Computational Methods for Reentry Trajectories and Risk Assessment

Transcription

1 Computational Methods for Reentry Trajectories and Risk Assessment Luciano Anselmo and Carmen Pardini Space Flight Dynamics Laboratory, ISTI/CNR, Via G. Moruzzi 1, Pisa, Italy Abstract The trajectory modeling of uncontrolled satellites close to reentry in the atmosphere is still a challenging activity. Tracking data may be sparse and not particularly accurate, the objects complicate shape and unknown attitude evolution may render difficult the aerodynamic computations and, last but not the least, the models used to predict the air density at the altitudes of interest, as a function of solar and geomagnetic activity, are affected by significant uncertainties. After a brief overview of the relevance of the risk related to satellite reentries and debris survival down to the ground, the paper describes some of the methods and techniques developed in support of the reentry predictions carried out for civil protection purposes. An appropriate management of the intrinsic uncertainties of the problem is in fact critical for the dissemination of the information, avoiding, as much as possible, misunderstandings and unjustified alarm. Special attention is paid to the evaluation of the risk, the availability of orbit determinations, the uncertainties of the residual lifetime estimation, and the definition of reentry and risk windows. When possible, the discussion is supported by real data, results and examples, often based on the authors direct experience and researches. 1. Satellite reentry Love and Brownlee (1993) have estimated that 40,000 metric tons (± 20,000) of meteoroids enter the Earth s atmosphere every year. Foschini (1997) has obtained a consistent estimate of 54,000 metric tons per year. The overwhelming majority of the impacting particles has a mass of a few milligrams or less, even though, each day, 4,800 (± 500) of them would have a mass greater than 0.01 kg (Ortiz et al., 1999) and a mass greater than 1 kg (Hartmann, 1993). Due to the physics of the atmospheric entry, and depending on the meteoroids composition, structure, entry velocity and angle, only the rare objects above a certain size threshold are able to survive down to the ground: smaller bodies are either entirely consumed by ablation, or experience a breakup at high altitude. However, even the air burst caused by the mid-air detonation of a m object may have tremendous consequences, as demonstrated by the Tunguska event in 1908, which flattened some 2,200 km 2 of Siberian forest. Since 1900, there have been around 100 documented meteorite crashes on Earth (Anonymous, 2002), but, due to the combined increase of meteor observations and population density, the reporting rate registered a substantial growth in the last decades. Between August 1972 and March 2000, the infrared sensors of the American early warning satellites (DSP) detected 518 natural entries into the atmosphere, all in the kiloton class or above, with an average of 30 events per year (Atkinson et al., 2000). After the launch of the first artificial satellite, in 1957, a new class of bodies began to enter the atmosphere from space. More than 19,000 artificial objects (1.1 per day, on average, since the beginning of the Space Age), catalogued by the American Space Surveillance Network (SSN), have returned to Earth so far. In the last four decades, metric tons per year, concentrated basically in intact spacecraft and rocket bodies, reentered in the atmosphere without control at the average rate of 2 intact objects per week (1 per week in 2003). In terms of falling mass and potential danger, the uncontrolled reentry of artificial satellites is still of minor concern. However, the Liability Convention, adopted by the United Nations in 1972, states (Article II): A launching State shall be absolutely liable to pay compensation for damage caused by its space object 1

