RE-ENTRY PREDICTION AND ON-GROUND RISK ASSESSMENT

H. Klinkrad

Of more than 28,000 Earth orbiting objects which USSPACECOM has tracked since 1957, some 19,000 have re-entered into the atmosphere by the year 2004. Most of these objects disintegrated and burnt up, posing only a minor risk on ground. In 2004 the number of unclassified, correlated objects in the USSPACECOM catalog was on the order of 9,000. Due to the limited sensor sensitivities, all of these objects have diameters larger than 10 to 30 cm. Out of the catalog population, about 1 object re-enters each day, and 1 to 2 objects with a radar cross-section (RCS) larger than 1 m² re-enter each week. The latter ones, which have a radius of about 1 m, have an increased survival potential, and they are generally followed more closely by USSPACECOM until their final entry.

At rates of one in several years orbital structures re-enter, which have geometric cross- sections of 100 m² or more, and masses of several 10 tons. Such spacecraft can be classified as high-risk objects, since they produce a significant mass percentage of break-up fragments which can withstand the aerothermal heat flux and structural loads during re-entry, and which can generate ground impacts with significant risk levels to the population within the debris swath. Theoretical analyses and object retrievals suggest that 10% to 40% of the mass of a large spacecraft can survive to ground impact. Historic examples of this category were the re- entries of Skylab (on 11-Jul-1979, with a mass of 74t), and Salyut-7 (on 07-Feb-1991, with a mass of 40t). The latest, most massive object in space history to re-enter was Mir (on 23-Mar- 2001, with a mass of 135 t). The decays of these large space structures will be used to analyze results of ESA's re-entry risk analysis methods. In early 2005 ESA will distribute the DRAMA software (Debris Risk Assessment and Mitigation Analysis). It also assesses re- entry survivability and on-ground risk, in support of ESA's Space Debris Mitigation Handbook and future European Debris Mitigation Standards. A preview of this software will be provided.

To monitor and forecast the long- to medium term evolution of an uncontrolled re-entry over periods of several years to a few weeks of the remaining lifetime, computationally efficient yet sufficiently accurate methods must be applied. For this purpose ESA uses a program called FOCUS-2. It integrates the combined time rates of change of singly averaged perturbations equations, taking into account a non-spherical Earth gravity potential, a dynamic Earth atmosphere, luni-solar gravity perturbations, and solar radiation pressure in combination with an oblate, cylindrical Earth shadow. The integration is performed by a robust 4th order Adams-Bashforth/Adams-Moulton predictor/corrector method, which is initiated by a self- starting 4th order Runge-Kutta-Fehlberg method, using fixed time steps of typically 0.1 to 5 orbits, depending on the time to go until reentry.

Perturbations from the Earth gravity potential are expressed in terms of the Lagrange equations for a truncated EGM-96 gravity model up to degree n ≤ 23 and order m ≤ n. To compute the derivatives of the Earth's gravity potential, the spherical harmonics are developed in recursively computed expansions, using inclination functions and eccentricity functions according to [7]. The infinite expansions in eccentricities reduce to finite summations after the analytical averaging operation with respect to mean anomaly M. A second order Earth oblateness perturbation term (J2)², adopted from [12], is superimposed on the results. Third body effects are computed for point masses of the Sun and Moon, applying analytical ephemerides. Again, the Lagrange equations are used, with recursive expansions of the perturbing third body potential in inclination and eccentricity functions according to [3]. As for the geopotential, the perturbation equations are averaged with respect to the mean anomaly, maintaining the positions of Sun and Moon constant over the averaging time interval of one orbit. The direct solar radiation pressure perturbations are determined with Aksnes' theory [1] for a given area-to-mass ratio A/m and momentum exchange coefficient CR. The perturbation equations are averaged in a closed form over the illuminated orbit arc, taking into account an oblate, cylindrical Earth shadow.

The main effort in the FOCUS-2 perturbation model is concentrated on the aerodynamic drag effects. They are computed from the Gauss perturbation equations, which are expressed in terms of first order (J2) osculating elements, with the perturbing acceleration p and its components p_a,U, p_a,V, and p_a,W in the radial, transversal, and out-of-plane direction. First order velocity corrections due to short periodic Earth oblateness effects are accounted for, and optional East and North wind components are provided by a horizontal wind model [6], which is superimposed on the Earth rotation rate. Local air densities are determined with the MSISe- 90 model [5], based on observed and predicted solar and geomagnetic activity proxies F10.7, F10.7, and A_p.

