Assessing the Risk of Uncontrolled Space Debris Re-entry: A Case for Airspace Management and Flight Safety

We explore the risks associated with uncontrolled space debris re-entry and the implications for airspace management and flight safety. With the increasing number of satellites and other objects being launched into space the potential for uncontrolled re-entry events poses a unique challenge for airspace management and public safety. While there have been no recorded instances of aircraft damage or human injury due to re-entering space debris, the increasing frequency of such events necessitates a comprehensive understanding of the associated risks and appropriate mitigation strategies. We briefly examine the current methods for tracking and predicting space debris re-entry, concentrating on the decision-making process for airspace closures, and the risk assessment for ground airborne safety. Our analysis aims to contribute to the ongoing dialogue on space debris management and to inform future policy and operational decisions in the context of civil aviation and public safety.


Introduction
Orbital debris are artificial objects on Low Earth Orbit (LEO), including uncontrolled space vehicles and leftovers from space vehicles collisions.NASA defines debris as "any man-made object in orbit around the Earth that no longer serves a useful purpose".Figure 1 illustrates the growth in the numbers of space debris over the past decades.Most of these debris eventually ends with an uncontrolled re-entry into the Earth's atmosphere.Currently 1-2 debris reentries (on average) are recorded daily [1].The majority are consumed by fire before reaching cruise flight levels, but 2-4% are big enough to reach the ground [2].There are several such occurrences per year [3].As of 2023 there are no recorded instances of aircraft damage, or human injury, due to reentering space debris (but there were some reports of material damage on ground) [3].Both controlled and uncontrolled reentries may impact ATM and cause airspace closures, but for controlled reentries the location is chosen (usually over oceans) so the impact will be minimal.Uncontrolled space debris reentries can cause disrupting airspace closures (most recent example is 4/11/2022 LEMD sector closure caused by the Chinese Long March 5B (CZ5B) booster re-entry [4]).
Given the increase in space activities, such events that impacted many flights, cause financial losses (more than 300 flights in the above example for a 30-minute airspace closure [4]) and generate negative media for the space industry, will become more frequent.This paper will try to respond to two main questions:  Are such airspace closures necessary given the uncertainty of the impact area? Where do the uncertainties on the re-entry on time/location come from?
We will briefly examine the current methods for tracking and predicting space debris re-entry, focusing on the causes of the uncertainties, and the risk assessment for ground/airborne safety.Before we begin, we should note a related problem: it is estimated that around 100 tons of space material, mostly in the form of dust and small meteoroids, enter the Earth's atmosphere every day [5].However, most of this material is so small that it burns up upon entering the atmosphere and never reaches the Earth's surface, but five to seven larger meteorites (over 0.5kg) do reach the surface in totally unpredictable locations [5] and can pose a risk to aircraft.Nothing is done about this kind of threat.

Methodology
Collision of a piece of space debris with an aircraft requires that both are in the same place at the same time.In mathematical terms the probability of the event is given by the product between the probability of an aircraft being at a certain position at the time of the re-entry and the probability of the debris striking that position.The numerical case tries to replicate the computation behind the decision process for the recent (4/11/2022) LEMD closure due to Chinese Long March 5B booster re-entry.
 We start by estimating the probability density for the given region (Spain) in a typical, unperturbed, traffic day.The result will be a probability density map for the predicted re-entry time.This is the first term in probability computation. The second term is evaluated running a Monte Carlo simulation on the dynamics of debris reentry.There are many factors affecting the re-entry.The best prediction error for the re-entry time is usually in the order of 1 hour [2] which translates in a danger zone spanning half the globe! We then compute the danger zone and the probability of a collision. Last, we analyze suggested alternative solutions to airspace closure and make a new proposal by transforming a spatial problem into a temporal one.
3. The aircraft: estimating the probability density of the air traffic.Analyzing air traffic density involves using large volumes of spatial-temporal data.The source of the data is in this case the tracking site Flightradar24, more precisely a captured movie for a full day of traffic [6].The typical methodology will be to use trajectory data, but they aren't available in bulk.We start by converting images of frames (the film was recorded at 1/30 fps) into target coordinates and then continue with a spatial-temporal interpolation.The usual steps for image recognition were followed:  Each frame was converted to grayscale and the adaptive Otsu method was used to eliminate the background. Small noise was filtered out using a morphological opening operation. The distance transform of the binary image was then computed.This provides a map where values represent the distance from each pixel to the nearest zero-pixel. Peaks in the distance transform helped us identify potential centers of the symbols. The image was then segmented using the watershed transform on the inverse of the distance transform. The connected component analysis was used to label each separated symbol and then the position of the center of mass was computed.
A visual summary of the transformation is given in Figure 3.The result is a list of x/y coordinates of targets (which were later converted to Lat/Lon).
To represent air traffic density in a region, we performed a spatial interpolation between frames.This estimates the density of probability of finding an aircraft at any given time and location, not just where measurements are taken.The Kriging method was used for spatial interpolation and linear interpolation was used for temporal interpolation.
Kernel Density Estimation was used to get a smooth, continuous density function.The 2D KDE can be represented as:

𝑦 ℎ
Where: (, ) is the estimated density at point (, ).N is the total number of data points.K is the kernel function.Both Gaussian and Epanechnikov kernel functions were tried but with a very small difference in the result.ℎ is the bandwidth.This is very important in the way the result looks.The usual 5NM separation was considered a good starting point for the value of h.
( ,  ) are the coordinates of the  data point.
All computation was done in Matlab.The resulted probability density (for the predicted re-entry time) is given in Figure 4.
Because the covered area is large, and the debris has a finite speed, this is strictly speaking valid just for the re-entry estimated moment.Any delay of the re-entry will move both the position and the time of the impact, and the density map will change.This change is progressing in time along the track with the orbital speed in a predictable way and the result is a time interpolated density map with the ground track as the interpolating axes.The difference is not great but should be taken into consideration.Uncontrolled space objects in low earth orbit are affected by drag due to vacuum not being actually vacuum.Density of the ionosphere is higher at lower altitudes, so the drag effect is stronger at the perigee, lowering the apogee.The result is a gradual decay in altitude and a circularization of the orbit.As drag reduces orbital speed and centrifugal force can no longer counteract gravity, the object will exit orbit and re-entry begins.Unfortunately, at this stage the orbit is near circular, so the re-entry angle is typically very small (minutes of arc) thus making the prediction very difficult.In contrast, controlled reentries (and meteors) have much steeper angles.CORDS was established to focus on the issues related to space debris, space surveillance, and re-entry, and it conducts analyses to help understand and mitigate the risks associated with these topics [2].

Debris re-entry simulation
Prediction starts with information about current status.These are summarized in a standard TLE file which, for large objects near re-entry, are updated usually once per orbit [7].The information in the TLE is quite accurate and include object identification and all its orbital elements [2]: The simulation is affected in principle by two types of errors:  Uncertainties related to ionosphere (primarily space environment density at altitudes between 80-200 km).This is highly related to solar activity and the geomagnetic field. Uncertainties related to the geometry and mass of the debris.Other error sources are related to unknown vehicle configuration, attitude and possible lift generating surfaces and the possibility of breaking up.
The first type of uncertainty generates the largest error because it affects the re-entry starting time.Each second of error in predicting the moment of the re-entry adds 7.6 km to the longitudinal error.It is also the most difficult to predict.We will start with the influence of the second type of unknowns.Starting from the last known position and using an average ionospheric model, the re-entry from a circular orbit span almost half the globe.The simulation is quite straightforward using point of mass equations and estimating possible values for the ballistic/drag coefficients.Figure 5 provides a small sample of the Monte Carlo run varying mass and ballistic coefficient ±10% around estimated values.There is a relatively large dispersion of the impact point (around 350 km along the track and 50 km on the cross track).This result matches average values from literature where advanced dynamics modeling was considered (Figures 6 and 7).(SI units) with a zoom-in on the final impact point Figure 7 Position dispersion at FL600 for 1000 trajectories [9] Figure 6 On-ground distribution varying the uncertainty in ballistic coefficient [10] EASN-2023 Journal of Physics: Conference Series 2716 (2024) 012102 IOP Publishing doi:10.1088/1742-6596/2716/1/0121026 4.3.The Ionosphere Ionospheric density prediction was an intense researched topic, and several models are available.The most used for re-entry prediction is NRLMSISE-00 (Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Extended) which is a semi-empirical model of the Earth's atmosphere and ionosphere.It was developed by the U.S. Naval Research Laboratory, and it is used to describe atmospheric properties such as temperature, density, and composition from the ground level up to outer space (about 1,000 km in altitude) [8].It is particularly useful for understanding how the Earth's atmosphere affects spacecraft and satellites, including drag calculations that influence orbital decay.
It produces local values for ionospheric parameters based on the geographic coordinates, altitude, date, time of day and current sun activity modeled using the number of sunspots and the 2800MHz -10.7 cm (F10.7)radio emission of the Sun (Figures 8 and 9).
The number of Suns spots varies slow and using post event measurements of F10.7 it is possible to estimate the ionospheric density along the last orbit of CZ5B, but this information was not available in real time.The ionospheric density estimated by the model is given in Figure 10.As stated before, changes in the ionospheric condition can induce errors for the beginning of the re-entry in the 1 hour range [2].This verifies also for the studied case were using different F10.7 possible values generate such variations.The predicted impact zone is a 55km band along the ground track of the debris.The length corresponds to approximative 28 minutes (spreading of the final time for minimum and maximum values of the forecasted ionospheric density) of orbit and is 12600km in length.Considering (as a first approximation) equal probability density for an impact in this zone the value of the probability is the inverse of the area and is 1.3228E-06 impact/km 2 .