2 on the surface of the Earth or to aircraft flight. Moreover, there is mounting evidence that the survival of a significant amount of certain satellite components to the reentry conditions is quite more widespread than originally believed. Therefore, the associated risk cannot be totally ignored. So far, about 60 uncontrolled reentry events resulting in the recovery of debris on the ground have been documented. Based on the available reports, it seems that only one person has been struck but not injured by a lightweight fragment of a reentering satellite. Taking into account that most reentries occur over the oceans or sparsely populated areas, these numbers are not too small, after all, being comparable to the meteorites falls documented during the same period. In addition, if there is a global public awareness of an incoming reentry, as was the case at the end of April 2003, when the widely publicized decay from orbit of the Italian BeppoSAX satellite was foreseen (April 29), the chances that such events are witnessed are much greater than usual. For instance, three other large objects reentered in the atmosphere in the days of the BeppoSAX final plunge and all of them were observed: a Proton upper stage above Brazil (April 26), a Centaur stage in Guatemala (April 27) and an Ariane 3 third stage in Malaysia (April 30). Concerning the real target of such widespread interest, BeppoSAX, no witness report of its reentry was issued (apart a few false accounts). 2. Debris survivability A satellite in circular orbit approaching the reentry in the atmosphere has a specific mechanical energy of J/kg. If all this energy were converted into heat entirely absorbed by the body, most material would be totally vaporized. However, only a small fraction (< 1% for BeppoSAX) of the energy theoretically available is converted into heat absorbed by the body (the total value and the heating rate depend on the entry conditions velocity and flight path angle and the object shape, area and mass), so the chance of having surviving satellite components hitting the ground is quite higher than originally supposed, as a growing body of evidence is attesting. Apart from some structurally loose components characterized by a high area to mass ratio (e.g. solar panels or large antennae), generally lost at an altitude around 100 km, most spacecraft and upper stages mainly disintegrate at an altitude of about 78 km, plus or minus ~ 10 km, due to the heat and the dynamic loads of the reentry. The survivability of specific components depends on a numbers of factors: structure, composition, shape, area to mass ratio, release sequence and shielding from other parts of the system during the critical phases of maximum heating. In general, aluminum parts are completely consumed, unless characterized by a very high area to mass ratio or released relatively late during the reentry, being protected by other components in the most critical phases. Empty steel and titanium tanks, or the titanium casings of solid rocket motors, have instead a very good probability to make it down to the ground. Today a few computer codes are available in Europe, Japan, Russia and the United States to model in detail the fragmentation and eventual demise of complex structures during reentry, taking into account both the thermal and dynamical aspects. The most known are SCARAB (Fritsche et al., 2000), developed for ESA and applied to the reentry destructive analysis of spacecraft like ATV, ROSAT and BeppoSAX, and ORSAT (Rochelle et al., 1999), used to model the fragmentation of NASA satellites, as EUVE, AURA and UARS. Even though a thorough comparison of the software predictions with actual data has been so far impossible, SCARAB and ORSAT have been compared against a few simple test cases, showing a reasonable qualitative and quantitative agreement. The application of such simulation tools to detailed spacecraft models has confirmed that a nonnegligible amount of debris is typically able to survive the harsh conditions of reentry, hitting the ground. In the case of BeppoSAX, a 1,350 kg spacecraft with a lot of refractory materials, the destructive analysis carried out with SCARAB predicted the survival of 49% of the initial mass (Lips, 2002). On the other hand, ORSAT obtained the following mass survival fractions: 37% for the Compton Gamma Ray Observatory, with an initial mass of approximately 15 metric tons (Ahmed et al., 2001); 4.3% for TRMM, with an initial mass of 2,620 kg (Smith et al., 2004b); 9.4% for UARS, with an initial mass of 5,670 kg (Rochelle and Marichalar, 2002); and 9.9% for GLAST, with an initial mass of 3,640 kg (Smith et al., 2004a). In addition, recovered debris on the ground has shown that at least 35% of the mass of the Delta II second stage (initial value: 920 kg) and 25% of the mass of the exhausted PAM-D solid rocket motor (initial value: 200 kg) is able to survive (Botha, 2001; Anonymous, 2001; Anonymous, 2004). 2

3 Researchers at The Aerospace Corporation (CORDS, 2004) have estimated that, globally, more than 1,400 metric tons of materials have probably survived reentry since the beginning of the Space Age (with no reported casualties). 3. Risk evaluation 3.1. Latitude belt potentially involved The definition of the latitude belt potentially affected by the impact of the surviving fragments of a reentering satellite results from the following relationships: L max = I + δ + Λ [for direct orbits]; (1) L max = 180 I + δ + Λ [for retrograde orbits]. (2) L max is the limiting latitude (North or South) of the above mentioned belt, I is the satellite orbit inclination, δ is a small corrective term, for the conversion from geocentric to geodetic coordinates, and Λ is the maximum cross-track dispersion of the fragments with respect to the nominal trajectory (expressed as an angle with respect to the center of the Earth). The term δ reaches its maximum (~ 0.2 ) at intermediate latitudes, but vanishes at the poles and the equator. In principle, the satellite surviving fragments might hit the Earth surface at any location in between L max degrees North and South. The reentry probability is latitude dependent, minimum on the equator and maximum close to the extreme latitudes for a near circular orbit (Klinkrad, 2003). As an example, BeppoSAX, with an orbital inclination of approximately 4, had the a priori reentry probability as a function of latitude given in Table Risky ground swath In addition to Λ, the half width of the risky ground swath (Σ) associated with the predicted reentry trajectory will depend also on a term, ε(λ), resulting from the inaccuracies of the propagated state vector: Σ ( λ ) = Λ + ε ( λ). (3) In this equation λ is the latitude of the corresponding sub-satellite point. The term ε(λ) is minimum (and equal to zero) when the absolute value of the sub-satellite geodetic latitude is maximum, while it assumes the highest value for near circular orbits on the Earth equator. There it is given, as a function of the error (±η) in the trajectory nodal crossing, by the expression: α cos I 1 ε (0 ) = η sin cos n, (4) 2 1/ 2 α α 1 2 cos I + 2 n n where n is the satellite mean motion and α is the sum of the Earth s angular velocity and the satellite nodal precession rate. For circular orbits close to reentry, in which n 16α, Eq. (4) may be approximated by the expression ε(0 ) η sin I. Regarding the size of the nodal crossing error, it is given, in kilometers, by: η = Δt, (5) 3

