Analysis of the Consequences in Low Earth Orbit of the Collision Between Cosmos 2251 and Iridium 33

Abstract

On 10 February 2009, Cosmos 2251 and Iridium 33 collided in orbit at an altitude of about 790 km. It was the first accidental catastrophic collision between two intact objects, leading to the formation of two sizable debris clouds in the orbital region already most affected by previous launch activity and breakups. Having no specific information on the physical characteristics of the fragments, the ballistic parameter, based on decay calibrations, was estimated for five random samples of the fragments, three for Cosmos 2251 and two for Iridium 33, and the statistical inference method was then applied to infer the properties of the whole populations. In particular, it was found that both clouds presented a significant fraction of cataloged fragments with very high area-to-mass ratios, hundreds or thousands of times greater than those of intact satellites, leading to the conclusion that the generation of such orbital debris might be more common than formerly supposed. In an attempt to assess the impact of the collision on the low Earth environment, the clouds of cataloged debris were propagated for 100 years, taking into account the relevant orbit perturbations and the debris ballistic coefficient distributions based on orbit decay calibrations. It was found that a substantial fraction of the fragments will remain in space for several decades and approximately one century will be needed to remove most of the wreckage from orbit. Concerning, finally, the four Italian satellites operational in low Earth orbit (AGILE and three COSMO-SkyMed), as of the end of June 2009, the collision probability with cataloged objects had been increased by less than 10%.

Full text

ANALYSIS OF THE CONSEQUENCES IN LOW EARTH ORBIT OF THE
COLLISION BETWEEN COSMOS 2251 AND IRIDIUM 33
Luciano Anselmo (1), Carmen Pardini (2)
Space Flight Dynamics Laboratory, ISTI/CNR, Via G. Moruzzi 1, 56124 Pisa, Italy
(1) phone: +39-050-315-2952; email: luciano.anselmo@isti.cnr.it
(2) phone: +39-050-315-2987; email: carmen.pardini@isti.cnr.it
ABSTRACT
On 10 February 2009, Cosmos 2251 and Iridium 33 collided in orbit at an altitude of about 790 km.
It was the first accidental catastrophic collision between two intact objects, leading to the formation
of two sizable debris clouds in the orbital region already most affected by previous launch activity
and breakups. Having no specific information on the physical characteristics of the fragments, the
ballistic parameter, based on decay calibrations, was estimated for five random samples of the
fragments, three for Cosmos 2251 and two for Iridium 33, and the statistical inference method was
then applied to infer the properties of the whole populations. In particular, it was found that both
clouds presented a significant fraction of cataloged fragments with very high area-to-mass ratios,
hundreds or thousands of times greater than those of intact satellites, leading to the conclusion that
the generation of such orbital debris might be more common than formerly supposed. In an attempt
to assess the impact of the collision on the low Earth environment, the clouds of cataloged debris
were propagated for 100 years, taking into account the relevant orbit perturbations and the debris
ballistic coefficient distributions based on orbit decay calibrations. It was found that a substantial
fraction of the fragments will remain in space for several decades and approximately one century
will be needed to remove most of the wreckage from orbit. Concerning, finally, the four Italian
satellites operational in low Earth orbit (AGILE and three COSMO-SkyMed), as of the end of June
2009, the collision probability with cataloged objects had been increased by less than 10%.
1. INTRODUCTION
On 10 February 2009, at 16:56 UTC, two satellites collided at a geodetic altitude of 788.6 km above
Siberia (latitude: 72.5°N; longitude: 97.9°E), generating two clouds of debris [1]. The relative
impact velocity was about 11.6 km/s and approximately 1700 fragments had been detected and
tracked by the US Space Surveillance Network (SSN) by the end of July 2009. Cosmos 2251
(COSPAR ID: 1993-036A; SSN Catalog Number: 22675) was a 900 kg Strela-2 Russian spacecraft
used for military communications, decommissioned more than ten years earlier. Iridium 33
(COSPAR ID: 1997-051C; SSN Catalog Number: 24946) was instead an operational 560 kg
spacecraft of the homonymous private constellation for worldwide voice and data communications
using handheld satellite phones.
Even though in the past at least three unintentional hypervelocity impacts between cataloged objects
had been documented in space, this was the first accidental catastrophic collision between two
intact objects, leading to the formation of two sizable debris clouds in the orbital region already
most affected by previous launch activity and fragmentation events (Fig. 1). As of 23 July 2009,
1182 fragments of Cosmos 2251, with inclinations in between 73.6° and 74.3° and altitudes in
between 246 and 1707 km, and 504 fragments of Iridium 33, with inclinations in between 85.6° and
86.6° and altitudes in between 389 and 1485 km, had been detected [2]. Of these, 30 Cosmos 2251
and 16 Iridium 33 cataloged fragments had already reentered in the atmosphere [3].
Immediately after the impact, the fragments produced, depending on the velocity variation
imparted, were scattered in various orbits sharing the collision point. Each of the two debris clouds
maintained orbital planes close to the original ones, but a significant spread in altitude, both above