In spite of several decades of research effort, the model accuracy for total densities is in general on the order of Δρ1_σ ≈ 15%, even for perfectly known input parameters. In phases of extreme solar or geomagnetic activities local density errors can temporarily exceed 100%. Even at mean activity levels differences between individual thermosphere models can be appreciable. This is particularly so at low altitudes of 120 km ≤ z ≤ 200 km, when comparing drag based models (e.g. CIRA-72), which integrate the diffusion equations for empirical temperature profiles, with mass-spectrometer based models (e.g. MSIS-86), which use analytical approximations of the diffusion and temperature profiles. In the course of the MSIS model developments the analytical profiles were adjusted to provide best fits at altitudes where most of the in-situ measurement data are concentrated. Since the shapes of the density profiles are fixed according to analytical expressions, the good fit at higher altitudes is achieved at the expense of larger model errors at low altitudes, where in-situ measurement data are sparse. As a consequence, the differences between CIRA-72 and MSIS-86 at low altitudes can reach 30% to 40%. From monitoring re-entry events one can conclude that drag based models (e.g. CIRA-72 or GOST-85) are mostly superior in accuracy at low thermospheric altitudes, and should get preference for final orbital decay predictions. The advantages of both model types (drag based at low altitudes and mass-spectrometry based at higher altitudes) can be combined in a hybrid model, for instance by an overlay of MSISe-90 and CIRA-72 density profiles, with altitude dependent weighting.

      (1)

According to Eq. 1 the MSISe-90 model is used above 200 km and below 90 km, the CIRA-72 model is used near 120 km (homopause), and a smooth fairing between the two density profiles is used at intermediate altitudes.

The mean rates of change due to aerodynamic drag x_d,i = a∙d, ..., M∙d, are determined by means of a 21-point Gauss-Legendre quadrature according to Eq. 2, based on the drag perturbation equations, expressed in osculating elements x = (x₁, ..., x₆), with drag perturbations p = (p_u, p_v, p_w) in an orbit oriented coordinate system.

      (2)

In the case of uncontrolled, natural re-entries, mainly due to aerodynamic drag, the orbital evolution of an object can only be monitored, with no or only limited possibilities to control the risk. Based on an observation and orbit determination history, solar and geomagnetic activity forecasts, and assumptions on the attitude dynamics, the re-entry time of a spacecraft can be predicted with typical accuracies of ±10% to ±20% of the remaining orbital lifetime. If no detailed results of a break-up analysis are available, one may assume that, depending on the entry angle and breakup altitude, the final ground dispersion of fragments can extend over more than ±2000 km along track and ±80 km cross track. Prior to the entry, the along track spread is governed by a ±20% uncertainty in the predicted re-entry epoch. The cross track extension of ±80 km remains almost unaffected, though the reference ground track drifts according to the altitude decay history. Based on the analysis of 15 historic re-entry events, we shall assume that the 2σ extension of the fragment dispersion area on ground is an ellipse, which is symmetric to the predicted COIW location (center of impact window), both in the along and cross track direction. The resulting probabilities of an impact within a 1σ, 2σ, and 3σ ellipse and rectangle are listed in Tab.1.

Table 1. Integrated impact probability for elliptic and rectangular fragment dispersion areas of 1σ, 2σ, and 3σ extensions along track and cross track.

impact probability	1σ	2σ	3σ
elliptic corridor	0.3935	0.8647	0.9889
rectangular corridor	0.4661	0.9111	0.9999

One of the key issues in re-entry risk analysis is the identification of components of a spacecraft which are likely to survive the deceleration and heating peaks following a break-up event at altitudes of typically 75 to 80 km. Simulations predict that certain materials (e.g. stainless steel and titanium), and certain shapes (e.g. tanks) have a high potential of re-entry survival, particularly if high melting temperatures are combined with low area-to-mass ratios. The retrieval of such objects at several re-entry sites has supported these assumptions (e.g. Delta-2 stainless steel tanks of 250 kg mass, and Titanium spheres of 30 kg mass which were retrieved in Texas on 22 Jan 1997, and in the Cape Province of South Africa on 27 Apr 2000).