4 where Δt is the nodal crossing time difference (in seconds) between the predicted and the actual trajectory, and km/sec is the Earth s rotation velocity at the equator. A reasonable estimate of η is available only during the last few days of satellite lifetime and its final value critically depends on the last orbital state vector available. Every minute of error in the nodal crossing time prediction translates into η 28 km. Λ may vary in between a few tens and km (42 km for BeppoSAX) Casualty expectancy If the fragments of a satellite fall in a region of area A R and total population N, the expected average number of casualties E c can be calculated with the following equation: E c = P I N (A c /A R ), (6) where P I is the probability of impact in the region and A c is the total effective casualty area for the impacting fragments. It should be emphasized that E c is not the probability of a casualty: in theory the casualty expectancy may be greater than one, while the probability of casualty can never be. The formula adopted in the NASA Safety Standard (Anonymous, 1995; Bouslog et al., 1995) to compute the effective casualty area due to a satellite reentry is: n i= 1 ( 2 A = A + A ), (7) c where A h = 0.36 m 2 is the projected cross-sectional area of a standing human and A i is the cross-section of each individual fragment reaching the ground. However, for people in the open, the effective casualty area of impacting inert debris is generally larger, due to winds, trajectory path angle, sliding, skidding or bouncing at ground impact, and splattering or cratering (Montgomery and Ward, 1995). In addition, explosive debris can significantly increase the casualty area (Smith, 1999). In the case of a reentering satellite, the fragments will generally rain down vertically, with respect to the local horizon, with only a minor horizontal velocity component due to local winds, with negligible consequences. Moreover, any material able to explode or burn should ignite at high altitude, during the breakup phase. Regarding sliding, bouncing or splattering at ground impact, the three effects are generally exclusive and, because soft soil tends to be more common than hard surfaces, the effective casualty area computed using Eq. (7) might be, at most, enhanced by a factor 2 (Smith, 1999). Following Eq. (6), the expected average number of casualties E c due to a satellite reentry can be computed as follow: h i E c NAc, (8) 4πR 2 sin L max where R is the radius of the Earth and N/(4πR 2 sin L max ) represents the average population density in the latitude belt potentially affected by the satellite debris impact. For the Italian spacecraft BeppoSAX, taking into account the average population density in the latitude band at risk, people per square kilometer, and adopting the method suggested by NASA (Anonymous, 1995; Bouslog et al., 1995), the debris casualty area (32.42 m 2 ) obtained by the destructive analysis (Lips, 2002) implied an a priori expected number of human casualties of about Assuming a further enhancement factor of 2 (Smith, 1999), to take into account debris sliding, bouncing or splattering after the ground impact on a typically soft soil, the expected average number of casualties in the latitude belt at risk (approximately ± 4.4 ) was about Table 1 summarizes the a priori casualty expectancy as a function of latitude, taking into account the population density distribution. This, of course, was a measure of collective risk. The individual risk associated with the BeppoSAX reentry was measured by E c /N To put such extremely low individual risk in perspective, the annual individual fatality rate due to a non-occupational accident in a developed country is of the order of 10-4 (Anselmo et al., 1999). It should also be emphasized that the orbital inclination of the BeppoSAX satellite ( 4 ) guaranteed the minimum expected number of casualties per unit casualty area (Kato, 2001). In other 4

5 words, the same satellite would have been potentially more risky in any other inclination, lower or higher, for instance by 15% at 0, by 38% at 15, and by 85% at 50. For people in the open, the casualty probability P(k) where k is the number of victims can be obtained from the average number of expected casualties E c using the following Poisson distribution: The values computed for BeppoSAX are presented in Table Risk assessment k E E e c c P( k) =. (9) k! The risk is the product of probability and consequence. For a satellite reentry with surviving fragments, and inside the ± L max latitude belt, the probability of debris fall is one, but the expected consequences, at least for people in the open, are not particularly adverse with respect to the common risks accepted in the everyday life. In fact, the a priori individual risk associated with a satellite reentry, even in the worst cases, is still much lower, by several orders of magnitude, than the annual individual fatality rate due to accidents. For people in buildings or shelters, the casualty area of a satellite surviving fragment may be larger or smaller than its maximum cross-sectional area. The exact outcome depends on the fragment capability of penetrating or gravely damaging the sheltering structure. If this is not the case, the effective casualty area of the fragment for that structure becomes zero. The risk associated with a reentry can be subdivided in primary and secondary. The primary risk is that due to a direct hit of people in the open by a falling fragment. The secondary risk is instead associated with the consequences of a debris impact on a building, a shelter, a high risk industrial plant (e.g. chemical, nuclear) or a vehicle (e.g. aircraft, ship, or train). The primary risk can be evaluated following, for instance, the approach described in the previous section, but no easy way to compute the secondary risk is available, also because, in many cases, a very small impact probability is associated with potentially catastrophic consequences. The best strategy, in these situations, would be to take simple and appropriate preventive measures, in order to significantly reduce the adverse consequences of a debris hit. Concerning the sheltering of people on the ground or the protection of high risk industrial plants, attention should be paid to the fragment s capacity to penetrate and seriously damage the structure, to the excess kinetic energy retained by the impactor if penetration occurs, and to the falling structural debris produced by the impact. The same applies, basically, to oceanic ships and low velocity trains, while high velocity trains could also incur in the secondary consequences of a high velocity impact and/or derailment. For airplanes in flight, moving around at several hundreds of kilometers per hour, the problem is quite different, because even the impact with a debris practically at rest in the air could have severe consequences for the passengers on board; in this case, the fragments mass and composition are more important, to assess the risk, than their kinetic energy in the ground reference frame. Cole et al. (1997) have analyzed the probability of fatality due to debris impact on the human body, averaged for different body parts and positions. The kinetic energy threshold for any injury was found to be 15 J, while probabilities of fatality of 1%, 50% and 99% correspond to kinetic energies, respectively, of 29 J, 103 J and 359 J. The survivability study carried out for BeppoSAX (Lips, 2002) has shown that 42 large fragments, with a total mass of about 656 kg, could have reached the ground, with terminal velocities in between 60 and 465 km/h, practically aligned to the local vertical. The corresponding debris footprint on the Earth surface, aligned with the sub-satellite track, should have been approximately 330 km long and 84 km wide. On the basis of the SCARAB simulations (Lips, 2002), all the above mentioned fragments should have impacted the ground in between 37 and 41 minutes after the crossing of the reentry interface, at an altitude of 120 km. Smaller centimeter sized fragments (mass ~ 1 g), not modeled in the destructive analysis, should have continued to rain down in the following 20 minutes, posing a negligible risk on the ground, but representing a potential hazard to the air traffic crossing the reentry air space. The casualty area obtained by SCARAB for all the fragments was m 2, reduced to m 2 (28.80 m 2 ) by neglecting the debris with kinetic energy smaller than 15 J (29 J). The total kinetic energy of the falling fragments was J, equivalent to the energy liberated by the explosion of 558 g of TNT. 5