and below the collision height, was generated approximately 180° away from the collision “pinch”
point, i.e. over the Antarctic region. However, the orbital perturbations progressively spread out the
clouds around the Earth in the following months (Fig. 2), both in right ascension of the ascending
node and argument of perigee, gradually creating two new shells of debris around the planet.
200 400 600 800 1000 1200 1400 1600 1800 2000
0
1
2
3
4
5
6
7x 10
-8
Altitude [km]
Objects spatial density [#/km3]
Cataloged objects including the collision fragments
Cataloged objects without the collision fragments
Fragments of Cosmos 2251
Fragments of Iridium 33
Fig. 1. Cataloged orbital debris spatial density in LEO, with and without the fragments of the
collision between Cosmos 2251 and Iridium 33 (end of June 2009).
Iridium debris cloud
Cosmos debris cloud
26 Mar 2009 12:00 UTC
AGILE
COSMO-Skymed
Fig. 2. Orbital dispersion of the two debris clouds 44 days after the collision. The orbits of the ASI
spacecraft in LEO, AGILE and the COSMO-SkyMed constellation, are represented as well.

The purpose of the work described in this paper was to analyze the long-term evolution of the new
debris clouds and their consequences on the orbital debris environment and the functioning
spacecraft in Low Earth Orbit (LEO). In particular, the increase of the collision risk with cataloged
objects for the satellites of the Italian Space Agency (ASI) operational in LEO was evaluated. For
instance, considering the flux of cataloged objects before the collision, 16 debris close approaches
at less than 1 km should have been expected, on average, every year for each satellite of the
COSMO-SkyMed constellation. This means an average of 64 conjunctions per year at less than 1
km for the four spacecraft of the complete system [4]. The new debris added by the recent collision
required an updated conjunction and collision probability assessment, in order to evaluate if
operational changes had to be implemented in the future to cope with the additional impact risk.
2. CHARACTERIZATION OF THE COLLISIONAL DEBRIS PROPERTIES
Knowledge of the ballistic parameter and orbit of each fragment was needed in order to assess the
evolution of the two debris clouds generated by the accidental collision. For the cataloged debris,
for which a reasonably accurate orbit was available, the simplest approach would have been to
compute the ballistic parameter B, defined as
B = CD
⋅
A/M (1)
where CD, A and M are, respectively, the fragment drag coefficient, cross-sectional area and mass,
using the “BSTAR” (B*) value of the Two Line Elements (TLEs) issued by SSN [5]. In fact,
according to the TLEs orbital theory, the ballistic parameter B could be obtained from B* in the
following way [6]:
*
12.741621
B
B=m2/kg. (2)
However, the underlying orbital theory leading to the generation of TLEs considers an atmospheric
model that does not vary with solar activity, i.e. a model with a fixed density at any given height, by
fitting the observed orbital decay with an appropriate value of the parameter B*. Therefore, during
periods of low solar activity, and correspondingly lower than average atmospheric densities at the
altitudes of interest, such as during the months of 2009 following the collision among Cosmos 2251
and Iridium 33, the values of B* are smaller than average and the corresponding ballistic parameters
obtained from Eq. 2 might be systematically underestimated, even by a large amount.
Much more accurate values of B could be determined by analyzing the observed orbital decay of
each fragment over relatively long time spans. However, due to the large amount of debris
produced, this would have required too great an effort in terms of computational time and dedicated
resources. Therefore, representative samples of the objects were selected and analyzed in detail.
As a consequence of the perigee (PH) distribution of the Cosmos 2251 fragments, initially much
more dispersed with respect to the Iridium 33 ones, three altitude shells were selected: 200 km ≤ PH
≤ 450 km, 450 km < PH < 750 km and PH ≥ 750 km. In each of the shells, approximately 10% of the
cataloged fragments were randomly sorted out and their ballistic parameters were directly
determined by fitting, in a least squares sense, the semi-major axis decay inferred from the TLEs
acquired over a period of about 45 days. In order to obtain a set of scaling factors mapping the
values of B* into the actual ballistic parameters, for each object the fitted ballistic parameter was
compared with the value of B obtained by applying Eq. 2 to the average B*, i.e. the arithmetic mean
of the values of B* determined by SSN over the same time interval used for the fit. Exactly the same
analysis was carried out for the Iridium 33 fragments, but due to their lesser initial perigee height
dispersion, the altitude intervals considered, in which to sort out approximately 10% of the objects,
were only two: 450 km < PH < 750 km and PH ≥ 750 km.
For all the five Cosmos 2251 and Iridium 33 debris samples, a mean scaling factor and its standard
deviation were computed. Then, assuming a Gaussian distribution, with the mean and standard