To predict the survival or demise of a re-entering object is a very complex exercise, in particular for complex spacecraft shapes with appendices and heterogeneous material compositions. In the most general case, a detailed computer model is necessary to define the spacecraft geometry, for a wide spectrum of material properties, and for the whole temperature range which is experienced during a re-entry. Based on initial orbit and attitude conditions at a given epoch the 6 degrees of freedom (DoF for orbit and attitude), or 3 DoF dynamic state equations (orbit only) can then be propagated to the first break-up event. During this propagation, the aerodynamic and aerothermal state are continuously adjusted for changing flight regimes, and the resulting heat flux is entered into the thermal analysis which establishes the temperatures inside the spacecraft and on its surface, in order to adjust temperature dependent material properties, and to initiate ablative mass loss, where applicable. Corresponding changes in shape and mass properties of the spacecraft are dynamically accounted for, and they are fed back into the mass and inertias. This concept is implemented in ESA's SCARAB software [4] for 6 DoF, and in NASA's ORSAT [2] and ESA's DRAMA code [10] for 3 DoF dynamics.

Table 2. Material properties relevant for re- entry survivability analysis (density ρ, specific heat cp at constant pressure, melting temperature Tm, and heat of melting qm). Material ρ [kg/m3] cp [J/kgK] Tm [K] qm [J/g] Ti 4420 750.0 1900 400 St. Steel 8030 611.5 1650 274 Inconel 8190 417.1 1570 309 Cu 8960 434.1 1356 243 Al 2800 751.1 870 385

Table 3. Analytical demise ranges of solid spheres, re-entering from He = 200 km with Ve = 7.8 km/s at γe = 2.5° (dmin, num shows numerical results). Material demise range d[mm] dmin (dmin,num) → dmax Ti 1.71 (2.43) → 29.0 St. Steel 0.62 (0.76) → 39.0 Inconel 0.17 (0.21) → 52.0 Cu 0.15 (0.19) → 62.0 Al 0.05 (0.07) → 88.0

For simple shapes of given material properties (see Tab.2), and for 3 DoF flight dynamics (no attitude propagation), results of different re-entry prediction tools can be validated analytically, or against independent numerical tools. For such simple bodies, thermal disintegration only may be considered, where for each volume element (voxel) the heat balance from convective, conductive, and radiative heat inputs and outputs is determined. Depending on the temperature level reached, two cases can be distinguished:

      (3)

      (4)

In eq.3 and 4, Q^• is the heat storage (Q^• > 0), or heat loss (Q^• < 0), T is temperature of the voxel, V is volume of the voxel, ρ is the density of the material, c_p is the heat capacity at constant pressure, q_m is the heat of melting (melting enthalpy), and T_m is the melting temperature.

Starting at typical initial conditions of a natural re-entry (e.g. altitude H_e = 200 km, velocity V_e = 7.8 km/s, and flight path angle γ_e = 2.5°), the integral heat flux during the free-molecular and continuum laminar flow regimes can be integrated along the trajectory. The re-radiation from the body surface may be considered according to , where T_eq is the equilibrium surface temperature, assuming a perfectly heat conducting material, and solid objects of simple geometric shapes. A complete demise is assumed, if the equilibrium temperature T_eq at the time of peak heat flux exceeds the melting temperature T_m. Based on an exponential atmosphere the peak heat flux q^•_max can be approximated analytically, for initial entry conditions, and object properties [11]. One can thus obtain the demise altitude as a function of the size, shape, and material. Such analytical results compare well with numerical verification outputs produced by ESA's numerical SCARAB software (see Tab.3).

One can show [11, 10] that in free-molecular flow the demise condition is not dependent on body size, whereas in laminar continuum conditions it is. All other dependencies on ambient conditions, trajectory, and material remain unaffected. Fig.1 shows the result of a numerical computation of demise altitudes of solid spheres as a function of object diameter and material. The curves indicate that below a certain minimum diameter d < d_min and above a certain maximum diameter d > d_max the objects tend to survive the re-entry. For d < d_min this is due to the low area-to-mass ratio (since ), and due to the resulting early deceleration at high altitudes, with free-molecular heating, and with good re-radiation capabilities (since the ratio re-radiation to heat storage goes with ). In case of large objects, where d > d_max, the altitude of peak heat flux is lowered into the laminar flow regime. In this case, the increased heat storage capacity (which goes with ) and the reduced integrated heat flux allows the object to survive. In general, Titanium has the best survival potential, followed by stainless steel, Inconel, and Copper. Due to its low melting temperature and poor re- radiation capability Aluminium has the lowest probability of survival. In case of solid, simple bodies, the survival potential is to a lesser degree affected by the object shape (see Fig.2). Even for a critical case (i.e. Titanium spheres), it is evident from Fig.1, that objects in the size regime between 5 mm and 2 cm do not survive the re-entry, and they will hence not contribute to the effective casualty cross-section at ground impact. This is an important finding, since most screws, nuts, and bolts used in spacecraft and rocket manufacturing fall into this domain. For the terminal velocity of solid spheres at ground impact the proportionality holds. Hence, the small survivor objects with d < d_min tend to carry a low risk potential due to their very low impact velocities ("rain down" effect). Re-entry objects which have sizes beyond the maximum demise diameter need to be analyzed with more sophisticated numerical tools, such as ESA's DRAMA or SCARAB software [4, 10].

