects and generating Conjunction Data Messages (CDMs) and risk trending metrics for our customers.

However, due to the initial analysis of debris fragments already characterized by LeoLabs and our experience in analysis of other relevant collision-induced breakups, our assessment of the overall ramifications of this event will likely not change drastically.

This event will have lasting effects in the LEO operating environment for years to come. We will continue to update our customers and the space community as the full effect of this event becomes clear, and we will continue to strongly advocate for transparency and accountability for such events in the public domain.

Tracking Beyond LEO

As most folks know, we at LeoLabs are focused on tracking objects in the Low Earth Orbit (LEO) regime. And with good reason. LEO is where the exponential growth is occurring in space, with an upcoming order of magnitude increase in the number of operational satellites across multiple large constellations. Additionally, there are hundreds of thousands of small pieces of space debris that have historically gone untracked by anyone, that we are rapidly working towards tracking ourselves. So we have our work cut out for us in LEO!

But sometimes it’s worthwhile to do some experiments, to show the art of the possible. Take our newest sensor — the Costa Rica Space Radar (CRSR). It’s a dual-radar system composed of two powerful S-band phased-array radars working in tandem. All CRSR hardware and software systems were designed by LeoLabs with the exclusive mission of tracking objects in LEO to support space traffic management and space domain awareness.

In April 2021, our team of data scientists put CRSR to the test in an attempt to detect some satellites in Geosynchronous Earth Orbit (GEO). Tracking anything in GEO with radars is traditionally quite difficult, as power requirements and complexity scale exponentially with distance to the target object.

For this experiment, we chose two large GEO satellites that happened to cross through the CRSR field of view — GOES-14 (35491) and AMOS-5i / AsiaSat-2 (23723). For context, these satellites are approximately 15x further away than the highest altitude cataloged objects we routinely track in LEO (36,000km vs. 2,400km).

LeoLabs visualization of GOES-14 (left) and AMOS-5i / AsiaSat-2 (right)

Upon completion of the observation experiments, the results were conclusive: we saw strong detections on both satellites!

LeoLabs data plot showing CRSR measurement data for the GOES-14 satellite

The plots above show data from a LeoLabs test observation on GOES-14, which was in the radar’s field of view for a total of 10 minutes over a two-hour period. The top and right plots are Range-Time-Intensity (RTI) and Doppler-Time-Intensity (DTI) plots, respectively, showing signal strength reflected back to the radar. The central plot shows LeoLabs-collected measurements (blue dots) along with the predicted location of the object via the publicly available TLE.

Given that CRSR was not designed to track objects beyond LEO, but was able to detect GEO satellites with no hardware modifications, is a testament to the flexibility of our radars, software systems, and the ingenuity of our team of skilled engineers and data scientists.

We consider this experiment a successful proof of concept that our phased-array radar systems are highly capable to track beyond LEO, including MEO, GEO, and cis-lunar regimes.

We’ll be sharing more information about these GEO experiments in a technical presentation at the upcoming in Maui, Hawaii, so we hope you’ll join us there in-person or virtually.

Detecting a breakup event in LEO

On July 12, 2020, LeoLabs detected a breakup event of a Japanese H-2A debris object (NORAD ID 43673) in space. The event was first reported by the 18th Space Control Squadron (18 SPCS) reporting an approximate breakup time of 08:44 UTC:

Upon receiving this news, the LeoLabs team rapidly looked at our tracking data for this object and immediately saw clear evidence of the breakup. This post will take a closer look at our evidence for this event and what exactly we observed.

For each LeoLabs radar observation, our automated processing system takes the collected measurement data and generates a number of unique products, one of which is a series of data plots corresponding to our Radar Signature Returns (RSRs). These RSR plots provide a visual means to understand the strength and location of the radar signals received back by LeoLabs radars when searching for an object.

The plot below shows an RSR for the H-2A debris object, prior to its breaking up, along with a 3D visualization of the same radar pass. The X-axis is time (seconds) of the observation and the Y-axis is the range (km) of the object from the radar making the measurements.

