﻿ 小行星撞击地球的能量 The Energy of an Asteroid Hitting the Earth

Astronomy and Astrophysics
Vol.04 No.03(2016), Article ID:18016,9 pages
10.12677/AAS.2016.43006

The Energy of an Asteroid Hitting the Earth

Chaoqiong He1,2, Jianpo Guo1,2, Rongqin Cang1,2, Juanxiu Hu1,2

1Department of Science and Technology, Puer University, Puer Yunnan

2Open Key Laboratory of Mechanics in Yunnan Province, Puer Yunnan

Received: Jun. 24th, 2016; accepted: Jul. 16th, 2016; published: Jul. 19th, 2016

ABSTRACT

An asteroid hitting the Earth may cause the extinction of dinosaurs, 65 million years ago. The research aim of this paper is how the energy of the asteroid hitting the Earth can be depending on the chosen of the aphelion distance and the perihelion distance, while the mass of the asteroid is fixed. The adopted aphelion distance of the asteroid is 1.90, 2.15, 2.65, 3.25, 3.95 and 5.2075 AU, respectively. The adopted perihelion distance of the asteroid is 1.0009, 0.95, 0.90, 0.85, 0.80, 0.75, 0.70, 0.65, 0.60, 0.55 and 0.50 AU, respectively. Our calculated results show that the larger the aphelion distance of the asteroid is, the larger the energy of its hitting the Earth is; the smaller the perihelion distance of the asteroid is, the larger the energy of its hitting the Earth is; the minimum kinetic energy of the asteroid hitting the earth is 1.0725 ´ 1023 J, and the maximum kinetic energy is 5.8280 ´ 1023 J.

Keywords:Asteroids, Earth, Solar System

1普洱学院理工学院，云南 普洱

2云南省高校力学开放重点实验室，云南 普洱

1. 引言

2. 计算方法

2.1. 小行星撞击地球过程中的几个近似假设

(1)

2.2. 轨道相切

(2)

(3)

(4)

(5)

(6)

(7)

2.3. 轨道穿插

(8)

(9)

Figure 1. The diagram that an asteroid’s orbit is tangential to the Earth’s orbit

Figure 2. The diagram that an asteroid’s orbit crosses the Earth’s orbit

(10)

(11)

(12)

(13)

2.4. 撞击升温

(14)

3. 计算结果

3.1. 小行星的质量

6500万年前，灭绝恐龙的那颗小行星的直径约为10千米 [17] ；大多数小行星的密度为 [2] [10] ，在本文中我们采用中间值。根据公式(1)，可以求出灭绝恐龙的那颗小行星的质量为

3.2. 小行星刚被地球捕获时的绝对速率

3.3. 小行星刚被地球捕获时的相对速率

Table 1. The absolute velocity of an asteroid, when it is just captured by the Earth. The velocity is in unit of m/s

Table 2. The relative velocity of an asteroid, when it is just captured by the Earth. The velocity is in unit of m/s

3.4. 小行星撞击地面时的速率和动能

Table 3. The velocity of an asteroid, when it is hitting the Earth. The velocity is in unit of m/s

Table 4. The kinetic energy of an asteroid, when it is hitting the Earth. The energy is in unit of the joule

Table 5. The kinetic energy of an asteroid, when it is hitting the Earth. The energy is in unit of trillion tons of TNT

[2] [17] ，那里的地壳厚度可以近似认为是20千米。小行星可以将194倍自身质量的地壳全部熔化，就意味着小行星可以将撞击点附近很大范围内的地壳全部撞穿，地幔物质喷涌而出，引起大规模的火山爆发，火山灰遮天蔽日达数年之久，气温骤降，最终导致恐龙灭绝。

4. 讨论

4.1. 与前人工作对比

4.2. 太阳演化对地球和小行星轨道的影响

The Energy of an Asteroid Hitting the Earth[J]. 天文与天体物理, 2016, 04(03): 47-55. http://dx.doi.org/10.12677/AAS.2016.43006

