International Network of Engineers and Scientists Against Proliferation

The Consequences of Using Kinetic Energy Anti-Satellite Weapons

Wang Ting

The goal of this article is to achieve a better understanding of the impact of using kinetic energy anti-satellite weapons (KE-ASAT) on the space environment. The lifetime of space debris produced when a KE-ASAT hits a Low Earth Orbit (LEO) satellite is calculated. In the calculations, NASA’s spacecrafts and rocket bodies breakup model and the latest atmosphere model NRLMSISE-00 are applied. The results show that the use of KE-ASAT against a satellite orbiting the earth above 800 km would cause a considerable threat to spacecrafts.

Introduction

KE-ASATs are designed to exploit the destructive kinetic energy that is released when a mass impacts a satellite at extremely high speed. The ASAT weapon could be based on land, in the air, or in space. KE-ASATs have been developed, tested, and deployed in the past and are likely to be used in a future space war. In October 1985, the aging satellite P78-1 was destroyed by a KE-ASAT launched from an F-15 aircraft in a U.S. Air Force ASAT test.[1] Apart from dedicated ASAT weapons, the ground-based interceptors already deployed as part of the U.S. Ballistic Missile Defense system as well as the planned space-based missile defense interceptors could also be used as KE-ASATs.[2]

When a KE-ASAT traveling at hypervelocity collides with a satellite, a large amount of debris is produced. A lot of the debris would not fall into Earth’s atmosphere quickly, but rather pose a long-term threat to manned and unmanned spacecrafts.

In this paper, the lifetime of debris caused by a hypervelocity impact of an KE-ASAT with a LEO satellite is calculated. The results show that if the engagement occurs 800 km or more above the Earth, most of the debris will remain in orbit for more than ten years and overall debris population will be significantly increased.

Current Debris Environment

To better understand the impact of a KE-ASAT on the overall space debris environment, it is necessary to first introduce the current situation.

Space debris is the term for any human-made object in orbit that no longer serves a useful purpose. It comes in the form of discarded hardware, abandoned satellites, and object breakup.

An object larger than 10 cm in diameter, which is commonly referred to as a large object, can be routinely detected, tracked, and cataloged by the U.S. space surveillance system.

The United States space surveillance system currently catalogues 9,000 objects larger than 10 cm.[3] Roughly 800 of these objects are active satellites, all the rest is debris.[4]

The collision probability between space assets has so far been rare, but a few incidences have occurred. In 1996, e.g., the French military satellite Cerise had its stabilization arm severed by a briefcase-sized portion of an Ariane rocket. And as early as July 1981, the Russian Kosmos 1275 military navigation satellite experienced an unexpected breakup, generally thought to have been a result of space debris.[5]

Calculation Method and Assumption

The whole debris lifetime calculation, as outlined in Figure 1, can be divided into two parts. The first is to use a satellite breakup model to calculate the debris status immediately after a KE-ASAT engagement, which includes the number, separation velocities, and area-mass ratio of the debris objects. Secondly, on the basis of that information and a lifetime algorithm, the lifetime of every piece of debris is calculated and statistical results are achieved. A precise atmosphere model which requires geomagnetic and solar flux data is the key element of that calculation.

Satellite Breakup Model

The satellite breakup calculations used in this study are based on NASA’s breakup model.[6]

To calculate satellite breakup, the first step is to determine whether a collision between the KE-ASAT and a target satellite is catastrophic, meaning both the weapon and the satellite are totally destroyed and converted to debris fragments. According to NASA’s model, “If the relative kinetic energy of the smaller object divided by the mass of the larger object is equal to or greater than ­40 J/g, then the collision is catastrophic.”[7] That means 1 kg mass with a relative speed of 10 km/s could result in a complete breakup of a 1.250 kg satellite.[8] The mass of the KE-ASAT used in the 1985 test was 16 kg,[9] and the dry mass of a kinetic energy vehicle of the missile defense system is about 20-40 kg.[10] Therefore, for a satellite with a mass below 10 tons, a KE-ASAT engagement will be catastrophic. However, if the weapon does not directly impact the satellite bus and hits a solar panel or an antenna instead, a catastrophic collision will not occur. But in this study, these cases are not considered.

