RADIO PHYSICS AND RADIO ASTRONOMY

PACS numbers: 93, 96.30.Ys

Purpose: Taking the altitude and time dependences of the meteoroid fragment speed, acceleration, mass, and the midsection from the measured trajectory data.

Design/methodology/approach: Numerical calculations have been made of the Chelyabinsk celestial body speed, acceleration, mass, and midsection variations with time and altitude. The third order spline fits have been shown to be acceptable. The model results have been compared to the measured optical radiation intensity.

Findings: Using the equations of meteorite physics with accounting for the deceleration, gravity and Coriolis forces the regression analysis for fitting the meteoroid altitude and geographic coordinates was made and the dependences of the meteoroid speed, acceleration, mass, and optical radiation intensity on time and altitude found. In all cases, the approximation is performed with cubic splines. The speed has been shown to decrease approximately by a factor of 3 when the altitude decreases from 40 to 15 km over the 03:20:32–03:20:36 UT interval. The average deceleration is equal to –4 km/s², while the maximum deceleration of –6 km/s² occurs within the same altitude range. Based on speed vs. time and optical radiation intensity vs. time dependences, the dependences of meteoroid mass vs. time and vs. altitude have been plotted. The most significant change in the mass occurs during the 03:20:32–03:20:33 UT interval and the calculations show a value of 5 kt/s. The air drag coefficient has been estimated from the determined dependences of speed, deceleration, mass loss rate, and meteoroid midsection on time and altitude.

Conclusions: The third order splines provide the best fit to the Chelyabinsk meteoroid altitude and geographic coordinate regression time dependences. The temporal dependences of the Chelyabinsk celestial body speed and deceleration have been calculated from the trajectory measurements. The equations of meteorite physics have been used to calculate mass, midsection, and meteoroid optical radiation intensity vs. time and vs. altitude dependences. The air drag coefficient have been presented.

Key words: Chelyabinsk meteoroid, time and altitude dependences, meteoroid speed, meteoroid acceleration, meteoroid mass, cubic splines, approximation  

Manuscript submitted  26.03.2018

Radio phys. radio astron. 2018, 23(2): 104-115

 REFERENCES

1. SOLAR SYSTEM RESEARCH. 2013. vol. 47, no. 4. (Thematical issue).

2. Proceedings of the international scientific-practical conference “Asteroids and comets. Chelyabinsk event and study of the meteorite falling into the lake Chebarkul”. Chelyabinsk, Russia: Krai Ra Publ. (in Russian).

3. ALPATOV, V. V., BUROV, V. N., VAGIN, J. P., GALKIN, K. A., GIVISHVILI, G. V., GLUHOV, J. V., DAVIDENKO, D. V., ZUBACHEV, D. S., IVANOV, V. N., KARHOV, A. N., KOLOMIN, M. V., KORSHUNOV, V. A., LAPSHIN, V. B., LESHENKO, L. N., LYSENKO, D. A.,MINLIGAREEV, V. T., MOROZOVA, M. A., PERMINOVA, E. S., PORTNYAGIN, J. I., RUSAKOV, J. S., STAL, N. L., SYROESHKIN, A. V., TERTYSHNIKOV, A. V., TULINOV, G. F., CHICHAEVA, M. A., CHUDNOVSKY, V. S. and SHTYRKOV, A. Y., 2013. Geophysical conditions at the explosion of the Chelyabinsk
(Chebarkulsky) meteoroid in February 15, 2013. Moscow, Russia: FGBU “IPG” Publ. (in Russian).

4. ANTIPIN, N. A., ed. 2014. The Chelyabinsk Meteorite – one year on the Earth: Proceedings of All-Russian Scientific Conference. Chelyabinsk, Russia: Kamennyi poyas Publ. (in Russian).

5. EMEL’YANENKO, V. V., POPOVA, O. P., CHUGAI, N. N., SHELYAKOV, M. A., PAKHOMOV, YU. V., SHUSTOV, B. M., SHUVALOV, V. V., BIRYUKOV, E. E., RYBNOV, YU. S., MAROV, M. YA., RYKHLOVA, L. V., NAROENKOV, S. A., KARTASHOVA, A. P., KHARLAMOV, V. A. and TRUBETSKAYA, I. A., 2013. Sol. Syst. Res. vol. 47, is. 4, pp. 240–254. DOI: https://doi.org/10.1134/S0038094613040114

6. GRIGORYAN, S. S., IBODOV, F. S. and IBADOV, S. I., 2013. Physical mechanism of Chelyabinsk superbolide explosion. Sol. Syst. Res. vol. 47, no. 4, pp. 268–274. DOI: https://doi.org/10.1134/S0038094613040151

7. POPOVA, O. P., RYBNOV, Y. S., HARLAMOV, V. A., GLAZACHEV, D. O., EMELIANENKO, V. V., KARTASHOVA, A. P. and JENNISKENS, P., 2013. Chelyabinsk meteoroid parameters: Data analysis. In: Dinamicheskie
protsessy v geosferah: sb. nauch. tr. IDG RAN. Moscow, Russia: Geos Publ. is. 4, pp. 10–21 (in Russian).