deviation thus found, randomly generated B scaling factors were applied to all fragments belonging
to the appropriate perigee altitude interval. By merging the resulting populations, three for Cosmos
2251 and two for Iridium 33, the rescaled ballistic parameters of the whole debris clouds were
eventually obtained.
6500 6600 6700 6800 6900 7000 7100 7200 7300 7400 7500 7600 7700
10-5
10-4
10-3
10-2
10-1
100
101
102
Semi-major axis [km]
Ballistic parameter [m
2
/kg]
B computed from B*
Rescaled B from decay analysis
Fig. 3. Ballistic parameters of the Cosmos 2251 cataloged fragments, as of 1 April 2009.
6950 7000 7050 7100 7150 7200 7250 7300 7350 7400
10-4
10-3
10-2
10-1
100
101
102
103
Semi-major axis [km]
Ballistic parameter [m
2
/kg]
Rescaled B from decay analysis
B computed from B*
Fig. 4. Ballistic parameters of the Iridium 33 cataloged fragments, as of 1 April 2009.

The distribution of the rescaled ballistic parameters as a function of semi-major axis, compared with
the values computed with Eq. 2, is shown in Fig. 3 for Cosmos 2251 and in Fig. 4 for Iridium 33.
As expected, the values obtained from B* were significantly underestimated (by almost two orders
of magnitude) in these cases, characterized by conditions of minimum solar activity. The
corresponding logarithmic area-to-mass ratio distributions of the fragments, assuming CD = 2.2, are
represented in Figs. 5 and 6, respectively. Having adopted the Jacchia-Roberts 1971 density model
to calibrate the ballistic parameters, by fitting the sample debris orbital decay, and that Jacchia
developed his models, based on satellite decay analyses, by assuming CD = 2.2, i.e. the “standard”
value adopted by King-Hele [7], it might be expected that the rescaled values plotted in Figs. 5 and
6 would indeed exhibit a realistic average A/M distribution of the fragments.
-6 -5 -4 -3 -2 -1 0 1 2 3 4
0
5
10
15
20
25
30
35
Log
10
A/M [m
2
/kg]
Number of fragments
(Ballistic parameter obtained from B
*
)/2.2
(Rescaled ballistic parameter)/2.2
Fig. 5. A/M distributions of the Cosmos 2251 cataloged fragments, as of 1 April 2009.
-5 -4 -3 -2 -1 01234
0
2
4
6
8
10
12
14
16
18
Log
10
A/M [m
2
/kg]
Number of fragments
(Ballistic parameter from B*)/2.2
(Rescaled ballistic parameter)/2.2
Fig. 6. A/M distributions of the Iridium 33 cataloged fragments, as of 1 April 2009.

