Analysis of the Briz-M Propellant Tank (35698) Fragmentation Using the Velocity Perturbations of the Fragments

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1 Advances in Aerospace Science and Applications. Volume 4, Number 1 (14), pp Research India Publications Analysis of the Briz-M Propellant Tank (35698) Fragmentation Using the Velocity Perturbations of the Fragments *Arjun Tan, Vernessa Edwards and Marius Schamschula Department of Physics, Alabama A & M University, Normal, AL 3576, U. S. A. * arjun.tan@aamu.edu Abstract On 11 August 9, Russia launched the Asiasat 5 communications satellite using a Briz-M final stage rocket which left a large propellant tank (Satellite Number 35698) in a fairly elliptical orbit. On 1 June 1, after passing through its perigee, the propellant tank disintegrated into a large number of fragments. This study analyzes the velocity perturbations of 79 fragments which were cataloged through Day 3 f 1 in the parent satellite s frame of reference. Significantly greater numbers of fragments received positive velocity perturbations in the down-range and cross-range directions, whereas all fragments received negative velocity perturbations in the radial direction. The Gabbard diagram confirms that the fragmentation took place at an intermediate location between the apsidal points at a true anomaly of 7 o. The radial velocity perturbations of 16 fragments well within the angle of the Gabbard diagram gave unrealistic values owing to the effects of atmospheric drag. Otherwise, the histograms of the velocity perturbations components were generally Gaussian. Scatter-plots of the velocity perturbations in the horizontal and two vertical planes showed random elliptical patters without any clear concentration of fragments. A forward analysis of the fragmentation event showed that the fragments orbits, and their perigee heights in particular, depended exclusively upon the velocity perturbations in the radial and downrange directions. A surface plot of the perigee heights indicate that fragments receiving positive radial velocity perturbations and large negative down-range velocity perturbations de-orbited immediately. It is estimated that there were roughly as many fragments which de-orbited as there were which survived. INTRODUCTION On 11 August 9, Russia launched the Asiasat 5 communications satellite using a

2 1 Arjun Tan, Vernessa Edwards and Marius Schamschula Briz-M final stage rocket on top of a Proton-M launch vehicle [1]. Before its final burn, a large propellant tank (International Designator 9-4C, U.S. Satellite Number 35698) was left in a 4 km by 35, 74 km orbit with an inclination of 49. o [1]. Over 1 months later, on 1 June 1, the orbit had fallen below 95 km by 15 km and re-entry was imminent [1]. At 145 GMT, about 15 minutes after passing through its perigee, the propellant tank disintegrated into a large number of fragments, 85 of which were officially cataloged by the U.S. Space Surveillance Network [1]. This was the second of a string of fragmentations involving Briz-M rockets since 7. The velocity perturbations of the fragments of a satellite provide important clues to the nature and intensity of the fragmentation []. They can be calculated from the orbital elements of the parent satellite and those of the fragments given the location of the fragmentation point. Exact solutions of the velocity perturbations were obtained by Badhwar, et al. [], which has been successfully utilized to analyze satellite fragmentations due to explosion [ - 4], collision [5, 6], ASAT experimentation [7, 8] and unknown causes [9]. In the present paper, we have used this method to study the Briz-M tank fragmentation retrospectively. We further compare the results with those predicted by a forward analysis. METHOD OF ANALYSIS It is most convenient to use the parent satellite s frame of reference at the instant of the fragmentation []. In a vertical plane, the velocity of the satellite v consists of a down-range component v d and a vertical component v r. 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, we have []: 1 v d a1 e (1) r And 1 v ae r a r () r a In Eq. (), the + sign corresponds to the ascending mode of the satellite (true anomaly ν < π), whereas the sign corresponds to the descending mode (ν > π). Upon fragmentation, the velocity of a fragment has the components v r + dv r, v d + dv d and dv x, where the velocity perturbation components of the fragment in the three orthogonal (radial, down-range and cross-range) directions are given by []: e vr dvr 1 a r a r (3) cos dvd a1 e vd r (4) And sin dv x r a1 e (5)

