Velocity Perturbations Analysis of the Explosive Fragmentation of Briz-M Rocket Body (38746)

Transcription

1 Advances in Aerospace Science and Applications. ISSN Volume 3, Number 2 (213), pp Research India Publications Velocity Perturbations Analysis of the Explosive Fragmentation of Briz-M Rocket Body (38746) Arjun Tan, Mark Dokhanian and Sheral Roberson Department of Physics, Alabama A & M University P.O. Box 447, Normal, AL 35762, U. S. A. Phone: , Fax: arjun.tan@aamu.edu Abstract On 16 October 212, a Briz-M rocket body (satellite number 38746) with propellants in its tanks suffered an explosive fragmentation above north Atlantic Ocean as it approached its perigee. This study analyzes the velocity perturbations of the resulting fragments in the parent satellite s frame of reference. Whereas roughly equal numbers of fragments were ejected above and below the horizontal plane, an overwhelming majority of the fragments were ejected backwards and a vast majority of the fragments were ejected to the right from the parent satellite s perspective, looking vertically downwards. The average values of the velocity perturbations in the three orthogonal directions were all negative while the velocity perturbations components of the were all positive, with a slightly positive correlation between the two. This also indicates a substantial mass for the and a recoil effect on the latter. The histograms of the velocity perturbations in the radial and cross-range directions were mainly Gaussian, but that in the downrange direction was greatly skewed towards the negative end. The scatter-plots of the velocity perturbations in a vertical plane containing the velocity vector of the parent satellite and in the horizontal plane betray the pattern of a bow shock, which was likely produced in the medium of gases of combustion. The received the greatest velocity perturbation in the radial direction, which sets it apart in the velocity perturbations scatter-plots in the vertical planes as well as in the three-dimensional space. The extensive spread of fragments in the negative downward direction was very much in evidence in the histogram, the scatter-plots and the three-dimensional plots of the velocity preturbations.

2 48 Arjun Tan, Mark Dokhanian and Sheral Roberson INTRODUCTION On 6 August 212, Russia launched two communication satellites aboard a Proton rocket using a Briz-M upper stage en route to a geosynchronous orbit. However, the upper stage (International designator C; U.S. satellite catalog number 38746) failed at the third of its planned four burns in the transfer orbit, leaving with much of its propellants in the primary and auxiliary fuel tanks. On 16 October 212, Briz-M suffered a massive explosive fragmentation (similar to two earlier Briz-M explosions in 27 and 21) as it encountered the denser layers of the atmosphere while approaching its perigee [1]. The fragmentation occurred at an altitude of 29 km [1] around 163 UT above North Atlantic Ocean at 35 o N latitude and 28 o W longitude [2]. Prior to the fragmentation, Briz-M was in a fairly eccentric orbit having apogee height of 515 km, perigee height of 265 km, period of 142 min and eccentricity of [3]. The fragmentation of the Briz-M upper stage produced many fragments, 112 of which have been cataloged from Day 298 until Day 314 of 212 [3]. In this study, we have calculated the velocity perturbations suffered by the 112 fragments (ejection velocities from the parent satellite) from the orbital elements sets and analyzed their magnitudes, directions and distributions. We have used the method prescribed by Badhwar, et al. [4], which has been successfully utilized to analyze the Solwind ASAT experiment [5], Delta 18 collision experiment [6], the Spot 1 Ariane rocket fragmentation [7], the collision of Iridium 33 and Cosmos 2251 satellites [8] and the Fengyn-1C ASAT experiment [9]. METHOD OF ANALYSIS It is most convenient to use the parent satellite s frame of reference at the instant of the fragmentation [4]. In a vertical plane, the velocity of the satellite consists of a down-range component and a vertical component. In terms of the gravitational parameter μ, the semi major axis a, eccentricity e and the radial distance from the center of the Earth r, one has: and (1) 1 (2) (3) In Eq. (3), the + sign corresponds to the ascending mode of the satellite (true anomaly ), whereas the sign corresponds to the descending mode ( ). Upon fragmentation, the velocity of a fragment has the components, and, where the velocity perturbation components of the fragment are in the three orthogonal directions (radial, down-range and cross-range) are given by [4]:

3 Velocity Perturbations Analysis of the Explosive Fragmentation 49 1 (4) 1 (5) and 1 (6) where (7) is the plane change angle of the fragment s orbit from the parent s orbit. In Eqs. (4) (6), is the semi major axis and the eccentricity of the fragment s orbit, while in Eq. (7), and are the inclinations of the parent s and fragment s orbits respectively, and the latitude of the fragmentation point. In Eq. (4), the + sign corresponds to the ascending mode of the fragment (true anomaly, whereas the sign corresponds to the descending mode (. In Eq. (7), the + sign corresponds to and the sign corresponds to on the northbound orbits with the opposite sense on the southbound orbits. The true anomaly of the fragment at the time of the breakup, which dictates the sign of in Eq. (6), is determined from the argument of latitude and the argument of perigee at the time of fragmentation as (8) The argument of latitude is given by (9) for northbound motion of the fragment at the time of fragmentation, or by (1) for southbound motion. RESULTS Prior to the fragmentation, the Briz-M rocket body had an inclination of o, eccentricity and mean motion [3] and hence a period of min and semi-major axis of a = km. This translates to an apogee height of km and a perigee height of km. The altitude of fragmentation of 29 km yields a true anomaly of o (descending mode). Eqs. (1) (3) furnish: km/s; km/s; and m/s. The velocity perturbations of the 112 cataloged fragments, including the relevant orbital parameters, are calculated using Eqs. (4) (1). Table I lists the fragment

4 5 Arjun Tan, Mark Dokhanian and Sheral Roberson counts in all quarters of space from the perspective of the Briz-M at the instant of fragmentation as defined by the velocity perturbations of the fragments. The eight octants are defined as follows: (1) Octant I:,, ; (2) Octant II:,, ; (3) Octant III:,, ; (4) Octant IV:,, ; (5) Octant V:,, ; (6) Octant VI:,, ; (7) Octant VII:,, ; and (8) Octant VIII:,,. Roughly half of the fragments were ejected above and below the horizontal plane. However, an overwhelming majority of the fragments (91 out of 112) were ejected backwards, while a vast majority (85 out of 112) of the fragments were ejected to the right from the perspective of the parent satellite looking vertically downwards. The largest numbers of fragments were found in Octant III (37) and Octant VII (34) vertically below. Only 1 fragment was found in Octant V and 3 in Octant IV. Table I. Briz-M fragment counts in various quarters of space Fragments in regions of space Count Fragments in all space all all all 112 Fragments ejected upwards all all + 55 Fragments ejected downwards all all 57 Fragments ejected forwards + all all 21 Fragments ejected backwards all all 91 Fragments ejected to the left* all + all 27 Fragments ejected to the right* all all 85 Fragments ejected in Octant I Fragments ejected in Octant II Fragments ejected in Octant III + 37 Fragments ejected in Octant IV Fragments ejected in Octant V Fragments ejected in Octant VI + 11 Fragments ejected in Octant VII 34 Fragments ejected in Octant VIII + 11 *looking downwards from the parent satellite at fragmentation Table II shows the range (maximum and minimum values) of the velocity perturbations of all fragments in the three orthogonal directions as well as their average values. Also shown in the table are the velocity perturbations received by the, which acquires the serial number of the parent satellite. Most conspicuously, the s have the greatest range, from a small positive value of m/s to a large negative value of m/s. Stated otherwise, most fragments were spread over the negative velocity region. The values had the narrowest range (from m/s to m/s) whereas the values had an intermediate range (between m/s and m/s). The average velocity perturbations were all