In the second step, using the formulas listed in Johnson’s paper[5] and considering the laws of conservation of mass and momentum, the mass-ratios and relative speeds of debris produced in the engagement can be obtained. The scenario is determined by the drag coefficient of debris required for lifetime calculations. Kessler shows that the coefficient is approx. 2.2.[11]The direction of the relative velocities of the debris is assumed to be uniformly distributed in a sphere.[12]

The number of large fragments (debris diameter >10 cm) and debris separation speeds are shown in Figures 2 and 3. It is obvious that a considerable amount of debris will be produced after satellite breakup. In addition, most of the debris will not immediately fall into Earth’s atmosphere, because, as compared with their speed in orbit (>7 km/s for LEO satellites), the relative speed of most debris is very small as compared to its orbit speed.

Space Debris Lifetime Calculation

After satellite breakup, every piece of debris has a different velocity, which equals the original satellite velocity plus the relative velocity received during breakup, and thus enters into a different orbit (Figure 4). Some fragments will enter into orbits that cross Earth or insert them into the high-density atmosphere; these objects have a short lifetime. The others will enter into long lifetime orbits. More seriously, as time goes by they will spread out into nearby orbits and threaten other satellites due to the impact of perturbation forces.[13]

Through calculating the lifetime of every piece of debris, we can determine the distribution of debris lifetime.

The algorithm used for calculating debris lifetime is a semi-analytical method that considers atmospheric drag and J2 gravity perturbations.[14] The method applies a series of simplified assumptions, which significantly increases the calculation speed but leads to calculation errors. The difference in calculation results between the semi-analytical method and the complete analytical method, which considers all kinds of perturbation forces, is indicated in Table 1. The comparison shows about 2% error in the results of the semi-analytical method.[15] Since the aim of these calculations is not to find the lifetime of special pieces of debris but the whole debris lifetime distribution, the precision of the semi-analytical algorithm is enough.

The atmosphere model is very important in these calculations, because the atmospheric drag is the main factor that determines debris lifetime.

In this study, four atmosphere models are compared: USSA 76, CRIA 61, MSIS 77, and ­­NRLMSIS 00. The widely used USSA 76 is a static atmosphere model, which means all the atmospheric parameters remain constant. The only factor that affects the model is altitude. CRIA 61, MSIS 77, and MSIS 00 are time-varying models, which consider more real world effects.[16] In this study, CRIA 61 and MSIS 77 are simplified. Only solar flux and altitude data are necessary for these two models. The NRLMSIS 00 model is one of the latest atmosphere models;[17] it requires not only solar flux data but also geomagnetic data,[18] time, longitude and latitude data.

According to Tables 2 and 3, the different atmosphere models lead to quite different calculation results. The maximum difference appears between USSA 76 and NRLMSIS in Table 2. The reason is that the former is a static model (i.e., it does not consider sun activity variations).

The activity of the sun, which is represented in solar flux,[19] strongly affects the atmosphere density at high altitude. As shown in Figure 5, with an increase of solar flux, atmosphere density above 300 km will increase significantly. At some altitudes, the difference of density is more than 1,000 per cent. Solar flux data varies widely, but aprroximately repeats itself every eleven years or so, as shown in Figure 6. That means, in some years, the air density is very high and debris de-orbits rather quickly. If the lifetime of debris is shorter than the solar flux period, the time at which it is produced will strongly affect its lifetime.

Although the effect of solar flux is partly eliminated in calculating long lifetime debris, USSA 76 still as has a huge error.

The simplified models CRIA 61 and MSIS 77 consider solar activity; however, their results still have a huge error relative to the latest model, NRLMSIS 00. The main reason is that geomagnetic data, another key element, are not considered in those simplified models. Therefore, NRLMSIS 00 is applied for the calculation, although it requires a considerably higher computation effort.

Results and Conclustions

The aim of the calculations described above is to to calculate the lifetime of debris caused by an attack of KE-ASAT. The Engagement times are selected at 1980 and 1986 because the former corresponds to a solar flux maximum year, which means high atmosphere density and short debris lifetime; the latter is the opposite.

The calculation results for the lifetime of debris particles that are created by catastrophic breakups of satellites with a mass of 1, 2, 5, and 10 tons, respectively, are shown in Figures 7 (debris size >10 cm) and Figure 8 (debris size 1-10 cm), both for debris with a lifetime of more than 1 and 10 years, respectively.

The calculation results show that two-thirds of the large debris created in an engagement at 1,000 km will remain in orbit for more than ten years. When the breakup occurs at 800 km, the number goes down to 40%. Moreover, if a big satellite (>10 tons) breaks up, the overall number of large debris will increase by 30% to 50% for more than ten years. Even in the case of a small satellite (1 ton) breakup, the population of large debris will still increase by up to 10%.