LeoLabs RSR plot for the H-2A object from the radar pass prior to the breakup event

The corresponding radar pass for the H-2A object prior to the breakup event

When an object is detected during a radar pass, multiple measurements are collected over a period of a few seconds while the object is in the radar’s field of view. The sloped line in range as a function of time is a result of the motion of the object as it passes through the radar field-of-view, as shown above. (Depending on whether the object is moving towards or away from the radar during the pass, the lines may slope upward or downward.)

The above plot shows a typical RSR for the H-2A object — a single, clear line indicating only one object is detected during the pass. However, following the breakup event for this object, the next radar pass occurring at 14:31:03 UTC generated this RSR:

LeoLabs RSR for the H-2A object immediately following the breakup event

We have annotated this plot with red boxes to indicate what are likely new individual objects that resulted from the breakup. Additional RSRs from subsequent radar passes provided similar information. LeoLabs then set its radars to search for additional debris objects in an expanded area for further data gathering.

It is worth noting that although the H-2A object that experienced this breakup is designated as a debris object, it is quite large. LeoLabs was tracking this object very well 2–4x per day prior to the event, and our measured radar cross section (RCS) data indicated an approximate size of 2.43 m². The breakup of a sizable object like this is expected to create a large number of new debris objects, depending on the nature of the breakup. Following detection of the breakup, 18 SPCS reported 53 new debris objects, which both 18 SPCS and LeoLabs will begin tracking and cataloging, and it is expected that a large number of additional debris objects below the tracking limits of current radars will also have been generated. Unfortunately, much of this debris is expected to stay in orbit for decades.

The question may then be asked, what caused this object to break up in the first place? We do not know for sure at this time. There is no initial evidence that this was caused by a collision with another object (an opinion also shared by 18 SPCS). The LeoLabs conjunction screening system did not flag any close approach events that would have been realistic candidates for a collision. However, it is still feasible that a collision with a small, untracked piece of debris may have occurred and caused the breakup. There are currently an estimated 250,000+ such small, untracked objects in LEO >2cm in size that pose a very real threat to both operational satellites and human spaceflight missions.

To address this, LeoLabs is continuing to build additional high-powered radars capable of tracking this small debris. Read more about our recent announcement to build our 4th radar in Costa Rica this year:

LeoLabs to construct fourth radar in Costa Rica – SpaceNews

SAN FRANCISCO – Silicon Valley startup LeoLabs announced plans July 22 to construct a phased-array radar in Costa Rica…

Earth’s Orbital Hot Spots

There’s a lot of growth happening in Low Earth Orbit (LEO). Over the next 5–10 years, we expect at least an order of magnitude increase in the number of operational satellites to be launched. However, not all satellites are distributed evenly in LEO. Just as we have varying amounts of driving traffic on different roads (e.g. back country roads vs. interstates), there is a parallel here for space as well. Some orbits are more advantageous to be in than others for operational satellites, and are thus more crowded.

The most notable of these orbits is referred to as a Sun-Synchronous Orbit, or SSO. SSOs are unique in that they “lock” the satellite into a precession rate around the Earth that matches the Earth’s movement around the Sun. This precession is made possible by the fact that the Earth is not a perfect sphere, but rather an oblate spheroid that is wider at the equator than at the poles. Those familiar with orbital mechanics will be well familiar with this fact and the resulting J2 effects that must be taken into account when predicting the motion of orbiting objects. This orbital precession for SSOs requires inclinations typically between 96 and 100 degrees, depending on the chosen orbital altitude.

Orbital path of a satellite in example SSO (98 degree inclination at 700km altitude)

In practical terms, the benefit of using SSOs for many types of satellite missions is that the satellite will pass over the same area of Earth at approximately the same local time each day. This results in consistent lighting conditions from one orbit to the next, a highly useful benefit for multiple aspects of mission operations including solar power generation and Earth imaging applications.

SSOs, and other high inclination polar orbits account for nearly 85% of all objects we track in the LeoLabs object catalog. This cumulative effect creates unique traffic hot spots near the North and South poles, and a visible near-empty ring of space that results from thousands of objects at high inclinations passing by one another.