8. POPOVA, O. P., JENNISKENS, P., EMELYANENKO, V., KARTASHOVA, A., BIRYUKOV, E., KHAIBRAKHMANOV, S., SHUVALOV, V., RYBNOV, Y., DUDOROV, A., GROKHOVSKY, V. I., BADYUKOV, D. D., YIN, Q.-Z., GURAL, P. S., ALBERS, J., GRANVIK, M., EVERS, L. G., KUIPER, J., HARLAMOV, V., SOLOVYOV, A., RUSAKOV, Y. S., KOROTKIY, S., SERDYUK, I., KOROCHANTSEV, A. V., LARIONOV, M. Y., GLAZACHEV, D., MAYER, A. E., GISLER, G., GLADKOVSKY, S. V., WIMPENNY, J., SANBORN, M. E., YAMAKAWA, A., VEROSUB, K. L., ROWLAND, D. J., ROESKE, S., BOTTO, N. W., FRIEDRICH, J. M., ZOLENSKY, M. E, LE, L., ROSS, D., ZIEGLER, K., NAKAMURA, T., AHN, I., LEE, J. I., ZHOU, Q., LI, X. H., LI, Q. L., LIU, Y., TANG, G.-Q., HIROI, T., SEARS, D., WEINSTEIN, I. A., VOKHMINTSEV, A. S., ISHCHENKO, A. V., SCHMITT-KOPPLIN, P., HERTKORN, N., NAGAO, K., HABA, M. K., KOMATSU, M. and MIKOUCHI, T., 2013. Chelyabinsk airburst, damage assessment, meteorite, and characterization. Science. vol. 342, is. 6162, pp. 1069–1073. DOI: https://doi.org/10.1126/science.1242642

9. POPOVA, O. P., JENNISKENS, P., EMELYANENKO, V., KARTASHOVA, A., BIRYUKOV, E., KHAIBRAKHMANOV, S., SHUVALOV, V., RYBNOV, Y., DUDOROV, A., GROKHOVSKY, V. I., BADYUKOV, D. D., YIN, Q.-Z., GURAL, P. S., ALBERS, J., GRANVIK, M., EVERS, L. G., KUIPER, J., HARLAMOV, V., SOLOVYOV, A., RUSAKOV, Y. S., KOROTKIY, S., SERDYUK, I., KOROCHANTSEV, A. V., LARIONOV, M. Y., GLAZACHEV, D., MAYER, A. E., GISLER, G., GLADKOVSKY, S. V., WIMPENNY, J., SANBORN, M. E., YAMAKAWA, A., VEROSUB, K. L., ROWLAND, D. J., ROESKE, S., BOTTO, N. W., FRIEDRICH, J. M., ZOLENSKY, M. E, LE, L., ROSS, D., ZIEGLER, K., NAKAMURA, T., AHN, I., LEE, J. I., ZHOU, Q., LI, X. H., LI, Q. L., LIU, Y., TANG, G.-Q., HIROI, T., SEARS, D., WEINSTEIN, I. A., VOKHMINTSEV, A. S., ISHCHENKO, A. V., SCHMITT-KOPPLIN, P., HERTKORN, N., NAGAO, K., HABA, M. K., KOMATSU, M. and MIKOUCHI, T., 2013. Supplementary materials for Chelyabinsk airburst, damage assessment, meteorite, and characterization. Science [online]. vol. 342. [viewed 30 January 2017]. Available from: www.sciencemag.org/cgi/
content/full/science.1242642/DC1

10. CHERNOGOR, L. F. and ROZUMENKO, V. T., 2013. The physical effects associated with Chelyabinsk meteorite’s passage. Probl. Atom. Sci. Tech. vol. 86, no 4, pp. 136–139.

11. CHERNOGOR, L. F., 2013. The main physical effects associated with the Chelyabinsk bolide passage. In: Asteroids and comets. Chelyabinsk event and study of the meteorite falling into the lake Chebarkul: Proceedings of the international scientific-practical conference. Chelyabinsk, Russia: Krai Ra Publ., pp. 148–152 (in Russian)

12. CHERNOGOR L. F., 2013. Plasma, electromagnetic and acoustic effects of meteorite Chelyabinsk. Inzhenernaya fizika. no. 8, pp. 23–40 (in Russian).