6 According to the analysis (Lips, 2002), more than 90% of this energy was concentrated in the top nine energetic objects, while the top ten accounted for 91.8% of the total kinetic energy and 83.7% of the surviving mass. All of them should have impacted the ground in between 38 and 39 minutes after the crossing of the reentry interface. 4. Orbit data Typically, the only orbital data generally available for reentry predictions are the Two-Line Elements (TLE), currently distributed by the Space Track Organization, managed by the US Air Force Space Command (Hoots and Roehrich, 1980). The catalog of some 9000 Earth orbiting objects, from active satellites to space debris, some of which may be as small as 10 cm, or less, is maintained by the Space Control Center, operated by the 1 st Space Control Squadron of the 21 st Space Wing (a unit of the Air Force Space Command), and is the product of a massive military space surveillance effort (CAIB, 2003). Therefore, classified objects basically satellites, upper stages and debris linked to certain classes of American secret missions and, more recently, a couple of Japanese reconnaissance spacecraft are not included in the version of the catalog available to commercial and foreign entities. They account for approximately 4% of the catalogued objects. State vector updates are carried out from every few hours to every few weeks, depending upon whether the space object has maneuvered, the type of orbit followed and the level of solar activity, which affects the magnitude of the air drag perturbation in low Earth orbit. A statistical analysis, carried out by the authors during the summer 2003, has shown that approximately 80% of the catalogued objects had a TLE age smaller than 7 days, while between 1/4 and 1/3 of them had a TLE age smaller than 3 days (Anselmo and Pardini, 2003b). However, the orbital elements of high priority objects and satellites approaching the reentry in the atmosphere are updated several times a day, compatibly with orbit geometry and coverage by the network of tracking sensors. Nevertheless, orbit determination gaps of several hours during critical phases cannot be excluded. The TLE accuracy depends upon a number of factors, like the particular tracking sensors used, the amount of data collected, the type of orbit and the conditions of the space environment. Having no other source of orbital information available, it is not possible to estimate such an accuracy, which varies for each element set. It is possible, however, to assess the consistency of the element data sets, i.e. how well the predictions based on one TLE set agree with those of the following or preceding element set. Often the TLE sets for a given object are obtained at irregular intervals and sometime individual two-line elements are inconsistent with the preceding or following data sets, due to processing errors or because the wrong object was tracked. Worse distortions occur when the wrong object is observed for a longer time or when two objects are permanently exchanged. TLE sets are the standard orbit information source used at ISTI (formerly CNUCE) for satellite decay predictions since During the last hours before reentry, the retro-fit of the TLE sets available, carried out with an accurate orbit propagator, gave typically root mean square (rms) semimajor axis residuals of m, but sometime smaller or greater errors were observed. Of course, due to the significantly increased air drag, a fit over the last few hours of orbital lifetime may be characterized by semimajor axis residuals exceeding 1 km. Occasionally, orbital information from other sources is available, provided by the Russian space surveillance network, or by German and/or French radars. In a couple of reentry campaigns, at ISTI/CNR, it was possible to compare American and Russian TLE sets by fitting the orbit data with an accurate trajectory propagator, including the appropriate perturbations. Even adopting different atmospheric density models, the semimajor axis residuals obtained with the Russian TLE sets were systematically lower by 20-30% (Pardini and Anselmo, 2004), but of course no generalization may be drawn from such limited series of comparisons. 5. Residual lifetime estimation The trajectory modeling of uncontrolled satellites close to reentry in the atmosphere is still a challenging activity. Tracking data may be sparse and not particularly accurate, the objects complicate shape and unknown attitude evolution may render difficult the aerodynamic computations and the models 6