1. 1. DeMeo F E, Carry B. Natur., 2014, 505: 629 http://dx.doi.org/10.1038/nature12908

2. 2. Fernández Y R, Li J Y, Howellc E S, Woodney L M. Treatiseon // Schubert, G., Editor in Chief, Spohn, T., Editor, Geophysics. 2nd Edition, Volume10 Chapter 15

3. 3. Clark B E, Ziffer J, Nesvorný D, et al. JGRE, 2010, 115: E06005

4. 4. Ockert-Bell M E, Clark B E, Shepard M K, et al. Icar., 2010, 210: 674 http://dx.doi.org/10.1016/j.icarus.2010.08.002

5. 5. Fornasier S, Clark B E, Dotto E. Icar., 2011, 214: 131 http://dx.doi.org/10.1016/j.icarus.2011.04.022

6. 6. Carry B. Planetary and Space Science, 2012, 73: 98 http://dx.doi.org/10.1016/j.pss.2012.03.009

7. 7. Bottke W F Jr, Durda D D, Nesvorný D, et al. Icar., 2005, 175: 111

8. 8. 约翰•巴利, 波•瑞普斯, 著. 萧耐园译. 恒星与行星的诞生. 长沙: 湖南科学技术出版社, 2009

9. 9. Morbidelli A, Lunine J I, O’Brien D P, et al. AREPS, 2012, 40: 251

10. 10. Britt D T, Consolmagno G J. M&PS, 2003, 38: 1161 http://dx.doi.org/10.1111/j.1945-5100.2003.tb00305.x

11. 11. Consolmagno G J, Britt D T. M&PS, 1998, 33: 1231 http://dx.doi.org/10.1111/j.1945-5100.1998.tb01308.x

12. 12. Pravec P, Harris A W. Icar., 2000, 148: 12 http://dx.doi.org/10.1006/icar.2000.6482

13. 13. Margot J L, Nolan M C, Benner L A M, et al. Sci., 2002, 296: 1445 http://dx.doi.org/10.1126/science.1072094

14. 14. Descamps P, Marchis F, Berthier J, et al. Icar., 2011, 211: 1022 http://dx.doi.org/10.1016/j.icarus.2010.11.016

15. 15. Taylor P A, Howell E S, Nolan M C, et al. AAS/DPSMA, 2013, 45: 208.08

16. 16. Brown P. JIMO, 2013, 41: 22.

17. 17. Alvarez L W, Alvarez W, Asaro F, Michel H V. Sci., 1980, 208: 1095 http://dx.doi.org/10.1126/science.208.4448.1095

18. 18. Allen C W. Astrophysical Quantities. London: The Athlone Press, 1973

19. 19. David F. APS/4CF, 1998, J1: 2

20. 20. Sackmann I-J, Booththroyd A I, Kraemer K E. ApJ, 1993, 418: 457 http://dx.doi.org/10.1086/173407

21. 21. Silvotti R, Schuh S, Janulis R, et al. Natur., 2007, 449: 189 http://dx.doi.org/10.1038/nature06143

22. 22. Schröder K-P, Smith R C. MNRAS, 2008, 386: 155 http://dx.doi.org/10.1111/j.1365-2966.2008.13022.x

23. 23. Kunitomo M, Ikoma M, Sato B, et al. ApJ, 2011, 737: 66 http://dx.doi.org/10.1088/0004-637X/737/2/66

24. 24. Veras D, Wyatt M C. MNRAS, 2012, 421: 2969 http://dx.doi.org/10.1111/j.1365-2966.2012.20522.x

25. 25. Veras D, Wyatt M C, Mustill A J, et al. MNRAS, 2011, 417: 2104 http://dx.doi.org/10.1111/j.1365-2966.2011.19393.x

26. 26. Guo J P, Lin L, Bai C Y, Liu J Z. Ap&SS, 2016, 361: 122 http://dx.doi.org/10.1007/s10509-016-2684-5