Modeling Motion, Ablation and Energy Deposition of Meteoroid in the Atmosphere Taking Account of the Curved Trajectory




The problem of modeling the motion, ablation, and energy release of a meteoroid or its fragments moving as a single body is considered. A computer program for calculating the system of meteor physics equations by the Runge-Kutta method is created and tested. The equations take into account the curvilinearity of the trajectory of meteor body, gravity, and change of the heat transfer coefficient along the trajectory. Test calculations were performed for meteor bodies of various sizes moving in the atmosphere. Change of the trajectory angle with respect to the horizon depending on the entry parameters is shown. The effect of taking into account the variability of the trajectory angle on the change of the velocity, mass loss, kinetic energy and trajectory of the meteoroid is estimated.

meteoroid, ablation, energy release, curved trajectory


Volume 21, issue 2, 2020 year


Моделирование движения, абляции и энерговыделения метеороида в атмосфере с учетом криволинейности траектории

Рассматривается задача моделирования движения, абляции и энерговыделения метеороида или его фрагментов, движущихся как единое тело. Создана и протестирована программа численного расчета системы уравнений метеорной физики методом Рунге-Кутты. В уравнениях учитывается криволинейность траектории метеорного тела, сила тяжести и изменение коэффициента теплопередачи вдоль траектории. Проведены тестовые расчеты для движущихся в атмосфере метеорных тел разных размеров, показано изменение угла наклона траектории по отношению к горизонту в зависимости от начальных параметров при входе в атмосферу. Оценивается влияние учета переменности угла наклона траектории на изменение скорости, массы, кинетической энергии и траекторию метеороида.