3 Analysis of the Briz-M Propellant Tank (35698) Fragmentation 13 Where cos cos icos cos i 1 cosicosi cos (6) cos is the plane change angle of the fragment s orbit from the parent s orbit. In Eqs. (3) (5), a is the semi major axis and e the eccentricity of the fragment s orbit, whereas in Eq. (6), i and i are the inclinations of the parent s and fragment s orbits respectively, and the latitude of the fragmentation point. In Eq. (3), the + sign corresponds to the ascending mode of the fragment (true anomaly < ), whereas the sign corresponds to the descending mode ( > ). In Eq. (6), the + sign corresponds to i >i and the sign corresponds to i <i for northbound motion and vice-versa for southbound motion. The true anomaly of the fragment at the time of the breakup, which dictates the sign of vr dvr in Eq. (5), is determined from the argument of latitude u and the argument of perigee at the time of fragmentation as u (7) The argument of latitude u is given by sin u sin 1 (8) sin i for northbound motion of the fragment at the time of fragmentation, or by sin u sin 1 (9) sin i for southbound motion. RESULTS The orbital elements data needed for this study are taken from the website Space- Track.org [1]. A total of 79 fragments definitely belonging to the Briz-M propellant tank fragmentation and cataloged through Day 3 of 1 (18 days following the fragmentation) were considered. Prior to the fragmentation, the Briz-M propellant tank had an inclination of i = o, eccentricity e = and mean motion n = [1] and hence a period of P = min and semi-major axis of a = 7, km. This translates to an apogee height of 1, km and a perigee height of 9.31 km. The true anomaly of the satellite ν is determined from the polar equation of the orbit a 1 e r (1) 1 ecos where r is the radial distance from the center of the Earth. The altitude of fragmentation was reported to be almost 5 km [1]. An estimated value of 495 km for the altitude yields a true anomaly of 7 o, which puts the satellite in the ascending mode. Eqs. (1) and () furnish: v d km/s; and v r km/s. The slope angle of the parent satellite is given by

4 14 Arjun Tan, Vernessa Edwards and Marius Schamschula v tan 1 r (11) vd or, α = o, thus confirming that the satellite was in ascending mode. The latitude of the fragmentation point λ can be determined from the right spherical triangle formed by the ground track of the parent satellite, the equator and the meridian. We have: sin sinisinu (1) where u is the argument of latitude given by u (13) and ω is the argument of perigee of the parent satellite. With ω = o [1], we get λ = 5 o. The velocity perturbations of the 79 fragments in the down-range, cross-range and vertical directions were calculated using Eqs. (1) (9). Since the orbits of the parent and fragment satellites intersect when viewed on the horizontal plane, the dv d and dv x calculations always give meaningful values. However, on account of air drag, the fragment s orbit sometimes lies entirely within that of the parent satellite such that they do not intersect in the vertical plane. In such a case the radical in Eq. (3) becomes imaginary. It is customary to set the radical equal to zero [] whence the dv r value is returned as v r. In the present study, 16 cases fell into this category. The dv r values of such fragments may be disregarded, but not their corresponding dv d and dv x values. Table I summarizes the results for the calculated values of the velocity perturbations of the Briz-M fragments. It shows the maximum, minimum and average values of dv d, dv x and dv r as well as the fragment counts in the positive and negative directions. Significantly greater numbers of fragments received positive dv d s and dv x s while all fragments received negative dv r s. This is also revealed in their average values. The ranges of the values in the three directions were comparable, particularly when only real dv r values are considered. The reasons for these lop-sided distributions are discussed later. The Gabbard diagram is one of the earliest tools used to study satellite fragmentations. It plots the apogee and perigee heights against the periods of the fragments of a satellite breakup. Figure 1 is the Gabbard diagram of the Briz-M fragments. The apogee and perigee of the parent satellite are shown by X and +, respectively. Also shown by is the altitude of fragmentation. The apogee and perigee lines are both inclined, which indicates that the parent satellite was in a significantly elliptic orbit and the fragmentation occurred at an intermediate altitude between the apsidal points. The gentler slope of the perigee line indicates that the fragmentation occurred closer to the perigee. The 16 fragments with unreal dv r s are represented by fragments well within the V of the diagram. Figure shows the histograms of dv r, dv d and dv x distributions of the Briz-M fragments. They were fitted with Gaussian-type of distribution curves. Whereas the dv x distribution was the narrowest as well as the most Gaussian, the dv d distribution is slightly skewed to the left. The dv r distribution is the least Gaussian and almost bimodal, not counting the 16 fragments to the far left outside the Gaussian envelope. If one could assign most of the 16 fragments to the bin centered around -75 m/s, then