Fig. 3. World population density (1° x 1° cells). The small circle of latitude average of land cover (in %), and of the mean and maximum population density (in 1/km²) is given to the right.

In order to assess the on-ground risk due to surviving debris of a single re-entry event, the NASA safety standard NSS 1740.14 [13] introduces an equivalent casualty cross-section A_c, which is composed of the cross-sections A_i of individual fragments, with each of them augmented by a projected human risk cross-section of A_h = 0.36m² (corresponding to r_h = 0.33 m). When assuming a vertical fall with an immediate rest upon impact, then the resulting effective cross-section for the i-th fragment is a circle of radius r_ci = r_i + r_h which circumscribes two touching circles of areas A_i = πr_i² and A_h = πr_h². The total casualty cross-section is then determined by a summation over all n survivor fragments of a re-entry event.

      (5)

The quantity A_c is a simple, yet very efficient way to concentrate the entire knowledge on the breakup process of a re-entering spacecraft into a single figure. It allows a spacecraft manufacturer to provide a means for a reliable re-entry risk assessment without disclosing sensitive information on construction details. The individual contributions to the casualty cross-section can be adjusted for the ground impact incident angle, for a re-bounce or slide on the surface, and for splatter by fragmentation and radial ejection upon ground impact. A theoretical analysis of Delta II survivor fragments indicated possible increases of the effective area A_c by a factor of 1.9 to 4.8, depending on soft or hard ground surfaces.

Population density maps with sufficient spatial resolution are necessary to associate the impact of re-entry survivor objects with a casualty risk in the affected groundtrack swath. Fig.3 shows a world map of 1° x 1° mean population densities, derived from 5' x 5' (9.25km x 9.25km) high resolution data of the Global Demography Project [15]. These population data for the year 1994 are supported by discretized maps of land masses. The total world population in 1994 was 5.63×10⁺⁹, distributed over a total land surface of 1.48×10⁺⁸ km², which accounts for 28.97% of the surface of the Earth reference ellipsoid. This corresponds to a global mean population density of 11.0/km², and to a mean land population density of 38.1/km². By the year 2000, the world population had reached 6.23×10⁺⁹. This value is predicted to double within the next 40 years.

Table 4. Land impact probability Pl, and casualty probability P_c, as a function of the orbit inclination (averaged over one orbit groundtrack, for a casualty cross-section of 10 m², in the year 2000).

The histograms on the right hand side of Fig.3 give the small circle of latitude averages of land cover (in %) and average population density (per km²), plus the maximum density in each latitude band of 1° width. An imbalance between the northern and southern hemisphere becomes evident from these charts. In fact, only 11.7% of the world population, and only 33.3% of the land masses are located south of the equator. This has a direct impact on an equally imbalanced risk distribution between the hemispheres, with a much higher risk of re- entry casualties at northern latitudes. A re-entry which occurs on the northern hemisphere carries a 1.75 times larger risk than a global mean event. The corresponding risk for a re-entry in the southern hemisphere is by a factor of 1/4.30 lower. This result is directly related to the corresponding mean population densities which are 12.3/km² for the whole world, 21.6/km² for the northern hemisphere, and 2.9/km² for the southern hemisphere (for the year 2000).