7 used to predict the air density at the altitudes of interest, as a function of solar and geomagnetic activity, are still affected by significant uncertainties Uncertainties due to the air drag modeling In principle, numerical special perturbations trajectory propagators are more than adequate to accurately describe the motion of an Earth s satellite, but reentering objects are by definition subjected to heavy air drag. Unfortunately, the atmospheric density affecting the trajectory propagations of a low altitude satellite is affected by two sources of uncertainty: 1. The intrinsic inaccuracies of the semi-empirical atmospheric density models used in astrodynamics; 2. The unavoidable uncertainties of the forecasts of the environmental indexes affecting the density models output (solar flux and geomagnetic activity). A detailed comparison and assessment of the accuracy of some of the most widely used semiempirical atmospheric density models (Jacchia-Roberts 1971 Cappellari et al., 1976; MSIS-86 Hedin, 1987; MSISE-90 Hedin, 1991; TD-88 Sehnal and Pospisilova, 1988) was carried out at ISTI by analyzing the orbital decay of several spherical satellites in the 150-1,500 km altitude range, over a full solar activity cycle (Pardini and Anselmo, 2001a). The drag coefficients, estimated by fitting the observed semimajor axis decay with a high accuracy orbit propagator, were compared with those computed by theoretical analysis. The results obtained have shown that at altitudes in between 150 km and 350 km the maximum errors occurred during low and high solar activity conditions. In periods of low solar activity the atmospheric models tended to overestimate the air density by 10-30%, while around the solar cycle maximum the air density was overestimated by 7-20%. At moderate solar activity, on the other hand, the agreement was much better, with discrepancies, positive or negative, below 10%, and often smaller than 5% (Pardini and Anselmo, 2001a). The difficulty to predict solar and geomagnetic activities, on which the atmospheric density depends, is another important source of uncertainty. In conditions of average solar activity, characterized by a radiation flux at 10.7 cm (F 10.7 ) of 130 standard units (1 standard unit corresponds to Wm 2 Hz 1 ), an error of ±25 standard units in the solar flux prediction translates into an error of approximately ±10% in the air density at the altitude of 200 km. In the last week of satellite lifetime, a significantly more dramatic effect may derive from an unpredicted geomagnetic storm, induced by a massive coronal mass ejection in the Sun. Such events are able to produce a sensible increase of the atmospheric density, which may persist for several hours (up to a few days), causing a sudden acceleration of the orbital decay rate and the consequent reduction of the residual lifetime. The size of the effect is a function of the geomagnetic storm severity and the satellite residual lifetime. For example, the nuclear reactor core (object C) of the satellite Cosmos 1402, at the beginning of 1983, anticipated its reentry by nearly 14 hours in the last 3-4 days of its lifetime, due to a big geomagnetic storm, on February 4-7, characterized by a maximum planetary amplitude of 143 nt (Anselmo and Trumpy, 1986) Solar flux proxies Even though the extreme ultraviolet (EUV) radiation constitutes a minute and quite variable portion of the total solar irradiance, the temperature of the atmosphere above 90 km is mainly dependent on its absorption. However, for the same reason that makes it so important for the heating of the thermosphere, the variable flux of the EUV radiation can be directly measured only with detectors on board of satellites. For this motive, the semi-empirical atmospheric models use a different solar flux proxy, the radio flux at 2800 MHz (F 10.7 ), which was found to be fairly well correlated with the EUV radiation since the sixties. However, the correlation is not perfect and the direct use of EUV measurements might improve the air density modeling. The situation has changed in recent years. Reliable studies and researches have been carried out to produce a solar flux proxy based on a full spectrum model of the EUV solar emissions. The new parameter, E 10.7, has the same units as the commonly used F 10.7 index and can be employed in the existing atmospheric density models in place of the F 10.7 flux (Tobiska, 2001, 2004). E 10.7 is derived from the SOLAR2000 model, 7

8 developed as a scientific collaborative project (Tobiska et al., 2000; Tobiska, 2000) for accurately characterizing the solar irradiance variability across the spectrum. The overarching scientific goal of SOLAR2000 is to understand how the Sun varies spectrally and through time from X-ray to infrared wavelengths. An extensive comparison of the performances of E 10.7 and F 10.7 in some of the atmospheric models most used in astrodynamics computations has been carried out at ISTI (Pardini et al., 2004), thanks to the historical E 10.7 values provided by the Space Environment Technologies (SET) SpaceWx Division, in Los Angeles (SET, 2004). Using E 10.7 instead of F 10.7, the trajectory fits of spherical satellites at low altitudes typically resulted in lower drag coefficients, and correspondingly higher air densities, in nearly all conditions of solar activity. The differences observed are of the order of 5-10%, but this bias between the two solar flux proxies has no influence on the trajectory modeling, because it is compensated by the appropriate value of the drag coefficient, treated as solve for parameter in the orbital decay fit. However, the fits obtained using E 10.7 are systematically characterized by smaller semimajor axis root mean square residuals, by as much as 30-50% in certain cases, and this might result in better trajectory predictions, with the models using E 10.7 evidently able to more effectively describe the air density changes due to a varying EUV flux Ballistic parameter Unfortunately, the risk satellites for which reentry predictions are generally carried out are never spherical, often displaying instead a very complicated shape and structure. Moreover, abandoned objects may have a varying attitude, along the orbit or during different phases of the decay, making not trivial the finding of an appropriate ballistic parameter B, to be used for trajectory predictions and defined as follows: A B = CD, (10) M where C D, M and A are, respectively, the satellite drag coefficient, mass and average cross-sectional area in the direction of the air flux. For a given satellite and during different phases of the final decay, the variation of the ballistic parameter may be quite significant, contributing to the reentry prediction uncertainty by an amount comparable, or even larger, than that expected from the other error sources discussed in the preceding subsections. For example, after the satellite deactivation, at the end of April 2002, the monthly averages of the ballistic parameter obtained for BeppoSAX (Figure 1) displayed variations of up to 25% with respect to the global mean computed until the reentry, at the end of April During the last month of orbital lifetime, the weekly averages of B showed a maximum excursion of 8% with respect to the mean value. In the last week the maximum difference between the weekly and 24-hour averages of B was 7%, but on shorter intervals of time (~ 12 hours) that difference exceeded 30% (Anselmo and Pardini, 2003a). 6. Reentry and risk windows As discussed in Section 5, reentry predictions are affected by significant uncertainties. For this reason, reentry uncertainty windows should be associated with any prediction. However, their estimation is not easy and the numerical values adopted are based, mainly, on past experience. In order to estimate the intrinsic accuracy of satellite reentry predictions, disregarding the uncertainties of solar flux and geomagnetic activity forecasts, the residual lifetime errors of eleven spacecraft and five rocket bodies, covering a broad range of inclinations and decaying from orbit in a period of high solar activity, were determined by the authors for predictions computed approximately one month, one week and one day before reentry (Pardini and Anselmo, 2003). For the most widely used atmospheric models, average residual lifetime errors smaller than 14% were found on estimations obtained one month before orbital decay, but in one case the error was significantly higher than 20%. One week before reentry the average residual lifetime errors were smaller than 10%, with one case slightly above 20%. The same applied to predictions computed one day before reentry (Pardini and Anselmo, 2003). Including the uncertainties of solar flux and geomagnetic activity forecasts, the experience has shown that reentry window amplitudes in between ±15% and ±25% of the residual lifetime may be adequate 8