When viewed from above, it has the appearance that the Earth has an orbital “bald spot” more than 1,000 km wide, surrounded by a ring of satellites corresponding to the inclination of most SSOs. Of course, this ring is not composed of satellites going around the pole itself, but is rather the superposition of many objects continuously passing within a few degrees from each pole. In mathematics this is known as a caustic, and is a familiar concept to anyone who has ever played with an old toy called a spirograph!

As you might expect, more crowded areas of traffic in space can lead to more potential collision events. Indeed, this is exactly what we see in our conjunction screening system — more close approaches are concentrated around the poles than anywhere else on Earth.

The 3D visualization below represents close approach events in LEO over the last 24 hours using LeoLabs’ object catalog. Each dot represents the crossing of two objects that pass within a few kilometers of each other; red dots represent the closest miss distances of a few hundred meters or less!

 

Quantifying Conjunction Risk in LEO

In addition to tracking thousands of objects in Low Earth Orbit (LEO) with our network of phased-array radar systems, LeoLabs also searches for potential conjunction events that can pose a danger to satellite operators. Our system detects and analyzes roughly 800,000 potential collision scenarios each day.

The vast majority of high risk conjunction events are not between active satellites, but rather between inactive objects such as orbital debris, spent rocket bodies, or inactive satellites.

This is not surprising, since only about 10% of the objects currently tracked in LEO are actively working satellites. For this inaugural blog post, let’s take a closer look at how we identify conjunctions and quantify risk for these events.

How Conjunction Risk is Calculated

There are multiple steps required to accurately characterize the risk of a collision occurring between two objects in space. Conjunction Data Messages, or CDMs, have long been the industry standard data product for quantifying risk for these types of events. They provide key information such as the IDs of the two objects that may collide, the time of closest approach (TCA), their positions and velocities, miss distance, Probability of Collision (Pc), and the computed measurement uncertainties for each object at TCA.

To understand CDMs, we first have to explain how Pc is calculated, and for that we need to understand the concept of a state vector and its associated uncertainty. The state vector is the position and velocity of an object at a particular time, known as the epoch. It is determined by fitting physical orbits through a series of recent observational passes, and looking for the orbital state vector which best fits those observations. Every time an object is tracked passing over one of our radars, we incorporate the new measurements and fit for an updated state vector at the new epoch corresponding to the time of the radar pass. There is never perfect knowledge of a state vector due to measurement errors, which means that even at epoch there is some level of uncertainty. This uncertainty arises because there is actually a range of state vectors which are all consistent with the observations. This uncertainty in the state vector will turn out to be a critical quantity in assessing collision risk.

From the orbital state vector, the position of the object can be propagated forward in time from the epoch to form a list of positions versus times in the future. This is known as an ephemeris. As mentioned earlier, there is uncertainty to these positions even at epoch due to measurement errors (LeoLabs measures the range to each target typically with an uncertainty of less than 15 meters). Furthermore, this uncertainty grows with time as it is propagated into the future. To add to this, there is also a component of uncertainty due to variations in the atmospheric drag profile of LEO objects which depends upon things like solar activity and the size, shape, and orientation of the object. Typically, the uncertainty from atmospheric drag comes to dominate after a few days of propagation in LEO, especially as we go lower in altitude. Thus, even if we knew exactly where a space object is at some given time, there would still be uncertainty in calculating its future location. It is critical that as part of the ephemeris we also calculate the growing uncertainties at each time step into the future, because that will form the basis for calculating potential collision probabilities.

Once we have ephemeris files for the objects we are tracking, we can search forward in time to find instances in the next seven days where two objects will be in close proximity. The fact that the fitted state vectors of two objects will pass close to each other does not tell the whole story though, as each of those state vectors has an associated uncertainty which must be taken into account in order to understand the seriousness of the event. Once we have all these pieces in place, we can now move to calculate the Pc using well known algorithms. The Pc is calculated by taking into account the range of possible positions of the two objects and finding what fraction of trajectories actually collide.

A Recent Close Approach

On December 8, 2019, LeoLabs determined that the Haiyang 1 and Cosmos 1354 satellites had an upcoming close approach on December 15 that was of concern. This link shows the evolution of the event over eight days, during which time our system generated 52 CDMs (one for each new state vector update on either object). Click on the map to see the ground track of the two objects and on the “View in 3D” button to visualize the event.