The probability P_i(φ) that an uncontrolled re-entry from a near circular orbit of inclination i occurs in a certain latitude band at φ ≤ i can be assessed by means of analytical equations [8], assuming that for long-term risk forecasts the impact probability distribution in geographic longitude λ is uniform, and the orbital inclination remains stable. Analytical results of P_i(φ) match well with a corresponding graphs in Fig.4, which were produced by numerical quadrature. Tab.4 summarizes results of land impact probability Pl and casualty probability P_c for inclinations of 7.0° (e.g. Beppo-SAX), 28.5° (e.g. Shuttle payloads), and 51.6° (e.g. Skylab, Salyut-7, Mir), 65.0° (e.g. Cosmos 954 and 1402), and 98.5° (Sun-synchronous orbits), for a latitude bin width of Δφ = 0.5°. In order to link ground impact probability with local land coverage and population density, single orbit arcs were produced in steps of argument of true latitude of Δu = 1°, and in steps of geographic longitude of ascending node of Δλ_n = 1° (for λ_n є [ 180°, +180°]). For each orbit arc the underlying maps of land masses and population densities were sampled, weighted with the resident probabilities, and assigned to bins of latitude φ (for Fig.5), bins of nodal longitude λ_n (for Fig.6), and (u,λ_n)-bins (for Fig.7).

Fig. 4. Impact probability for orbit inclinations of i = 7.0° (dolled), 28.8° (dashed), and 51.6° (solid line), as a function of geodetic latitude.

According to Fig.4, the highest impact probability P_i(φ) can be expected close to the extreme latitudes, where φ ≈ ±i. Since the integral value over all latitude bands is 1 by definition, the peak probability of P_i(φ) increases with decreasing inclination. After weighting of P_i with underlying land masses, the resulting land impact probability P_l shows a strong latitude asymmetry, as could be expected from Fig.3. This imbalance towards the northern hemisphere is further emphasized after weighting of P_i with local population densities to obtain a casualty probability P_c. Tab.4 summarizes the global land impact probabilities P_l and casualty probabilities P_с for orbits of different inclinations (for an assumed spacecraft casualty cross-section of A_c = 10 m², and for the year 2000). The highest land impact probability is noted for i = 98.5°, while the largest mean casualty risk is encountered on orbits of i = 28.5°.

Fig. 7. Skylab, Salyut-7, and Mir re-entry groundtracks on a world population density map, for a common inclination of 51°, as a function of geographic longitude of the ascending node λ_n, and of the orbit position (argument of true latitude u). The argument of true latitude average of land cover (in %), and mean and max. population density (per km²) is given to the left.

When the predicted orbital lifetime of an uncontrolled re-entry drops below a few days, a more detailed risk assessment should be performed. In this case, the drift corrected ground impact corridor (e.g. of 2σ extension ±80 km cross track and ±2,000 km along track) needs to be analyzed with the proper weighting by a 2D impact probability density function (PDF). Such a PDF distribution may be obtained from a detailed analysis (e.g. by SCARAB) of a disintegration process, and of the resulting survivor fragments. Their dispersion on ground can be obtained by a variation of angle of attack and bank angle. A subsequent weighting of the determined impact locations with probabilities of occurrence of the aerodynamic assumptions leads to a probability density function PDF_j(λ, φ) for the j-th ground impactor. In the case of no fragmentations, or in case only the global casualty cross-section A_c of the event is known, PDF(λ, φ) may be approximated by a 2D Gaussian distribution PDF_nσ(s_x,s_y) in long track direction s_x, and cross track direction s_y (centered at the predicted impact location), with corresponding nσ variances. For the subsequent analysis, a 2σ distribution shall be assumed, with properties as shown in Tab.1. A detailed on-ground risk analysis can be performed by quadrature of the 2-dimensional, 2σ probability density integrals via finite summations. One obtains the following results for the impact probability P_i,2σ, the land impact probability P_l,2σ, and the probability of population casualties P_с,2σ for a given re-entry event [8].

      (6)

      (7)

      (8)

Here, the local impact probability is defined as

      (9)

(f_l)_n,m is the fraction of land coverage, and (ρ_p)_n,m is the average population density in the sampled ground swath area bin. A_c is the spacecraft specific casualty cross-section, which shall be adopted to be constant at 10m² for all risk calculations within this paper (NASA guidelines require that A_c ≤ 8m² for all uncontrolled re-entries). In case of a fragment-wise analysis, eq.7 and eq.8 would have another outer summation over all survivor fragments.