For a KE-ASAT engagement at around 600 km, the lifetime of debris is highly dependent on the time the engagement occurs. About two thirds remain in orbit for several years if the breakup happens in a low solar flux year; in a high flux year, three quarters of the debris will decay within a year.

If the engagement happens on a low orbit (400-500 km altitude), the atmospheric drag will cause the fragments to de-orbit relatively quickly - typically within weeks or months. Because the number of fragments is large, however, there is still a significant risk of collisions while they remain in orbit.

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1.   GlobalSecurity.org, Air-Launched Miniature Vehicle (ALMV); www.globalsecurity.org/space/systems/almv.htm.
2.   David Wright and Laura Grego, Anti-Satellite Capabilities of Planned US Missile Defense Systems, December 9, 2002; www.ucsusa.org/global_security/space_weapons/page.cfm?pageID=1152.
3.   NASA Orbital Debris Program Office, The Orbital Debris Quarterly News, Johnson Space Center, Volume 9, Issue 1, January 2005; www.orbitaldebris.jsc.nasa.gov/newsletter/newsletter.html.
4.   For a database of active satellites, see: Union of Concerned Scientists, UCS Satellite Database at www.ucsusa.org/global_security/space_weapons/satellite_database.html.
5.   Simon Collard-Wexler et.al., Space Security 2004, June 2005; www.spacesecurity.org/SSI2004.pdf.
6.   N.L. Johnson, P.H. Krisko, J.-C. Liou, and P.D. Anz-Meador, NASA’s New Breakup Model of Evolve 4.0, Advances in Space Research, Vol. 28 No. 9, pp. 1377-1384, 2001.
7.   Ibid. p. 1379.
8.   Donald J. Kessler and Burton G. Cour-Palais, Collision Frequency of Artificial Satellites: The Creation of a Debris Belt, Journal of Geophysical Research, Vol. 83, Issue A6, pp. 2637-2646, 1 June 1978. In Kessler’s paper, the ratio is 115 instead of 1,250; this paper does not adopt the number, because Kessler’s paper is relative old.
9.   Stephen Karl Remillard, Debris Production in Hypervelocity Impact ASAT Engagements, Thesis presented to the Faculty of the School of Engineering of the Air Force Institute of Technology Air University, December 1990, p. 64.
10.   American Physical Society, Report of the American Physical Society Study Group on Boost Phase Intercept Systems for National Missile Defense: Scientific and Technical Issues, July 15, 2003, p. 255; www.aps.org/public_affairs/popa/reports/nmd03.cfm.
11.   Donald J. Kessler, Phillip D. Anz-Meador, Critical Number of Spacecraft in Low Earth Orbit: Using Satellite Fragmentation Data to Evaluate the Stability of the Orbital Debris Environment, Proceedings of the Third European Conference on Space Debris, March 2001; http://webpages.charter.net/dkessler/files/CriticalNumberofSpacecraftinLow.pdf.
12.   H. Klinkrad, H. Sdunnus, and J. Bendisch, Development Status of The ESA Space Debris Reference Model, Advance in Space Research, Vol. 16, No. 11, pp. 93-102, 1995, p. 96.
13.   Kevin R. Housen, The Short-Term Evolution of Orbital Debris Clouds , The Journal of the Astronautical Sciences, Vol. 40, No.2, April-June 1992, pp. 203-213.
14.   Wang Ting and Dong Yunfeng, An Algorithm for the Orbital Lifetime of Space Debris from a Spacecraft Breakup Event, Space debris research, Special 2006, pp. 31-37.
15.   The complete numerical method still has errors, because even the most accuracy atmosphere model still has 10% error. Moreover, the attitude of debris, which also effects the lifetime, is hard to determine and is not considered in the calculations.
16.   For more detailed information about atmosphere models see: David A. Vallado, Fundamentals of Astrodynamics and Applications, 2nd ed., E Segundo, CA: Microcosm Press, 2001, p. 528.
17.   A brief introduction to the MSIS model and FORTRAN source code is available at http://uap-www.nrl.navy.mil/models_web/msis/msis_home.htm.
18.   The history of solar flux and geomagnetic data used in this study is downloaded from ftp://ftp.stk.com/pub/STKData/CentralBodies/Earth.
19.   Although the solar flux is impossible to measure from the Earth’s surface, solar radiation with a wavelength of 10.7 cm can be used to determine the solar flux. For more information see David A. Vallado, op.cit., p. 533.