5 Velocity Perturbations Analysis of the Explosive Fragmentation 51 negative, with the largest value in the down-range direction and the smallest value in the radial direction. Interestingly, the largest fragment had positive velocity perturbations in all three directions, in contrast with the average velocity perturbations. There was thus a correlation between the average fragment and the largest fragment, the correlation coefficient being Incidentally, the largest of all fragments belonged to the largest fragment. As the majority of the fragments headed in a general direction opposite to that of the, this indicates a recoil effect on the latter and also suggests that the latter possessed a substantial mass. Table II. Velocity perturbations of the average fragment and (in m/s) Maximum among all fragments Minimum among all fragments Average of all fragments Largest fragment Figure 1 shows the histograms of the velocity perturbations components (, and ) of the Briz-M fragments in the three orthogonal directions in the parent satellite s frame of reference. They were fitted with Gaussian distribution curves centered about their mean values (from Table II). Also shown in the Fig. 1 is the histogram of, which was fitted with a Maxwellian type of distribution. The locations of the within the histograms are also indicated. The distribution was fairly Gaussian, shifted slightly towards the negative values, but with the far outside the Gaussian envelope on the extreme right. The distribution was also largely Gaussian, shifted more to the left. However, the distribution was the least Gaussian and well skewed to the negative end, with a large number of fragments well outside the envelope, indicating their unusual ejection in the backward direction. Figure 2 shows the scatter-plots of the velocity perturbations of the Briz-M fragments in two vertical planes: one, containing the momentum vector of the parent (down-range radial plane); the other containing the orbital angular momentum vector (cross-range radial plane); and the horizontal (down-range cross-range) plane. The numbers of fragments in each quadrant are marked as well as the locations of the largest fragment, which sets itself apart in the vertical plane scatter-plots. The down-range radial and down-range cross-range plots betray the appearance of a bow-shock, which is produced by the supersonic passage of a body through a fluid medium [1]. Even though the explosion of the Briz-M rocket body was believed to be caused by atmospheric heating, the density of air at 29 km altitude normally varies between 1-11 kg/m 3 and 1-1 kg/m 3 [11]. Thus the ambient medium responsible for the generation of the bow shock was most likely the gases of combustion rather the atmosphere itself.

6 52 Arjun Tan, Mark Dokhanian and Sheral Roberson 6 4 y=56.5exp[-.5(x+8) 2 ] (91) (21) 5 35 (57) (55) frequency 3 frequency 2 y=35.8exp[-.2(x+6) 2 ] dv r, m/s dv d, m/s (85) (27) (112 fragments) y=43.8exp[-.3(x+35) 2 ] 4 frequency frequency 3 y=.6459x 2 exp(-.288x) dv x, m/s dv, m/s Fig. 1. Frequency distributions of (upper left), (upper right), (lower left) and (lower right) of the Briz-M fragments with their corresponding distribution functions. The numbers of fragments in the positive and negative directions are marked.

7 Velocity Perturbations Analysis of the Explosive Fragmentation (46) (9) (4) (15) dv r, m/s Briz-M dv r, m/s (45 (12) (45) (12) dv d, m/s dv x, m/s (2) (7) dv x, m/s Briz-M (71) (14) -6. dv d, m/s -8. Fig. 2. Scatter-plots of the velocity perturbations components of the Briz-M fragments in a vertical plane containing the momentum of the parent (upper left); a vertical plane containing the orbital angular momentum of the parent (upper right); and the horizontal plane (lower). The numbers of fragments in each quadrant are marked as well as the directions of Briz-M prior to fragmentation.