9 in 90% of the cases, depending on satellite characteristics, decay phase, solar activity level and atmospheric model. Residual lifetime errors well in excess of 30% cannot be completely avoided, however, due to unpredicted geomagnetic storms in the last few days of flight or to ballistic parameter and atmospheric density mismodeling in the hours preceding the reentry (Anselmo and Trumpy, 1986; Pardini and Anselmo, 2001b, 2003; Anselmo and Pardini, 2003a). In absolute terms (days, hours or minutes), the amplitude of a reentry uncertainty window depends, obviously, on how far away from reentry is the epoch of the last reliable state vector available. For instance, assuming a residual lifetime uncertainty of ±15%, a TLE set referring to 6 hours before reentry would reduce the final uncertainty on the predicted reentry time to about ±55 minutes, corresponding to more than one full orbital ground track for a low Earth satellite in circular orbit. An orbit determination as close as possible to the reentry time is therefore desirable, but unfortunately there is an unavoidable delay, up to a few hours, between the orbit solution epoch and the public distribution of the results, and often the very last orbit determinations can only be used for post-reentry assessments. Moreover, in certain cases there may be for diverse reasons quite long orbital data gaps (8-12 hours) just before reentry, leaving the final uncertainty window very wide (corresponding to 2-3 full orbital ground tracks for a low Earth satellite in circular orbit). The amplitude of the final reentry uncertainty window has a substantial influence on the amount and quality of the data that may be provided to the competent civil protection authorities for the prevention, control or reduction of the reentry risk. In any case, the final window typically includes a few orbital ground tracks (hopefully just one), with an associated risk swath of ± km, which is satellite specific. Depending on the particular event, the debris impact area extends along the predicted ground track, by a few hundred up to a few thousand kilometers, with the light pieces preferentially falling at the heel and the heavy ones concentrated at the toe of the footprint (the detailed distribution depends on the fragmentation sequence). Even though the final reentry uncertainty window is in practice quite more spatially extended along-track, the possible impact time of the fragments at a given sub-satellite location may be computed with reasonable accuracy. This allows, for any sub-satellite location included in the reentry window, to define a risk time window. In other words, for each sub-satellite location included in the reentry window, debris impact is possible, but not certain; however, the eventual impact may occur only during a specific risk time window, which can be therefore used to plan risk mitigation measures on the ground and in the overhead airspace. For the BeppoSAX reentry, the risk time window amplitude adopted (40 minutes) took into account the uncertainty on the time of ground impact of the main objects (±10 minutes) and the time needed for the small centimeter sized particulate, eventually produced by the event, to rain down through the affected airspace (+20 minutes). Accordingly, the risk time window for a specific location along the sub-satellite track included in the final reentry window was defined as follows (Anselmo, 2003): Risk Time Window = Predicted Main Object Impact Time + 30min. (11) 10min 8. Conclusions The reentry of artificial satellites in the atmosphere is a natural consequence of space activities. So far the risk represented by such events was quite small, but the situation may change in the future, due to the launch of larger spacecraft and upper stages, due to the growth of population density and populated areas, due to the increase of end-of-life de-orbiting or re-orbiting at lower altitude as orbital debris mitigation measure and, possibly, due to a broader use of materials able to withstand the harsh reentry conditions. The individual risk associated with satellite reentries will remain, all considered, extremely low, if compared with the fatality rate due other causes commonly accepted in everyday life, but the global collective risk cannot be completely ignored, due to the disproportionate and adverse impact of space accidents on the public. In fact, for historical reasons deeply rooted in the mythology and sociology of the Space Race, the public and the politicians expect much higher safety standards in the space sector compared to other fields of activity, making a balanced technical approach to safety concerns not always possible. Taking into account both technical and political aspects, a casualty expectancy of 10-4 per reentry event is generally considered a reasonable risk threshold compromise: if exceeded, it can be used to justify a controlled de-orbiting at the end-of-life (e.g. Compton Gamma Ray Observatory), the issuing of an 9

