Computer Detection and Rocket Interception of Asteroids at an Atmospheric Boundary

Transcription

1 Computer Detection and Rocket Interception of Asteroids at an Atmospheric Boundary A.S. Alekseev a, Yu.A. Vedernikov a, I.I. Velichko b, V.A. Volkov b, B.P. Kryukov a, B.M. Pushnoi a, G.G. Sytii b, S.A. Zelepugin c a Institute of Computational Mathematics and Mathematical Geophysics, Novosibirsk, , Russia b State Rocket Centre, Acad. Makeyev Design Office, Miass, Chelyabinsk, Russia c Institute of Applied Mathematics and Mechanics, Tomsk State University, Russia Abstract A non-nuclear method for the destruction of asteroids 0,5-1 km in diameter that threaten the Earth at an atmospheric boundary is proposed. The method is as follows. Several rocket ENERGY carriers are launched. The controllable rockets carry kinetic star-like penetrators (KSP) 115 m in length. During the flight they line up one after another at an optimal distance, and in such an arrangement penetrate into an asteroid. Introduction A method of computer interception of small celestial bodies is used at all stages of rocket interception. It includes an algorithm of computer transformation of the number arrays received from the CCD-matrix into the parameters of asteroid ephemerides. The algorithm is designed for work with images, which cannot be visualized in detail. It provides the functioning of a telescopic system automatically without human intervention. A technology to detect and destroy asteroids up to 1 km in diameter is thus proposed and developed. Possible methods to destroy asteroids approaching the Earth The main methods to diminish the dangerous effect of DSO on the Earth are as follows: œ œ rocket delivery of a group of kinetic penetrators to the point of collision with a dangerous asteroid [1] ballistic throwing of kinetic penetrators towards an asteroid approaching the Earth [2].

2 The system of rocket attack on asteroids 0,5 1 km in diameter by long kinetic penetrators The asteroid Ikar is expected to approach the Earth in The diameter of the asteroid is approximately 1 km, and the velocity is up to 40 km/s. Launching of two-three ENERGY rockets [3] moving one after another at an efficient distance from each other towards the asteroid will be necessary to destroy it (if collision with our planet will be inevitable). Some kinetic penetrators (installed instead of the aerospace BURAN airplanes) with caliber fin assembly and about 115 m in length are launched from the ENERGY rockets near the asteroid. Thereby a destroying group consisting of 2-3 elements is formed, including rocket bodies, which also affect the dangerous asteroid. The use of BURAN for delivery of long kinetic penetrators (LKP) to the point of collision with the asteroid IKAR does not seem reasonable, because the mass of an LKP is comparable to that of the third stage of ENERGY. Therefore, the installation of an LKP instead of BURAN is preferable. The LKP must have a nose spike that extends above the nose of ENERGY. Investigations [1, 4] form a basis for the design of a superlong penetrator with caliber fin assembly. They have shown the importance of connecting the penetrating segments by star-like connecting strips and of using a nose spike that can be pulled out practically to the entire length of the LKP body. A high-power explosion device at the rear end of the fin assembly is an important supplement to such a kinetic penetrator. It causes the radial destruction as the LKP enters an asteroid. A general view of an LKP of the proposed construction is shown in Fig.1. Figure 1 - Proposed LKP Construction Computer calculations using the method of individual particles were carried out to estimate the efficiency of an LKP with a rear explosion device [5]. The computational algorithm of this method is based on the conservation laws of mass, energy, and momentum in integral form: d dt v rdw = 0 ; d dt v ru t dw = s ij U i ds;

3 d dt v r(e+ U ) dw = 2 sijui njds ; i, j = 1,2,3. Here W is the volume of an element of the medium; S is the surface that limits this volume; nj is the vector of the outward normal; ui is the velocity; sij are the components of the stress tensor. A general picture of the flow caused by the impact of an LKP with a rear explosion device of power of 3 megatons against a sand asteroid 0,5 km in diameter is given in Fig. 2. The steel LKP of length 115 m and diameter 1 m penetrates at a total speed of 30 km/s to a depth of 0,4 km and primes the explosion device to destroy the asteroid. Figure 2 a & b Flow caused by LKP impact on sand asteroid The impact parameters of kinetic star-like penetrators on small DSO Prompt interception of fragments of the IKAR asteroid less than 20 m in diameter is considered. Kinetic star-like penetrators (KSPs) having a multi-beam maximum midsection are used as the means of the action. A set consisting of one large and six small KSPs is arranged at an outer space interceptor. Each of them has a star-like construction consisting of three fins rectangular in plan (see Fig. 3). Figure 3 - KSP Construction The KSP material is 30XCHA steel with perforation, which is hardened to 6=160 kg/mm. Aluminum and titanium alloys can be used for small KSPs. KSPs made of