As shown more clearly in Figs. 7 and 8, both A/M distributions present a significant number of
objects with average A/M ≥ 1 m2/kg [8] [9], that is with very high area-to-mass ratios, similar to
those of a debris population discovered a few years ago in geosynchronous orbits [10] [11] [12]. In
particular, in the case of Cosmos 2251 (Fig. 7), it was found that about 5% of the cataloged
fragments had average A/M ≥ 1 m2/kg and slightly more than 1% had average A/M ≥ 10 m2/kg.
Very similar results (Fig. 9) had been previously obtained with a statistical decay analysis of the
Fengyun 1C debris, produced by the Chinese anti-satellite test carried out on 11 January 2007 [8]
[9] [13]. However, a quite larger fraction of high A/M objects was obtained in the Iridium 33 case
(Fig. 8), leading to a faster debris decay rate: 26% of the cataloged fragments resulted to have, in
fact, average A/M ≥ 1 m2/kg and 5% had average A/M ≥ 10 m2/kg [9].
-4 -3 -2 -1 0 1 2
0
5
10
15
20
25
30
Log
10
A/M [m
2
/kg]
Debris Number
High A/M Objects
Fig. 7. A/M distribution of the Cosmos 2251 cataloged fragments deduced from decay analysis.
-2 -1.5 -1 -0.5 00.5 11.5 2
0
2
4
6
8
10
12
14
16
18
Log
10
A/M [m
2
/kg]
Debris Number
High A/M Objects
Fig. 8. A/M distribution of the Iridium 33 cataloged fragments deduced from decay analysis.

Fig. 9. A/M distribution of the Fengyun 1C cataloged fragments deduced from decay analysis.
Therefore, the generation of trackable orbital debris with average A/M hundreds or thousands of
times greater than those of intact satellites might be more common than previously supposed, being
one of the standard consequences of fragmentation events, both at high and low energy, involving,
for instance, spacecraft or rocket bodies with multi-layered insulation blankets or other low density
composite materials.
In order to infer the characteristics of the two clouds of fragments, deduced from the five random
debris samples, three for Cosmos 2251 and two for Iridium 33, the statistical inference method was
applied.
Concerning Cosmos 2251, for the sample with 200 km ≤ PH ≤ 450 km, the mean (μ200 ≤ PH ≤ 450) of
the scaling factors (i.e. the ratios between the rescaled ballistic parameter based on the orbital decay
fit and the ballistic parameter computed from B*) was 10.12. The corresponding standard deviation
(σ200 ≤ PH ≤ 450) was 4.82. By applying the statistical inference, P(5.12 < μ200 ≤ PH ≤ 450 < 15.12) = 0.99
was obtained, i.e. a probability P of 99% of finding the mean of the overall population of objects
with 200 km ≤ PH ≤ 450 km in between 5.12 and 15.12. Then, using the χ2 distribution for the given
99% confidence level, the confidence interval where the standard deviation for all the objects with
200 km ≤ PH ≤ 450 km would lie was 3.11 < σ200 ≤ PH ≤ 450 < 13.71.
Similarly, for the sample of objects with 450 km < PH < 750 km, the mean (μ450 < PH < 750) of the
scaling factors was 98.59. The corresponding standard deviation (σ450 < PH < 750) was 51.08. By
applying the statistical inference, P(73.59 < μ450 < PH < 750 < 123.59) = 0.99 was obtained, i.e. a
probability P of 99% of finding the mean of the overall population of objects with 450 km < PH <
750 km in between 73.59 and 123.59. Then, using the χ2 distribution for the given 99% confidence
level, the confidence interval where the standard deviation for all the objects with 450 km < PH <
750 km would lie was 39.45 < σ450 < PH < 750 < 75.28.
Finally, for the sample of objects with PH ≥ 750 km, the mean (μPH ≥ 750) of the scaling factors was
188.34 and the standard deviation (σPH ≥ 750) was 84.62. By applying the methods of statistical
inference, it was found P(123.34 < μPH ≥ 750 < 253.34) = 0.99 and the 99% confidence interval where
the standard deviation would lie was 58.98 < σPH ≥ 750 < 167.51.
Concerning Iridium 33, for the sample with 450 km < PH < 750 km, the mean (μ450 < PH < 750) of the
scaling factors was 94.77. The corresponding standard deviation (σ450 < PH < 750) was 7.39. By
applying the methods of statistical inference, it was found P(88.77 < μ450 < PH < 750 < 102.77) = 0.99
and the 99% confidence interval where the standard deviation would lie was 4.77 < σ450 < PH < 750 <
21.02.