8 54 Arjun Tan, Mark Dokhanian and Sheral Roberson Figure 3 is a three-dimensional scatter-plot of the velocity perturbations components of the Briz-M fragments in the parent s frame of reference in the downrange, cross-range and radial directions, giving a bird s eye-view perspective of the disintegration. Prior to the fragmentation, the direction of Briz-M was mostly downrange, with a small radially downward component. Most of the fragments are concentrated in the forward end with many fragments strewn backwards. The largest remnant, once again, sets itself part from the rest as if by a recoil effect. In order to gain a better three-dimensional perspective of the fragmentation, we utilize the three mutually orthogonal axes of, and to define the eight octants of space in the parent satellite s frame of reference as defined earlier. The numbers of fragments dispersed in each octant are shown in Fig. 4. Nearly 35% of the fragments (37 out of 112) were ejected in Octant III and nearly 3% (34 out of 112) were ejected in Octant VII below. Octants I, IV and V contained only 6, 3 and 1 fragments, respectively. The was ejected in Octant I, generally opposite to the Octants III and VII, where most of the fragments were dispersed. 4 3 dv r, m/s Briz-M dv d, m/s dv x, m/s Fig. 3. Three-dimensional scatter-plot of the velocity perturbations components of the Briz-M fragments in the radial, down-range and cross-range directions in the parent satellite s frame of reference at fragmentation. The sets itself apart from the rest of the fragments.

9 Velocity Perturbations Analysis of the Explosive Fragmentation 55 dv r II (9) dv x III (37) IV(3) I (6) V (1) dv d VII (34) VIII (11) VI (11) Fig. 4. Fragment counts in octants of space in Briz-M s frame of reference prior to breakup defined by the down-range ( ), cross-range ( ) and radial ( ) directions. DISCUSSION It was generally believed that an internal explosion within a satellite produced a more uniform and isotropic dispersion of fragments than an external collision [12]. This study indicated that in the case of the Briz-M rocket body fragmentation, this was clearly not the case. The fragment spread was quite lop-sided with a bow shock pattern in front and many fragments ejected in the backward direction. It would be interesting to see if such a pattern existed in other explosive satellite fragmentation events.

10 56 Arjun Tan, Mark Dokhanian and Sheral Roberson REFERENCES [1] Orbital Debris Quarterly News, Vol. 17, Issue 1, 213, pp [2] Kelso, T.S., electronic communication; also, Breakup/. [3] [4] Badhwar, G.D., Tan, A., and Reynolds, R.C. Velocity Perturbations Distributions in the Breakup of Artificial Satellites, Journal of Spacecraft and Rockets, Vol. 27, 199, pp [5] Tan, A., Badhwar, G.D., Allahdadi, F.A., and Medina, D.F. Analysis of the Solwind Fragmentation Event Using Theory and Computations, Journal of Spacecraft and Rockets, Vol. 33, 1996, pp [6] Tan, A. and Zhang, D. Analysis and Interpretation of the Delta 18 Collision Experiment in Space, The Journal of the Astronautical Sciences, Vol. 49, 21, pp [7] Tan, A. and Ramachandran, R. Velocity Perturbations Analysis of the Spot 1 Ariane Rocket Fragmentation, The Journal of the Astronautical Sciences, Vol. 53, 25, pp [8] Tan, A., Zhang, T.X., and Dokhanian, M. Analysis of the Iridium 33 and Cosmos 2251 Collision Using Velocity Perturbations of the Fragments, Advances in Aerospace Science and Applications, Vol. 3, 213, pp [9] Tan, A. and Dokhanian, M. Velocity Perturbations Analysis of the Fengyun- 1C Satellite Fragmentation Event, Advances in Aerospace Science and Applications, Vol. 3, 213, pp [1] Courant, R. and Friedrichs, K.O. Supersonic Flow and Shock Waves, Interscience Publishers, New York, 1956, pp [11] COSPAR International Reference Atmosphere, Akademie-Verlag, Berlin, 1972, pp [12] Tan, A., Allahdadi, F., Maethner, S. and Winter, J. Satellite Fragmentation: Explosion vs. Collision, Orbital Debris Monitor, Vol. 6, Issue 2, 1993, pp