Let’s look at the evolution of computed risk for this event.

  • Seven days prior to TCA: Upon initial event detection, a Pc of 1.6e-4 and miss distance of 158 (+/-308) meters
  • Five days prior to TCA: Pc has increased to 8.9e-3 and miss distance of 39m (+/-192)
  • Three days prior to TCA: Pc has increased again to 1.8e-2 and miss distance of 13m (+/-111)

This turned out to be the highest risk CDM generated over the course of the event. These computed risk values can and often do fluctuate from one CDM update to the next due to reasons described above. Luckily as we got closer to TCA, subsequent updates for this event showed the risk starting to decrease.

  • 2.5 days to TCA: Pc has decreased to 9.7e-4 and miss distance of 69m (+/-80)
  • 21 hours to TCA: Pc has decreased to 4.6e-5 and miss distance of 119m (+/-55)
  • 1 hour to TCA: Pc has decreased to 1.8e-7 and miss distance of 121m (+/-47)

So why did the collision probability fall so quickly in the last 24 hours? As we approached TCA, the computed miss distance increased slightly, while our uncertainty in the miss distance further decreased. Note that regardless of the reported miss distances above, the (+/-) margin of uncertainty always decreases as we approach TCA. Eventually, our uncertainties in the spacecraft positions fell below the predicted distance of close approach, resulting in our being able to confidently rule out this as a collision roughly 24 hours prior to TCA.

Herein lies an advantage of a distributed global sensor network: frequent radar observations yield more frequent and more accurate state vectors, due to minimized uncertainty growth in between updates. For this conjunction event, our system provided new state vectors more than six times per day on average.

This conjunction risk information is also graphically depicted in the Error Ellipse section where we show the evolution of the relative position prediction. Zoom in and hover over some of the plot ellipsoids to see the values (each one corresponding to a CDM).

The origin of the plot (0,0) represents the center of mass of the primary object. The location of each ellipsoid represents the distance of the center of mass of the secondary object to the primary object at TCA, and the size of the ellipsoid corresponds to our calculated positional uncertainties for the two objects (smaller ellipsoids mean lower uncertainty, and better confidence in the accuracy of our state vectors).

Keep in mind that the estimate of the Pc depends on the size and orientation of the two objects, which we do not know exactly. In other words, the smaller the two objects, the closer they have to be to (0,0) in order for there to be a collision. In this case, both objects were large spacecraft, and for the purposes of estimating Pc we assume the sum of the linear size of the two spacecraft to be five meters. This is known as the combined hard body radius (HBR), and this assumption is listed at the top of the Conjunction Analysis Report.

Finally, at the bottom of the page we depict how varying the combined HBR and state vector uncertainties will affect the computed Pc value. In some instances, Pc results can be extremely sensitive to small variations in inputs to the algorithm. As we can see in this example, if we keep the same HBR but decrease our uncertainties by 50% (thus, our knowledge of position is improved by 50%), the already low final Pc value of 8.1e-8 drops by another 16 orders of magnitude!

As there is no one “correct” Pc for any conjunction event (in reality, either the objects will hit or they won’t), these sensitivity diagrams are helpful to understand collision risk in the larger context of the assumptions used in computing it. We can also see the value in having a large number of CDMs generated for each event so that we can study the data in aggregate, identifying patterns and trends from one update to the next as we attempt to better understand the event risk.

Final Observations

This example demonstrates the power of the LeoLabs worldwide network of radars. The more frequently objects are tracked, the smaller the uncertainty in the state vectors at epoch (i.e. the more tracking data we have, the better we can fit the state vector) and the more recent the latest epoch time will be. This results in earlier determination either that a potential collision is not of concern, or in cases where the close approach is within the uncertainty region, that a collision is possible and a collision avoidance maneuver is warranted. LeoLabs currently has three operational radars, and plans to build three more over the next two years to further improve our space tracking services. Our completed radar network will be capable of monitoring a predicted catalog of 250,000 objects including small debris down to 2cm in size, while continuously monitoring for dangerous conjunctions.

These capabilities described will become available to satellite operators worldwide as a commercial collision prevention service starting in Spring 2020.

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