Lastly, for the sample with PH ≥ 750 km, the mean (μPH ≥ 750) of the scaling factors was 115.14 and
the standard deviation (σPH ≥ 750) was 20.07. By applying the methods of statistical inference, it was
found P(100.14 < μPH ≥ 750 < 130.14) = 0.99 and the 99% confidence interval where the standard
deviation would lie was 13.99 < σPH ≥ 750 < 39.72.
-4 -3 -2 -1 0 1 2
0
5
10
15
20
25
30
Log10 A/M [m2/kg]
Number of fragments
Lower bound of confidence interval
Upper bound of confidence interval
Nominal distribution
Fig. 10. Comparison of the A/M distributions of the Cosmos 2251 cataloged fragments obtained by
considering the lower, medium and upper values of the 99% confidence intervals
of the mean and the standard deviation.
-3 -2 -1 0 1 2 3
0
2
4
6
8
10
12
14
16
18
Log10 A/M [m2/kg]
Number of fragments
Lower bound of confidence interval
Upper bound of confidence interval
Nominal distribution
Fig. 11. Comparison of the A/M distributions of the Iridium 33 cataloged fragments obtained by
considering the lower, medium and upper values of the 99% confidence intervals
of the mean and the standard deviation.

By merging the various populations, three for Cosmos 2251 and two for Iridium 33, the
distributions of the rescaled ballistic parameters were then obtained relative to the average scaling
factor and standard deviation (nominal case), as well as to the bounds of their 99% confidence
intervals. Figs. 10 and 11 show, for Cosmos 2251 and Iridium 33, respectively, the shift with
respect to the nominal average A/M distribution of the two distributions obtained by using the lower
and upper bounds of the 99% confidence intervals of the mean and the standard deviation. It should
be noted that there is no appreciable difference between the three distributions. Therefore, from a
statistical point of view, the nominal rescaled ballistic parameters seem to be appropriate for
characterizing the aerodynamic properties of the Cosmos 2251 and Iridium 33 debris clouds.
3. DEBRIS CLOUDS EVOLUTION
The cataloged fragments of the collision between Cosmos 2251 and Iridium 33, for which a
rescaled ballistic parameter had been computed, were individually propagated with the last version
of a numerical code [14], taking into account the most important perturbations, namely the Earth’s
gravity field harmonics, up to the 5th order and degree, air drag, luni-solar third body attraction and
solar radiation pressure with eclipses. To estimate the effects of air drag, the Jacchia-Roberts 1971
density model was adopted, together with the National Oceanic and Atmospheric Administration
(NOAA)/Space Weather Prediction Center (SWPC) forecasts of the planetary geomagnetic index
and the 10.7 cm solar flux proxy [15]. The solar flux predictions were based on an average of the
International Space Environment Service (ISES) panel forecasts for solar cycle 24, as of 6 April
2009, valid until 31 December 2015. Fig. 12 shows the predicted 10.7 cm solar flux. Besides the
nominal cycle, the maximum and minimum forecasts, both based on the predictions of the ISES
solar cycle 24 panel, are also represented.
2009 2010 2011 2012 2013 2014 2015
60
80
100
120
140
160
180
200
Year
Solar radio flux at 10.7 cm (10
4
Jy)
maximum
nominal
minimum
Fig. 12. Solar radio flux at 10.7 cm predictions for cycle 24.
The results obtained in the time span covered by the current solar cycle 24 forecasts are presented in
Figs. 13 and 14, for the debris clouds of Cosmos 2251 and Iridium 33, respectively. The evolution,
in terms of percentage of fragments left in orbit, will depend, of course, on the expected solar flux
(minimum, nominal or maximum) and the actual average A/M distribution. However, the
uncertainty associated with the solar flux predictions affected the Iridium 33 cloud evolution
significantly more than the uncertainty associated with the A/M distribution, while their mutual