A casualty probability of P_c < 1:10,000 per entry event is a figure which is proposed by NASA and which is also proposed (but not yet endorsed) for ESA projects. This number appears to be an analytically justified balance between current risk levels (for today's world population) on the one hand, and technically feasible mitigation and control measures on the other hand. According to eq.8, P_c can be reduced below a given limit (P_c)_max by controlling the casualty cross-section A_c for the re-entering object (by engineering in the early design phase), by selecting the re-entry area (and hence the incurred population density), or by combining both strategies. If one assumes an accepted casualty probability of P_c ≤ 1:10,000 per re-entry event, Fig.8 shows how much casualty cross-section A_c may reach the ground for a given orbital inclination. The center curve shows the global average over all nodal longitudes, while the vertical bars indicate the ranges within which A_c can vary, depending on the geographic longitude λ_n of the ascending node of the orbit. λ_n(A_c,max) and λ_n(A_c,min) are indicated for each inclination. In this analysis, single-orbit averages over one nodal revolution are used. One can note that the ratios A_c,max(i)/A_c,min(i) may be on the order of 1,000 for some inclinations. For typical space station orbits near i = 50° (e.g. Skylab, Salyut-7, Mir and ISS) this ratio of maximum to minimum disposable casualty cross-section is still on the order of 50. Hence, a control of the nodal longitude of the final orbit can greatly reduce the on-ground risk, or (for a given tolerated risk level) increase the allowed casualty cross-section. When looking at the mean allowed A_c for P_c < 1:10,000 (see Fig.8), averaged over all inclinations, and all nodal longitudes, then A_c is close to 8 m² for the year 2000. This is the limit stipulated by NASA in [13] for an uncontrolled re-entry. Hence, A_c < 8 m² and P_c < 1:10,000 are equivalent requirements for this epoch. In order to be unambiguous, it is, however, recommended to adopt a limit on P_c, which will remain applicable as the world population grows (in contrast to a limiting A_c). The acceptable level of casualty probability P_c could be lower for special missions (e.g. the US Department of Transportation and FAA recommend P_c < 1:33,333 for launch phases and dedicated re-entry missions [16]).

Fig. 8. Ranges of permitted casualty cross-section (minimum, mean, and maximum) for an accepted risk of 1 in 10,000 per event, and for near-circular re-entry orbits, as a function of inclination, for a world population in 2000.

The Salyut-7/Cosmos-1686 compound of 40 tons mass and 26 m length was left mothballed at 475 km in Aug 1986. From there it started its descent, which led to a final re-entry above South America at 03:45 UTC on 07-Feb-1991 (see Fig.7). Due to an insufficient remnant of propellant, a planned attitude change and corresponding drag modulation to control the impact footprint could not be realized, and at least 3 major fragments could be retrieved after ground impact. The geographic longitude of the ascending node of the Salyut-7/Cosmos-1686 re- entry orbit was in the vicinity of λ_n ≈ 13°W. According to Fig.7 (label "Salyut-7") such a groundtrack leads to a global maximum of land coverage. The final casualty probability was estimated to be P_c2σ ~ 1/7,050 (for A_c = 10m²). This value is close to the global average of 1/7,650 for this orbit inclination of 51.5°.

In Feb 1974 Skylab, a 74 ton compound of dimensions 25.6 m × 6.6 m, was left in a 441 km near-circular orbit of 50.0° inclination. Due to an unexpected high level of solar activity with the approach of the maximum of solar cycle 21, the 10 year lifetime predicted in early 1974, was significantly shortened, and Skylab re-entered on 11-Jul-1979. Prior to the re-entry, Skylab was reactivated on 06-Mar-1978. Re-entry predictions during the last 24 hours of the orbital lifetime were all located on a single groundtrack with an ascending node at λ_n = 174°W. Fig.7 shows that this longitude, which was attained by an orbit energy management strategy, results in a re-entry ground swath with a global minimum in mean population density, and hence in mean casualty probability. Forecasts indicated, however, that the predicted impact location started to settle on the densely populated USA. At T-13h before the predicted entry, the land impact probability was 19.3%, and the casualty probability was 1/31,600 (for A_c = 10m²). In order to reduce the risk further, Skylab was taken out of its torque-equilibrium attitude (TEA) and put into a tumbling motion at 07:45 UTC on 11-Jul-1979. This led to a drag reduction by some 20%, moving the impact location down track by about one half orbit, and placing the impact right between two successive passes of the North American landmass. Thus, the probability of land impact was reduced to 16.5%, and the population casualty risk was reduced by almost 25% to 1/40,509. This risk figure corresponds to less than 20% of the global mean casualty risk of 1/7,750 for a reference spacecraft casualty cross section of 10m². The reconstructed impact of Skylab was determined to be at 16:37 UTC, in Australia, at 32°S and 124°E. Several large fragments could be retrieved from ground, including a water tank, a heat exchanger, an airlock shroud, oxygen bottles, and a film vault (sequence according to down-track range).