метеороид, абляция, энерговыделение, криволинейная траектория


Volume 21, issue 2, 2020 year



1. Grigoryan, S. S., “Meteorites motion and destruction in planet atmospheres”, Cosmic Res., Vol. 17, 1979, pp. 724–740. http://adsabs.harvard.edu/abs/1980CosRe..17..724G
2. Melosh, H. J., “Atmospheric breakup of terrestrial impactors,” Proc. Lunar Planet. Sci., Vol. 12A 1981, pp.29–35. http://adsabs.harvard.edu/full/1981mrbf.conf...29M
3. Chyba, C. F., Thomas, P. J., Zahnle, K. J., “The 1908 Tunguska explosion – Atmospheric disruption of a stony asteroid,” Nature, Vol. 361, 1993, pp. 40–44. https://www.nature.com/articles/361040a0
4. Hills, J. G., Goda, M. P., “The fragmentation of small asteroids in the atmosphere,” Astron. J., Vol. 105. No.3, 1993, pp. 1114–1144. http://adsabs.harvard.edu/full/1993AJ....105.1114H
5. Grigoryan, S. S., Ibodov, F. S., Ibadov, S. I., “Physical mechanism of Chelyabinsk superbolide explotion”, Solar Syst. Res., Vol. 47, 2013. pp. 268–274. https://doi.org/10.1134/S0038094613040151
6. Brykina, I. G., “Large meteoroid fragmentation: modeling the interaction of the Chelyabinsk meteoroid with the atmosphere”, Solar Syst. Res., Vol. 52, 2018, pp. 426–434. https://doi.org/10.1134/S0038094618050027
7. Brykina, I. G., Bragin, M. D., Egorova, L. A., “O modeljah fragmentacii meteoroidov v atmosphere,” Fiziko-himicheskaja kinetika v gazovoj dinamike (Phisical-Chemical Kinetics in Gas Dynamics), Vol. 20, No. 2, 2019. (in Russian) http://chemphys.edu.ru/issues/2019-20-2/articles/822/
8. Baldwin, B., Sheaffer, Y., “Ablation and breakup of large meteoroids during atmospheric entry”, J. Geophys. Res., Vol. 76, 1971, pp. 4653–4668. https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/JA076i019p04653
9. Nemchinov, I. V., Popova, O. P., “An analysis of the 1947 Sikhote-Alin event and a comparison with the phenomenon of February 1, 1994”, Sol. Syst. Res., Vol. 31, 1997, pp. 408–420. https://ui.adsabs.harvard.edu/abs/1997SoSyR..31..408N/abstract
10. Ceplecha, Z., Borovička, J., Elford, W. G., ReVelle, D. O., Hawkes, R. L., Porubcan, V. Í., Šimek, M., “Meteor phenomena and bodies”, Space Sci. Rev., Vol. 84, 1998, pp. 327–471. https://link.springer.com/article/10.1023%2FA%3A1005069928850
11. ReVelle, D. O., “NEO fireball diversity: Energetics-based entry modeling and analysis techniques”, Proc. International Astronomical Union Symposium, Vol. 236, 2007, pp. 95–106. Cambridge Univ. Press, Cambridge, United Kingdom. https://doi.org/10.1017/S1743921307003122
12. Avramenko, M. I., Glazyrin, I.,V., Ionov, G.,V., Karpeev, A.,V., “Simulation of the airwave caused by the Chelyabinsk superbolide”, J. Geophys. Res. Atmospheres, Vol. 119, 2014, P. 7035–7050. https://doi.org/10.1002/2013JD021028
13. Ceplecha, Z., ReVelle, D. O., “Fragmentation model of meteoroid motion, mass loss, and radiation in the atmosphere”, Meteorit. & Planet. Sci., Vol. 40, 2005, pp. 35–54. https://doi.org/10.1111/j.1945-5100.2005.tb00363.x
14. Borovička, J., Toth, J., Igaz, A., Spurny, P., Kalenda, P., Haloda, J., Svoren, J., Kornos, L., Silber, E., Brown, P., Husarik, M., “The Košice meteorite fall: Atmospheric trajectory, fragmentation, and orbit”, Meteorit. & Planet. Sci., Vol. 48, 2013, pp. 1757–1779. https://doi.org/10.1111/maps.12078
15. Borovička, J., Spurný, P., Brown, P., Wiegert, P., Kalenda, P., Clark, D., Shrbený, L., “The trajectory, structure and origin of the Chelyabinsk asteroidal impactor,” Nature, Vol. 503, 2013, pp. 235–237. https://doi.org/10.1038/nature12671
16. Wheeler, L. F., Register, P. J., Mathias, D. L., “A fragment-cloud model for asteroid breakup and atmospheric energy deposition”, Icarus, Vol. 295, 2017, pp. 149–169. https://doi.org/10.1016/j.icarus.2017.02.011
17. Borovička, J., Popova, O., Spurný P., “The Maribo CM2 meteorite fall—Survival of weak material at high entry speed”, Meteorit. & Planet. Sci., Vol. 54, 2019, pp. 1024–1041. https://doi.org/10.1111/maps.13259
18. Bronshten, V. A., “Fizika meteornyh yavlenij”, M.: Nauka, 1981. 416 p.
19. Meshcherskiy, I. V., “Raboty po dinamike tel peremennoy massy”, M.: Izd-vo tekhniko-teoreticheskoy literatury, 1952, 280 p.
20. Astapovich, I. S., “Meteornyye yavleniya v atmosfere Zemli”, M.: Fiz-Mat, Lit., 1958. 640 p.
21. Levin, B. Yu., “Fizicheskaya teoriya meteorov i meteornoye veshchestvo v solnechnoy sisteme”, M.: Izd-vo AN SSSR, 1956. 293 p.
22. Brykina, I. G., Egorova, L.,A., “Approximation formulas for the radiative heat flux at high velocities”, Fluid Dyn., Vol. 54, 2019, pp. 562–574. https://doi.org/10.1134/S0015462819040037
23. Johnston, C. O., Mazaheri, A., Gnoffo, P., Kleb, B., Sutton, K., Prabhu, D., Brandis, A. M., Bose, D., “Radiative heating uncertainty for hyperbolic Earth entry, part 1: flight simulation modeling and uncertainty,” J. Spacecraft & Rockets, Vol. 50, No. 1, 2013, pp. 19–38. https://doi.org/10.2514/1.A32254
24. Brykina, I. G., Bragin, M.,D., “On models of meteoroid disruption into the cloud of fragments”, Planetary & Space Sci., Vol. 187, 2020, No 104942. https://doi.org/10.1016/j.pss.2020.104942
25. Turchak, L. I., “Osnovy chislennykh metodov: uchebnoye posobiye dlya studentov vuzov”, M.: Vyssh. shk., 1987, 320 p.
26. Suttles, J. T., Sullivan, E. M., Margolis, S. B., “Curve fits of predicted inviscid stagnation-point radiative heating rates, cooling factors, and shock standoff distances for hyperbolic earth entry,” NASA TN D-7622, 1974. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19740021216.pdf