impact was roughly comparable in the case of the Cosmos 2251 cloud. Anyway, it was found that,
by the end of 2015, the percentage of Cosmos 2251 cataloged fragments still in orbit will be in
between 42% and 70%, while the percentage of Iridium 33 cataloged fragments in space will be in
between 21% and 52%, confirming the higher decay and reentry rate of the Iridium 33 debris,
generally characterized by a greater area-to-mass ratio (Figs. 10 and 11).
2009 2010 2011 2012 2013 2014 2015 2016
40
45
50
55
60
65
70
75
80
85
90
95
100
Year
Percentage of fragments in orbit
Minimum solar flux, B minimum
Nominal solar flux, B minimum
Nominal solar flux, B nominal
Nominal solar flux, B maximum
Maximum solar flux, B maximum
Fig. 13. Evolution of the Cosmos 2251 debris cloud during solar cycle 24, as a function of solar flux
prediction (Fig. 12) and ballistic parameter distribution (lower, medium and upper values
of the 99% confidence intervals of the mean and the standard deviation).
2009 2010 2011 2012 2013 2014 2015 2016
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Year
Percentage of fragments in orbit
Minumum solar flux, B minimum
Nominal solar flux, B minimum
Nominal solar flux, B nominal
Nominal solar flux, B maximum
Maximum solar flux, B maximum
Fig. 14. Evolution of the Iridium 33 debris cloud during solar cycle 24, as a function of solar flux
prediction (Fig. 12) and ballistic parameter distribution (lower, medium and upper values
of the 99% confidence intervals of the mean and the standard deviation).

In order to evaluate the debris clouds evolution during one century, all the cataloged fragments were
individually propagated for 100 years, with the same models and assumptions previously described.
However, in this case the predicted solar flux available on the Inter-Agency Space Debris
Coordination Committee (IADC) Common Database [16] was adopted (Fig. 15) and only the mean
ballistic parameter distributions for the Cosmos 2251 and Iridium 33 fragments were considered.
2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
60
80
100
120
140
160
180
Year
Solar radio flux at 10.7 cm (104 Jy)
Predicted radio flux from 19 May 2009 to 19 May 2107
Fig. 15. Solar radio flux predictions for one century.
2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 2110
0
10
20
30
40
50
60
70
80
90
100
Year
Percentage of fragments in orbit
Cosmos 2251
Iridium 33
Fig. 16. Evolution of the Cosmos 2251 and Iridium 33 debris clouds during one century, with
nominal solar flux prediction and mean ballistic parameter distributions.
The results obtained, again in terms of percentage of fragments left in orbit, are presented in Fig.
16. They confirmed the quite faster decay of the Iridium 33 debris cloud, with 90% of the cataloged