Mir, a successor of the Salyut-7 space station with a mass of 135 tons, and an extension of 30 m in all three dimensions, was de-orbited in a controlled manner on 23-Mar-2001. Following a natural orbital decay to about 215 km mean altitude, the space station re-entered, following a 3-burn maneuver strategy within 4 consecutive orbits, leading to a splash down near λ = -160.0° and φ = -40.0°, at 06:00 UTC, well inside its envisaged re-entry zone in the South Pacific. With 51.6° Mir had the same orbital inclination as Salyut-7. Moreover, its de- orbit took place on almost the same final groundtrack as the decay of Salyut-7, with the major difference that the phasing of the Mir re-entry position on that orbit was fully controlled and optimized, such that the distance to the nearest land masses was maximized, and the on ground risk was minimized to virtually zero (compare Fig.7). This demonstrates that even large, massive objects can be safely de-orbited, if adequate design and operational provisions are taken (for ISS similar de-orbiting procedures are considered).

Several space agencies and international entities have adopted space debris mitigation standards, guidelines, or codes of conduct. An important issue, which is addressed in most of these, is the post-mission removal of space systems, particularly from the densely populated low Earth orbit (LEO) region. This is an important measure to conserve the stability of the LEO environment in the long-term. It can be accomplished by direct de-orbiting, delayed de- orbiting to a reduced lifetime orbit, or re-orbiting to super-LEO altitudes. In the case of de- orbiting, a spacecraft or upper stage should enter into the Earth atmosphere within 25 years or less for delayed de-orbiting, and within less that one revolution for direct de-orbiting. Some space debris mitigation standards also request that the risk on ground due to a single re-entry event must not exceed a certain tolerated casualty probability (e.g. 1 in 10,000 [8]). Since mission operators should ideally comply with both, the 25 year rule for maximum post- mission lifetime, and the limitation of on-ground risk, they must be provided with a means to verify their compliance. For this purpose, NASA has developed the DAS tool (NASA Debris Assessment Software [14]). In one of its analysis modes DAS checks the survival of a spacecraft which is composed of several simplified object shapes of uniform material properties, and which is exposed to a re-entry, starting with given initial conditions of the trajectory. The risk is evaluated on the basis of the surviving casualty cross-section [13], for a latitude dependent world population model. A tool similar to DAS is nearing completion in Europe. Under ESA contract and with ESA participation the DRAMA software has been developed (ESA Debris Risk Assessment and Mitigation Analysis [10]). One of the purposes of DRAMA is to check compliance of a re-entry event with requirements from a future European Space Debris Mitigation Standard. The tool allows to define a re-entry object as a composite of simple-shape bodies, each with uniform material properties. This composite is propagated from an initial condition near 120 km altitude to burn-up altitude or ground impact location of its individual components. The on-ground risk for each survivor object is integrated over a 1? impact swath, and cumulated into an overall event-related risk. Two different assessment modes are offered: (1) a high-resolution, short-term analysis mode, using longitude and latitude dependent population densities within a 1? impact swath, and (2) a low-resolution, long-term analysis mode, assuming a purely latitude dependent population density distribution, and a uniform impact probability over the orbit. As of early 2005 the DRAMA software will be available free-of-charge for Solaris, Linux, and Window systems. Requests can be addressed to the author.

The risk analysis for uncontrolled re-entries from orbits of 51.5° inclination (e.g. Skylab, Salyut-7, Mir, and ISS), and the long-term, globally averaged risk assessment for such inclinations results in 2σ population casualty probabilities P_c,2σ which are of the same order of magnitude as the permissible threshold of P_c,2σ ≤ 1/10,000, which NASA defines for a single uncontrolled re-entry event (assuming a spacecraft casualty cross section of A_c ≤ 8m²). For the partially controlled natural re-entry of Skylab, this risk level was reduced by more than a factor of 5. In case of the fully controlled de-orbit of Mir, the casualty risk was virtually reduced to zero, by placing the impact footprint in an uninhabited area.