10 international alert and the adoption of preventive measures (e.g. BeppoSAX), or the introduction of design changes to minimize the reentry survivability of satellite components (e.g. GLAST). However, casualty expectancy estimations are far from straightforward, depending on a combination of several basic and often simplistic assumptions and very complex destructive analyses, carried out with specialized computer codes. In any case, the reentry predictions of uncontrolled satellites able to disseminate debris on the ground will become more and more important in the coming years. They are and will remain affected by some unavoidable uncertainties, and then critical aspects of this activity will continue to be the careful management of such uncertainties and the release of suitable information to the authorities and the public. As an example, the strategy adopted for the BeppoSAX uncontrolled reentry, when Italy decided to provide detailed and updated information to the countries overflown by the satellite, to the relevant international organizations and to the public at large (Salotti et al., 2003), was extremely useful to avoid potential misunderstandings and unjustified alarm. At the same time, it was possible to plan risk prevention measures and quick reactions to any eventual substantiated claim. Such experience was very valuable and might be helpful to manage similar cases in the future. References Ahmed, M., Mangus, D., Burch, P. Risk management approach for de-orbiting of the Compton Gamma Ray Observatory, in: Sawaya-Lacoste, H. (Ed.), Proceedings of the Third European Conference on Space Debris. ESA SP-473, Volume 2, Noordwijk, The Netherlands, pp , Anselmo, L., Risk Analysis and Management of the BeppoSAX Reentry, ISTI Technical Report 2003-TR- 23, Pisa, Italy, 5 March Anselmo, L., Pardini, C. BeppoSAX Reentry Campaign Final Report. ISTI Technical Report 2003-TR-24, Pisa, Italy, 21 May 2003(a). Anselmo, L., Pardini, C. TerraSAR-X Orbital Debris Assessment. ISTI Technical Report 2003-TR-70, Pisa, Italy, 29 October 2003(b). Anselmo, L., Trumpy, S. Short-term predictions of Cosmos 1402 reentry. The Journal of the Astronautical Sciences 34, , Anonymous. NASA Safety Standard: Guidelines and Assessment Procedures for Limiting Orbital Debris. NSS , Washington, D.C., USA, August Anonymous. PAM-D debris falls in Saudi Arabia. The Orbital Debris Quarterly News 6, Issue 2, p. 1, April Anonymous. Meteorites: (another) underestimated accumulation risk? In: Munich Re Topics 2001, 9 th Year. Münchener Rück, Munich Re Group, Munich, Germany, pp , Anonymous. Rocket body debris falls in Argentina. The Orbital Debris Quarterly News 8, Issue 2, p. 1, April Anselmo, L., Bertotti, B., Farinella, P. Detriti Spaziali: Un fattore di rischio che incombe sul futuro delle attività in orbita. Chapter 5, CUEN, Naples, Italy, Atkinson, H., Tickell, C., Williams, D., Tremayne-Smith, R. Report of the Task Force on Potentially Hazardous Near Earth Objects. London, United Kingdom, p. 40, September Botha, W. Orbital debris: a case study of an impact event in South Africa, in: Sawaya-Lacoste, H. (Ed.), Proceedings of the Third European Conference on Space Debris. ESA SP-473, Volume 2, Noordwijk, The Netherlands, pp , Bouslog, S., Wang, K., Ross, B., Madden, C. Reentry Survivability and Risk Analysis, NASA JSC-27232, Houston, Texas, USA, September CAIB (Columbia Accident Investigation Board). Report Volume I. Government Printing Office, Washington, D.C., USA, p. 63, August Cappellari, J.O., Velez, C.E., Fuchs, A.J. (eds.). Mathematical Theory of the Goddard Trajectory Determination System. NASA/GSFC Report, GSFC X , Greenbelt, Maryland, USA, Cole, J.K., Young, L.W., Jordan-Culler, T. Hazards of Falling Debris to People, Aircraft, and Watercraft, Sandia Report, SAND UC-706, Sandia National Laboratories, Albuquerque, New Mexico, USA,