fragments left in orbit in 2010, 50% in 2013, 10% in 2040 and 3% after one century. Concerning
the Cosmos 2251 debris cloud, the corresponding figures were 90% of the cataloged fragments left
in orbit in 2011, 50% in 2022 and 10% after one century. Therefore, the adverse effects of the
accidental satellite collision on the LEO environment will be felt for several decades, being needed
approximately one century to sweep most of the wreckage from orbit.
4. IMPACT RISK ASSESSMENT FOR THE ASI SATELLITES IN LEO
A software tool specifically developed for orbital debris impact risk assessment [17] [18] was used
to estimate the additional impact flux of the Cosmos 2251 and Iridium 33 cataloged debris on the
spacecraft of the Italian Space Agency in LEO, at the reference epoch of 29 June 2009. The
satellites were: AGILE, an astrophysical spacecraft in low equatorial orbit (altitude: 522 × 551 km;
inclination: 2.47°) and COSMO-SkyMed 1, 2 and 3, three sun-synchronous remote sensing
spacecraft (of a constellation of four), put on the same orbital plane (altitude: 622 × 623 km;
inclination: 97.86°).
Ignoring the objects generated by the collision, the flux of cataloged debris on AGILE was found to
be 1.62 × 10-6 m-2 per year, with an average collision velocity of 10.234 km/s. The inclusion of the
Cosmos 2251 and Iridium 33 cataloged debris increased the flux by 9.5%, to 1.78 × 10-6 m-2 per
year. The average collision velocity slightly decreased, instead, to 10.186 km/s, due to the relative
geometry of the new flux. This is made clear in Fig. 17, showing the cross-sectional area flux as a
function of the relative velocity of the incoming debris. Due to the orbit geometry and debris
distribution, the collisional flux is dominated by objects in high inclination orbits crossing the
equatorial region where AGILE resides.
Concerning the three satellites of the COSMO-SkyMed constellation, the flux of cataloged debris
was found to be 5.01 × 10-6 m-2 per year, with an average collision velocity of 13.088 km/s,
disregarding the objects generated by the collision among Cosmos 2251 and Iridium 33. The
inclusion of the cataloged collisional debris increased the flux by 8.6%, to 5.44 × 10-6 m-2 per year.
On the other hand, even in this case the average collision velocity slightly decreased to 12.895
km/s, due to the relative geometry of the new flux. Fig. 18, showing the cross-sectional area flux as
a function of the relative velocity of the incoming debris, confirms this fact. It is clear that, due to
the orbit geometry (sun-synchronous) and debris distribution, the collisional flux is dominated by
objects in high inclination orbits moving approximately in the opposite direction to the spacecraft.
This explains the high value of the average collision velocity.
In conclusion, at the end of June 2009, the wreckage of Cosmos 2251 and Iridium 33 had increased
by less than 10% the collision probability with cataloged debris of the AGILE and COSMO-
SkyMed satellites of the Italian Space Agency.
5. CONCLUSIONS
The first accidental catastrophic collision in orbit between two intact objects led to the formation of
two sizable debris clouds in the circumterrestrial region already most affected by previous launch
activity and breakups. This event significantly increased the amount of debris in LEO and a
substantial fraction of it will remain in space for several decades. Approximately one century of
atmospheric drag will be needed to remove most of the wreckage from orbit.
An obvious consequence of the collision was to significantly increase the probability of collision
between intact objects, i.e. spacecraft and upper stages, and man-made debris. However, for the four
ASI satellites operational in LEO, the collision probability with cataloged objects had been
increased by less than 10%, as of the end of June 2009.
Having no specific information on the physical properties of the fragments resulting from the
collision, it was necessary to introduce a number of assumptions to simulate the evolution of the
resulting debris clouds. The ballistic parameter, based on decay calibrations, was estimated for five

random samples of the fragments, three for Cosmos 2251 and two for Iridium 33, and the statistical
inference method was then applied to infer the characteristics of the whole populations.
0246810 12 14 16 18 20
0
1
2
3
4
5
6x 10
-7
Relative velocity [km/s]
Cross-sectional area flux [#/m2/year]
Cataloged objects including the collision debris
Cataloged objects without the collision debris
Fig. 17. AGILE: cross-sectional area flux as a function of the incoming debris relative velocity.
0246810 12 14 16 18
0
0.5
1
1.5
2
2.5x 10
-6
Relative velocity [km/s]
Cross-sectional area flux [#/m2/year]
Cataloged objects including the collision debris
Cataloged objects without the collision debris
Fig. 18. COSMO-SkyMed constellation: cross-sectional area flux as a function of
the incoming debris relative velocity.
In particular, it was found that both clouds presented a significant fraction of cataloged fragments
with very high area-to-mass ratios, leading to the conclusion, supported by previous analyses, that
the generation of trackable orbital debris with average A/M hundreds or thousands of times greater
than those of intact satellites might be more common than formerly supposed, being one of the
standard consequences of fragmentation events, both at high and low energy.

6. ACKNOWLEDGMENTS
The authors are deeply grateful to the US Space Surveillance Network, for making available the
TLEs of the collision fragments. The results presented were obtained within the framework of the
ASI/CISAS Contract No. I/046/07/0.
7. REFERENCES
[1] Anselmo L., ASI Report on Debris Mitigation at the 27th IADC, Presented at the 27th Inter-
Agency Space Debris Coordination Committee (IADC) Plenary Meeting, Darmstadt, Germany, 25-
27 March 2009.
[2] Joint Space Operations Center (JSpOC), Iridium/Cosmos Debris, JSpOC Hot Topics, Space
Track, The Source for Space Surveillance Data, web site: www.space-track.org, 23 July 2009.
[3] Space Track, The Source for Space Surveillance Data, web site: www.space-track.org, 27 July
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