13. CHERNOGOR, L. F. and GARMASH, K. P., 2013. Disturbances in Geospace Associated with the Chelyabinsk Meteorite Passage. Radio Phys. Radio Astron. vol. 18, no. 3, pp. 231–243 (in Russian).

14. CHERNOGOR, L. F., 2013. Large-scale disturbances in the Earth’s magnetic field associated with the Chelyabinsk meteorite. Radiofizika i elektronika. vol. 4 (18), no. 3, pp. 47–54 (in Russian).

15. CHERNOGOR, L. F., MILOVANOV, YU. B., FEDORENKO, V. N. and TSYMBAL, A. M., 2013. Satellite observations of the ionospheric disturbances followed by the fall of Chelyabinsk meteorite. Kosmіchna nauka і tekhnologіya. vol. 19, no. 6, pp. 38–46 (in Russian).

16. CHERNOGOR, L. F. and BARABASH, V. V., 2014. Ionosphere disturbances accompanying the flight of the Chelyabinsk body. Kinemat. Phys. Celest. Bodies. vol. 30, no. 3, pp. 126–136. DOI: https://doi.org/10.3103/S0884591314030039

17. CHERNOGOR, L. F., 2014. Geomagnetic field effects of the Chelyabinsk meteoroid. Geomagn. Aeron. vol. 54, no. 5, pp. 613–624. DOI: https://doi.org/10.1134/S001679321405003X

18. CHERNOGOR, L. F., 2015. Ionospheric effects of Chelyabinsk meteoroid. Geomagn. Aeron. vol. 55, no. 3, pp. 353–368. DOI: https://doi.org/10.1134/S0016793215030044

19. POPOVA, O. P., SHUVALOV, V. V., RYBNOV, Y. S., KHARLAMOV, V. A., GLAZACHEV, D. O., EMELIANENKO, V. V., KARTASHOVA, A. P. and JENNISKENS, P., 2014. Chelyabinsk meteoroid: data analysis. In: ANTIPIN, N. A., ed. 2014. The Chelyabinsk Meteorite – one year on the Earth: Proceedings of All-Russian Scientific Conference. Chelyabinsk, Russia: Kamennyi poyas Publ., pp. 364–376 (in Russian).

20. CHERNOGOR L. F., 2014. Main effects of Chelyabinsk meteorite fall: the results of physical and mathematical modelling. In: ANTIPIN, N. A., ed. The Chelyabinsk Meteorite – one year on the Earth: Proceedings of All-Russian Scientific Conference. Chelyabinsk, Russia: Kamennyi poyas Publ., pp. 229–264 (in Russian).

21. CHERNOGOR, L. F., 2017. Chelyabinsk meteoroid acoustic effects. Radio Phys. Radio Astron. vol. 22, no. 1, pp. 53–66 (in Russian). DOI: https://doi.org/10.15407/rpra22.01.053

22. CHERNOGOR, L. F., 2017. Atmospheric-seismic effect of Chelyabinsk meteoroid. Radio Phys. Radio Astron. vol. 22, no. 2, pp. 123–137 (in Russian). DOI: https://doi.org/10.15407/rpra22.02.123

23. BRONSTEN, V. A., 1983. Physics of Meteoric Phenomena. Dordrecht, Holland: D. Reidel Publ. Co. DOI: https://doi.org/10.1007/978-94-009-7222-3

24. KRUCHINENKO, V. G., 2012. Mathematical and physical analysis of the meteor phenomena. Kyiv, Ukraine: Naukova Dumka Publ. (in Ukrainian).

25. STULOV, V. P., MIRSKII, V. N. and VISLYI, A. I., 1995. Aerodynamics of Bolides. Moscow: Nauka Publ. (in Russian).

26. BROWN, P., SPALDING, R. E., REVELLE, D. O., TAGLIAFERRI, E. and WORDEN, S. P., 2002. The flux of small near-Earth objects colliding with the Earth. Nature. vol. 420, no. 6913, pp. 294–296. DOI: https://doi.org/10.1038/nature01238

27. ADUSHKIN, V. V. and NEMCHINOV, I. V. (eds.), 2005. Catastrophic Impacts of Cosmic Bodies. Moscow, Russia: ECC, Akademkniga Publ. (in Russian).

28. SEDUNOV, YU. S., AVDIUSHIN, S. I., BORISENKOV, E. P., et al (eds.), 1991. Atmosphere. Handbook. Leningrad, Russia: Gidrometeoizdat Publ. (in Russian).

29. MILOVANOV, YU. B. and CHERNOGOR, L. F., 2017. Regularization Algorithm for Calculating Height and Temporal Characteristics Describing the Dynamics of Chelyabinsk Meteoroid Passage Through the Atmosphere. Visnyk Kharkivs’koho Natsional’noho Universytetu. Radiofizyka i elektronika. vol. 26, pp. 75–79 (in Russian).