11 CORDS (Center for Orbital and Reentry Debris Studies). Spacecraft reentry breakup overview and FAQs. The Aerospace Corporation, El Segundo, California, USA, Foschini, L. On radar measurements of the terrestrial mass accretion rate of meteoroids. Il Nuovo Cimento 20 C, , Fritsche, B., Koppenwallner, G., Ivanov, M., Kashkovsky, A., Grinberg, O., Boriskin, O. Advanced Model for Spacecraft Disintegration During Atmospheric Re-entry, Executive Summary. ESOC Contract No /98/D/IM, Katlenburg-Lindau, Germany, Hartmann, W.K. Moons and Planets, Third Edition. Wadsworth Publishing Company, Belmont, California, USA, pp , Hedin, A.E. MSIS-86 thermospheric model. Journal of Geophysical Research 92, , Hedin, A.E. Extension of the MSIS thermosphere model into the middle and lower atmosphere. Journal of Geophysical Research 96, , Hoots, F.R., Roehrich, R.L. Models for Propagation of NORAD Elements Sets. Spacetrack Report No. 3, Project Spacetrack, Aerospace Defense Command, United States Air Force, Colorado Springs, Colorado, USA, December Kato, A. Study for IADC Re-entry Safety Assessment Procedure. NASDA-CRE01004, Tsukuba, Japan, 9 March Klinkrad, H. (ed.), ESA Space Debris Mitigation Handbook, Second Edition, ESA/ESOC, Darmstadt, Germany, Chapter 9, Lips, T., BeppoSAX Re-entry Analysis with SCARAB. HTG-Report-02-8, Revision 1.0, Katlenburg-Lindau, Germany, 30 September Love, S.G., Brownlee, D.E. A direct measurement of the terrestrial mass accretion rate of cosmic dust. Science 262, , Montgomery, R.M., Ward Jr., J.A. Casualty Areas from Impacting Inert Debris for People in the Open. RTI Report No. RTI/5180/60-31F, Cocoa Beach, Florida, USA, 13 April Ortiz, J.L., Aceituno, F.J., Aceituno, J. A search for meteoritic flashes on the Moon. Astronomy and Astrophysics 343, L57-L60, Pardini, C., Anselmo, L. Comparison and accuracy assessment of semi-empirical atmosphere models through the orbital decay of spherical satellites. The Journal of the Astronautical Sciences 49, , 2001(a). Pardini, C., Anselmo, L. Re-entry predictions in support of the Inter-Agency Space Debris Co-ordination Committee test campaigns, in: Sawaya-Lacoste, H. (Ed.), Proceedings of the Third European Conference on Space Debris. ESA SP-473, Volume 2, Noordwijk, The Netherlands, pp , 2001(b). Pardini, C., Anselmo, L. Performance evaluation of atmospheric density models for satellite reentry predictions with high solar activity levels. Transactions of The Japan Society for Aeronautical and Space Sciences 46, 42-46, Pardini, C., Anselmo, L. On the accuracy of satellite reentry predictions. Advances in Space Research 34, , Pardini, C., Tobiska, W.K., Anselmo, L. Analysis of the orbital decay of spherical satellites using different solar flux proxies and atmospheric density models. Advances in Space Research, Digital Object Identifier (DOI) /j.asr , Rochelle, W.C., Kirk, B.S., Ting, B.C. User s Guide for Object Reentry Survival Analysis Tool (ORSAT), Version 5.0. Volumes I and II, NASA JSC-28742, Houston, Texas, USA, July Rochelle, W.C., Marichalar, J.J., Reentry survivability analysis of the Upper Atmosphere Research Satellite (UARS). The Orbital Debris Quarterly News 7, Issue 2, pp. 2-3, April Salotti, L., et al. BeppoSAX Reentry. Agenzia Spaziale Italiana (ASI), Rome, Italy, Sehnal, L., Pospisilova, L. Thermospheric Model TD 88. Preprint No. 67, Astronomical Institute, Czechoslovak Academy of Sciences, Prague, Czechoslovakia, SET (Space Environment Technologies). Los Angeles, California, USA, Smith, P.G. Expected Casualty Calculations for Commercial Space Launch and Reentry Missions. Advisory Circular No , Draft, Federal Aviation Administration, Washington, D.C., USA, 12 April Smith, R., Dobarco-Otero, J., Rochelle, W.C. Reentry survivability analysis of Gamma-ray Large Area Space Telescope (GLAST) satellite. The Orbital Debris Quarterly News 8, Issue 2, p. 6, April 2004(a). 11

12 Smith, R., Dobarco-Otero, J., Marichalar, J., Rochelle, W.C. Reentry survivability analysis of the Tropical Rainfall Measuring Mission (TRMM) spacecraft. The Orbital Debris Quarterly News 8, Issue 1, pp. 4-5, January 2004(b). Tobiska, W.K. Status of the SOLAR2000 solar irradiance model. Phys. Chem. Earth 25, , Tobiska, W.K. Validating the solar EUV proxy, E10.7. Journal of Geophysical Research 106, A12, , Tobiska, W.K. Second generation space environment forecasting for satellite and ground system operations. Paper AIAA , 42 nd AIAA Aerospace Sciences Meeting, Reno Nevada, USA, January 5-8, Tobiska, W.K, Woods, T., Eparvier, F., Viereck, R., Floyd, L., Bouwer, D., Rottman, G., White, O.R. The SOLAR2000 empirical solar irradiance model and forecast tool. Journal of Atmospheric and Solar- Terrestrial Physics 62, , United Nations. Convention on International Liability for Damage Caused by Space Objects ( Approved by the General Assembly in 1971 (resolution 2777 (XVI)), entered into force in September

13 Tables Table 1 BeppoSAX Reentry Probability and Average Casualty Expectancy as a Function of Latitude Latitude Belt Reentry Probability Casualty Expectancy 3 4 N N N N S S S S Table 2 BeppoSAX Reentry: Casualty Probability for People in the Open Number of Victims Probability

14 Figure 1. Evolution (monthly averages) of the ballistic parameter (B = C D A/M) of the BeppoSAX satellite from deactivation to reentry. 14