Estimating the probability of a collision
The last step for estimating the probability of a collision is to multiply the two probability densities maps followed by an integration over the whole area.Due to temporal shifting this involves re-estimating Figure 4 for 28 minutes.This actually generates a movie but for obvious reasons just a frame is presented.As it can be seen in Figure 12 (where only areas across Europe are represented) indeed Spain has the highest risk of collision but there is also a non-zero probability associated with Sardinia, the Tyrrhenian Sea and the south of Italy.Only Spain chose to close the airspace.The final pieces missing to estimate the probability of collision are the dimensions of the two objects.Assuming a value of 100m in diameter for any aircraft, a 25m diameter cross-section for CZ5B and considering that all aircraft are at FL360 the final probability of a collision between any aircraft and CZ5B, anywhere over Europe, is 9.528 10E-8.
As the probability is almost 1E-7 (which classifies as Extremely Remote) it is 100 times more probable than AC25 (FAA AC25.13091A -System Design and Analysis is the certification standard for transport airplanes) requirements (1.0E-9) for critical events.The closure of the airspace seems justified.

Alternatives to airspace closure
A representation of the altitude and velocity during reentry as functions of time (Figure 13) allows for an interesting observation.The re-entry necessitates time: it takes more than 5 minutes for a debris passing the Karman line to reach FL360.If a re-entry is detected at 100km altitude the only uncertainties remaining are related to the geometry of the debris and they give a statistical spread of 350x50km.
Based on this observation, Bernelli & all [9] propose a dynamic evacuation of the hazard area (Figure 14).When the re-entry is detected, the ATC will trigger an emergency evacuation of the danger area.

Figure 2
Figure2EUROCONTROL close the airspace under the orbit as the re-entry of the booster was imminent[4]

Figure 3 4 Figure 4
Figure 3 Visual summary of target recognition process

TLEFigure 5
Figure 5 Orbital 2D (in plane) simulation starting from the last known TLE. (SI units) with a zoom-in on the final impact point

Figure 8
Figure 8 Annual predicted variation of total density at Madrid location.

Figure 9
Figure 9  Daily solar radio flux variation at 10.7 cm (2800 MHz).F10.7 is used as a proxy of solar activity in the ionospheric model.[8]

Figure 12
Figure 12 Probability density for a collision between an aircraft and CZ5B

Figure 13
Figure 13 Altitude (blue) and speed of the debris as function of time (SI units).
4.1.Space debris awareness Several military, public and private organizations operate in this domain.The main sources of information are:  Space Surveillance Network (SSN): Part of the United States Space Command, it tracks artificial objects orbiting Earth.SSN is one of the most comprehensive systems, shares data with other countries and entities and is currently operated by 18th Space Defense Squadron.Is the primary source for TLE's files which summarize the orbital elements of an object. European Union Agency for the Space Program: Managed by the European Space Agency (ESA), it focuses on various aspects of space missions, including debris tracking through its Space Debris Office [3].For operational purposes the EU Commission funds the EUSST. Center for Orbital and Reentry Debris Studies (CORDS) is a part of The Aerospace Corporation, a U.S. nonprofit corporation that operates a federally funded research and development center.