5 Analysis of the Briz-M Propellant Tank (35698) Fragmentation 15 that would have rendered the distribution more Gaussian. Figure 3 shows the scatter-plots of the velocity perturbations components of the Briz-M fragments in the horizontal plane (upper panel) and two mutually perpendicular vertical planes containing the momentum of the parent (lower left panel) and the orbital angular momentum of the parent (lower right panel). All three plot exhibit slightly elongated random elliptical patterns. But no comet-like structures like those seen in the explosive Briz-M rocket fragmentations [3, 4] were evident. The 16 fragments with unrealistic dv r s lie well below and outside of the main elliptical patterns in the lower panels of Fig. 3. Figure 4 is a three-dimensional scatter-plot of the velocity perturbations components of the Briz-M fragments in the parent s frame of reference giving a bird s eye-view perspective of the disintegration. No distinct pattern or signs of anisotropy is discernible. Nor is there appearance of any concentration of fragment points. The 16 fragments with unrealistic dv r s are relegated near the basement of the dv d dv x plane. Finally, it would be instructive to analyze this fragmentation event from the perspective of a forward analysis. Lagrange s planetary equations provide the orbital elements changes of the fragments due to the velocity perturbations dv r, dv d and dv x [11]. Whereas dv r and dv d affect the semi-major axis ( a ), eccentricity ( e ) and true anomaly ( ) of the fragment, dv x affects the inclination ( i ), longitude of ascending node ( ) and argument of perigee ( ) [11]. Thus the size and shape of the fragment s orbit, characterized by a and e respectively, are affected only by dv r and dv d and not by dv x. We have [11]: esin a 1e da dvr dvd (14) n 1 e r and 1 e a1 e r de sin dvr dvd (15) na er ae Of particular interest is the resulting perigee height of a fragment due to dv r and dv d : h p a da 1 e de r (16) where r is the reference radius of the Earth (6, km). If p h is less than a critical value of 1 km or so, the fragment should de-orbit immediately. It may be recalled that the perigee height of the Briz-M propellant tank had actually dropped to below this critical value and re-entry was imminent. In order to assess the survivability of a fragment in orbit, we consider the following special cases. In the first case, let dv r =. Then for all negative dv d s, h will be below critical height and the fragment will de-orbit. In the second case, let dv d =. Then for all positive dv r values, h will be below critical height and the fragment will de-orbit. The p p h values due to the combined effects of dv r and dv d were calculated using Eqs. (14 16). Figure 5 shows the contour plot of h p on a surface defined by dv r and dv d. p

6 16 Arjun Tan, Vernessa Edwards and Marius Schamschula Fragments with h p in the brown and red sectors produced by the higher values of dv r and lower values of dv d would de-orbit rapidly and only fragments in the upper sectors are to remain in orbit. This explains why no fragments with positive dv r s were actually found. It further explains why more fragments were found with positive dv d s values. Table I. Velocity perturbations summary of the Briz-M fragments dv d dv x dv r dv r * Maximum value (m/s) Minimum value (m/s) Average value (m/s) Range (m/s) Fragment count with + values Fragment count with - values * Fragments with real dv r values 3 5 Apogee Perigee Altitude, km 15 X Period, min Fig. 1. Gabbard diagram of the Briz-M fragments showing the apogee and perigee heights of each fragment versus their periods. Sixteen fragments with points well within the V had highly eroded orbits due to atmospheric drag.