4 depleted uranium with perforation are promising. Cylindrical cumulative tubes can be used instead of small KSPs [6]. Steel, aluminum, and copper tubes were used in the investigations on creation of cylindrical charges with the detonation speed D < 6 km/s. It has been shown that stationary cylindrical cumulation takes place at 0,9 Co < D < (1,1 1,3) Co, where Co is the sound speed in the material of the tube. The condition Sa > a lim is another condition of the process of cylindrical cumulation, where a lim = arctg V/Co is the limiting (Walsh) angle of jet formation, V is the tube compression speed, Sa is the change in the compression angle of the tube (Sa = arctgv/d + arctg( V V ¼r); D is the detonation speed of the explosive substance, r is the tube radius. Model experimental investigations on penetration of long strikers into various metallic obstacles over collision velocity range of 0.2 to 3.2 km/s were carried out. Copper cumulative jets of star-like and circular cross-sections were thrown at velocities up to 6 km/s. A considerable increase in the area of lateral destruction of the obstacle by star-like strikers (see Fig. 4) and jets was observed. This effect is associated with additional zones of destruction, which are formed under interaction of shock waves in the areas between separate spikes of the moving penetrator. The results of experiments with lead and aluminum (see Figures 4 and 5) obstacles are used to estimate the size of the destruction by star-like strikers at collision velocities of 10 and 25 km/s using N.A. Zlatin s simulation curve [7]. This empirical curve makes it possible to predict the results of collisions of steel pairs at velocities of km/s using the experiments with lead pairs at the collision velocities that are smaller by an order of magnitude. Figure 4 - Volume, W, of plug forced Figures 5a - Piercing by star-like out from Al and Steel targets of finite penetrators at 65 from normal & length, where 5b - Ricochet of an axially symmetric are for Al; œ, are for Steel and equivalent at 60 from normal to target., œ are for star-like penetrators The effect of some geometrical parameters of star-like penetrators on their penetration ability and the limiting penetration speed for a given obstacle is considered. The most important factors are as follows:

5 1. The length of the nose part and 2. The efficient bluntness of its top. The number of striker spikes has but minor effect on the results of penetration (the number of spikes was varied from 3 to 6). The optimal range of spikes was determined as a compromise between the strength of the penetrator as a construction and the sizes of the destruction area of the obstacle at collision velocities of 1-3 km/s. In accordance with [7], the observed effects are qualitatively repeated at velocities of about 30 km/s. The anti-ricochet properties of star-like penetrators were investigated in a collision velocity range of km/s in comparison to similar results for the same bodies of rotation. Considerable advantages of star-like penetrators with nose wedges of sweep forward (see Fig. 5) were revealed. These advantages are especially essential when three-dimensional obstacles are penetrated. An abrupt worsening of the effect of rotating star-like penetrators was observed. A method using a nose spike with knurling is proposed [6] to eliminate this limitation. The attainment of an acceptable scattering speed of fragments is a key question of DSO fragmentation. As they approach the Earth from some height of interception, a given scattering must be provided. The estimates and analysis of the available experimental and calculation data of the configurations of shock layers and bottom traces ( local atmosphere ) of bodies of various shapes have shown the following: œ the front distance between flying fragments must not be less than the 1.5 of the maximal size of fragments in the plane perpendicular to the direction of motion, and not less than of it when the sizes of the preceding and the œ following fragments are the same the front distance must change linearly depending on the relative sizes of fragments following each other (up to y = 12, when the size of the following fragment is by a factor of 3 larger than that of the preceding fragment; y = 0.5 for a factor 3.5). This can guarantee the absence of the interaction which can bring flying fragments together due to the interference effects and peculiarities of the flow in the local atmosphere. It should be noted that these estimates of the distance between fragments do not preclude a chance of their approach and subsequent joint flight, because some configurations of fragments can cause the appearance of lateral aerodynamic forces. These forces will lead to a maneuvering flight of one or more fragments. Besides, because of the differences in sizes and masses, some following fragments can approach preceding fragments. A numerical method of the gas dynamics calculation of a high-speed impact is used to estimate the effect of the central KSP [5]. In 1986 it was successfully used to determine the thickness of protective screens of space apparatus approaching Halley s comet. An approximate model of the interaction was used. We studied the

6 collision between a sand meteorite 22 m in diameter with an uranium axially symmetric KSP equivalent 0.33 m in diameter and 6 m in length, the total collision speed being 30 km/s. The results of a numerical calculation of the equivalent penetration into the meteorite for different times are presented in Fig. 6. The third frame shows that the cylindrical equivalent of KSP in mass, length, and cross-sections pierces the meteorite, leaving it practically intact. The presence of radial KSP spikes will evidently lead to the formation of a system of cracks, by which the meteorite will break up into a number of fragments (Fig. 2b). Figure 6 a,b,c Results of Numerical Calculations of Penetration vs. Time Data base of DSO interception A conventional method for detection of asteroids and comets is as follows. In contrast to stars, asteroids move and, provided they are observed for a long time, leave a trace in the form of a small stroke on a photographic or computer image. The light from an asteroid is distributed in a light-sensitive material along the entire length of a stroke. The stroke has very little contrast. If a small asteroid did not move, it could be detected at a sufficient distance under long exposure. Visible motion along the celestial sphere is the main informative sign of asteroid detection. A moving asteroid leaves a blurred image, and this prevents distant detection. An algorithm for computer transformation of the number arrays obtained from the CCD-matrix to the parameters of orbital motion is proposed. The images of bodies moving along the ephemerides of a given class are represented immobile, and can be effectively exposed for a long time. Possible paths of asteroids approaching the Earth viewed in a telescope are shown in Fig.7. They are characterized by a certain relation between the direction of visible motion and the velocity.