If one cumulates several pessimistic assumptions (i.e. all 19,000 historic re-entries caused a ground impact with a mean casualty cross-section of 8 m², and the Earth population was constant at the year 2000 level), then the cumulated risk of casualties would be about 1 in 45 years. This risk can be translated into an equivalent personal risk. For a US citizen, the risk to be killed before reaching the age 50 is about 1 in 7 × 10⁺⁹ due to debris impacts, 1 in 20,000 due to asteroid impacts, 1 in 300 due to homicides, and 1 in 150 due to car accidents. Hence, in spite of the wide public attention which is paid to uncontrolled re-entries, the associated probability of casualties is several orders of magnitude below the level of day to day risks which are commonly accepted.

1. Aksnes, K., Short-Period and Long-Period Perturbations of a Spherical Satellite Due to Direct Solar Radiation Pressure, Celestial Mechanics, Vol.13, pp. 89-104, 1976
2. Bouslog, S.A., Ross, B.P., and Madden, C.B., Space Debris Re-Entry Risk Analysis, AIAA 94-0591, 32nd Aerospace Sciences Meeting, Reno/NV, Jan 10-13, 1994
3. Cook, G.E., Basic Theory of PROD, a Program for Computing the Development of Satellite Orbits, Celestial Mechanics, Vol. 7, pp. 301-314, 1972
4. Fritsche, B., Roberts, T., Romay, M., Ivanov, M., Grinberg, E., and Klinkrad, H., Spacecraft Disintegration During Uncontrolled Atmospheric Re-Entry, proceedings of the Second European Conference on Space Debris, ESA SP-393, pp. 581-586, Darmstadt, 1996
5. Hedin, A.E., Extension of the MSIS Thermosphere Model into the Lower Atmosphere, Journal of Geophysical Research, Vol.96, No.A2, pp. 1159-1172, 1991
6. Hedin, A.E., et al., Revised Model of the Thermosphere Winds Using Satellite and Ground-Based Observations, Journal of Geophysical Research, Vol.96, No.A5, pp. 7657-7688,1991
7. Kaula, W.M., Theory of Satellite Geodesy, Blaisdell Publishing Company, Waltam (Mass.) /Toronto/London, 1966
8. Klinkrad, H. (editor), ESA Space Debris Mitigation Handbook, Second Edition, Issue 1.0, ESA/ESOC, Darmstadt, Germany, March 3, 2003
9. Klinkrad, H., Evolution of the On-Ground Risk During Uncontrolled Re-Entries, paper IAA-99-IAA.6.7.05, 50th IAF Congress, Amsterdam/The Netherlands, 1999
10. Klinkrad, H., Fritsche, B., and Lips, T., A Standardized Method for Re-Entry Risk Evaluation, paper IAA- 04-IAA.5.12.2.07, 55th IAF Congress, Vancouver/Canada, Oct 2004
11. Koppenwallner, G., Fritsche, B., and Lips, T., Survivability and Ground-Risk Potential of Screws and Bolts of Disintegrating Spacecraft During Uncontrolled Re-Entry, proceedings of the Third European Conference on Space Debris, ESA SP-473, pp. 533-539, Darmstadt, 2001
12. Liu, J.J.F., Alford, R.L., A Semi-Analytic Theory for the Motion of a Close-Earth Artificial Satellite with Drag, AIAA Paper No.79-0123, 17th Aerospace Sciences Meeting, New Orleans, 1979
13. NASA Safety Standard: Guidelines and Assessment Procedures for Limiting Orbital Debris, NSS 1740.14, Aug, 1995
14. O'Hara, R., Matney, M., Jansen, M., Anz-Meador, P., Latest Revisions to the NASA Debris Assessment Software (DAS), paper IAA-01-IAA.6.6.06, 52nd IAF Congress, Toulouse, France, Oct., 2001
15. Tobler, W., Deichmann, U., Gottsegen, J., and Maloy, K., The Global Demography Project, Technical Report TR-95-6, National Center for Geographic Information and Analysis, Dept. of Geography, University of California, Santa Barbara/CA, Apr, 1995
16. Smith, P.G., Expected Casualty Calculations for Commercial Space Launch and Reentry Missions, US Dept. of Transportation/FAA, Advisory Circular 431.35-1, Apr 12, 1999

Размещен 21 декабря 2006.