7 Analysis of the Briz-M Propellant Tank (35698) Fragmentation Frequency 1 8 Frequency 8 Frequency dv r, m/s dv d, m/s dv x, m/s Fig.. Frequency distributions of dv r (upper panel), dv d (lower left panel) and dv x (lower right panel) of the Briz-M fragments with their corresponding Gaussian envelopes dvx, m /s dv r, m /s -4-5 dvr, m/s dvd, m/s -8 dvd, m/s -8 dvx, m/s Fig. 3. Scatter-plots of the velocity perturbations components of the Briz-M fragments in the horizontal plane (upper panel) and two mutually perpendicular vertical planes containing the momentum of the parent (lower left panel) and the orbital angular momentum of the parent (lower right panel).

8 18 Arjun Tan, Vernessa Edwards and Marius Schamschula Fig. 4. 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 h p, km dv r, m/s dv d, m/s Fig. 5. Contour plot of the perigee height of the Briz-M fragments as functions of the down-range and radial components of the velocity perturbations. Fragments in the region of high positive dv d s and high negative dv r s are likely to remain in orbit.

9 Analysis of the Briz-M Propellant Tank (35698) Fragmentation 19 DISCUSSION The Briz-M propellant tank (35698) fragmentation event was quite a unique one, unlike anything witnessed before. The satellite was near the end of its orbital life ready to make re-entry into the atmosphere before it fragmented. Had it not fragmented, it would not have created any orbital debris. As the fragments were ejected in different orbits with a range of perigee heights, many of them were likely to have de-orbited, while others with perigee heights above the critical value survived. Based on the forward analysis, it would be fair to state that there were at least as many fragments which made re-entry immediately as there were which did not. REFERENCES [1] Orbital Debris Quarterly News, Vol. 14, Issue 4, 1, p.. [] Badhwar, G.D., Tan, A., and Reynolds, R.C. Velocity Perturbations Distributions in the Breakup of Artificial Satellites, Journal of Spacecraft and Rockets, Vol. 7, 199, pp [3] Tan, A., Dokhanian, M. and Roberson, S., Velocity Perturbations Analysis of the Explosive Fragmentation of Briz-M Rocket Body (38746), Advances in Aerospace Science and Applications, Vol. 3, 13, pp [4] Tan, A., Sheng, S. and Dokhanian, M., Velocity Perturbations Analysis of the Briz-M Rocket (Arabsat-4A) Explosion, Advances in Aerospace Science and Applications, Vol. 4, 14, pp [5] Tan, A. and Zhang, D. Analysis and Interpretation of the Delta 18 Collision Experiment in Space, The Journal of the Astronautical Sciences, Vol. 49, 1, pp [6] Tan, A., Zhang, T.X., and Dokhanian, M. Analysis of the Iridium 33 and Cosmos 51 Collision Using Velocity Perturbations of the Fragments, Advances in Aerospace Science and Applications, Vol. 3, 13, pp [7] 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 [8] Tan, A. and Dokhanian, M. Velocity Perturbations Analysis of the Fengyun- 1C Satellite Fragmentation Event, Advances in Aerospace Science and Applications, Vol. 3, 13, pp [9] Tan, A. and Ramachandran, R. Velocity Perturbations Analysis of the Spot 1 Ariane Rocket Fragmentation, The Journal of the Astronautical Sciences, Vol. 53, 5, pp [1] [11] Meirovitch, L. Methods of Analytical Dynamics, McGraw-Hill, New York, 197, pp

10 Arjun Tan, Vernessa Edwards and Marius Schamschula