7 The discrete structure of the CCD-matrix makes it possible to consider a discrete set of possible ephemerides in the telescope field-of-vision. The number of ephemerides is determined by the practical limitations of a specific task of observation. The effectiveness of the algorithm was investigated by numerical modeling. The algorithm (Fig. 8) calculates possible variants of motion, scans the CCD-matrix using the ephemerides, accumulates signals (data) at specific addresses (address), and determines whether a luminous body moves in accordance with a certain law. The maximal physical capabilities of the optical observation method as applied to moving image elements are realized in this method. Figure 7 Possible Observed Paths of Asteroids that are approaching the Earth Figure 8 Scheme of a CCD-Matrix Data Processing A characteristic feature of the algorithm is as follows. Data are processed mainly for the original number arrays obtained directly from the CCD-matrix in real time.

8 This allows editing of arrays to choose, for the subsequent analysis, only those fragments of the star sky image where there is no intensive exposure from stars, planets, large asteroids, space apparatus, flashes, and other optical noise. This is possible, because the intensity of useful radiation at distant detection is substantially lower than the level of the celestial background. A simple estimate of the efficiency of the distant detection system is valid under these conditions. It is based on a relation between the exposure time in conventional and computerized systems. Whereas in a conventional system a moving asteroid illuminates one pixel of the matrix during one minute and goes to a neighboring pixel, in the present algorithm the exposure is proportional to the number of pixels, through which the image of the asteroid passed during the observation. The accumulation effect increases in proportion to the square root of the exposure time. During 5 hours an asteroid can pass 300 pixels of the CCD-matrix. This corresponds to a 16-fold decrease in the amount of light reflected by the body being observed. Thus, a conventional system reliably detects bodies 200 m in diameter in an asteroid band at a distance of 300 million kilometers, and the computer system can detect, under the same conditions, bodies 50 m in diameter. Such an asteroid can approach the Earth after a year or later. This depends on the parameters of the orbit. The asteroid can move to perihelion and also approach the Earth from the daily side. It is clear that a real system for the detection of dangerous celestial bodies must regularly observe a considerable part of the sky. The investigations have shown that an observation area around a certain band in the celestial sphere orthogonal to the ecliptic is sufficient. Any body approaching the Earth is first to intersect this line. The place, direction, velocity, and time of the intersection are determined by the parameters of the body motion. Under these conditions the time interval between the detection and actual approach depend considerably on the body orbit and the location of the observation area. This approach is suitable also for the case[1], which is shown schematically in Figure 9. Conclusions The investigations performed have made it possible to design a rocket space interceptor on the basis of advances in the rocket and explosion technologies. They, together with achievements in the computer detection of celestial bodies, should serve as a basis for the formation of a system of Earth protection against the asteroid-comet danger.

9 Figure 9 - A Scenario of the Destruction of an Asteroid by Kinetic Penetrators from Figures 3a and 3b References [1] A. S. Alekseev, Yu..A. Vedernikov, I.I. Velichko, and V.A. Volkov, The rocket conception of cumulative impact defence of the Earth against dangerous space objects, Impact Engineering, 1997, V. 20, No. 1-5, [2] P.V. Kryukov, V.K. Gribova, Ballistic system for anti-asteroid defence, Special Issue: Space Protection of the Earth, Part II, Russia, Snezhinsk, RFNC-VNIITF, 1997, [3] B. Gubanov, Energy - Buran: a step into the future, Science and Life, 1989, No. 4, 2-9. [4] L. Westerling, P. Lundberg, L. Holmberg, High velocity penetration of homogeneous segmented and telescopic projectiles into alumina targets, Impact Engineering, 1997, V. 20, No. 6-10, [5] V.A. Agureikin, B.P. Kryukov, A numerical method of individual particles to calculate flows with large deformations, Numerical Methods of Continuum Mechanics, Computing Center and the Institute of Theoretical and Applied Mechanics of SB RAS, Novosibirsk, 1986, V. 17, No. 1. [6] Yu.A. Vedernikov and V.A. Shchepanovskii, Optimization of rheological gas dynamics systems, Nauka, Novosibirsk, 1995, 236 p. [7] N.A. Zlatin, G.I. Mishin (eds.), Ballistic Units and Their Application to Experimental Investigations [in Russian], Nauka, Moscow, 1974, 344 p.