小行星形状和自转参量的观测研究
摘要
按照太阳系的行星由星云塌缩而成的演化理论，对在太阳系中处于特殊位置和具有特殊存在形态的小行星的物理参数的研究，可以为太阳系早期演化条件提供证据；为小行星碰撞演化研究提供边界条件。对其中具有代表意义的小行星样本的物理参数进行观测研究更有意义。
光电测光观测是研究小行星物理参数的主要手段之一，由小行星自转光变曲线推断出的小行星的形状和自转参数是以上两方面研究工作所必需的数据。在对现有自转速率的小行星进行统计分析时发现，直径在100—150公里之内的小行星的自转速率具有较为特殊的性质，这一特性与小行星的碰撞经历有关。为此，我选定了一些直径在125公里左右的小行星进行观测和分析；一方面，测定它们的自转周期，进行“角动量衰减”现象的研究，另一方面，对小行星形状和自转轴指向进行估算，为小行星碰撞演化研究提供更为有利的证据。
论文首先介绍了较为基础的有关小行星形状和自转参数的测定方法，然后描述了本人的研究工作内容。第一章说明了对小行星进行测光观测的意义。为了了解小行星的光度这个物理量，在第二章中介绍了两种经典的小行星光度模型，讨论了小行星光度随相位角的变化及冲效应对光度的影响，分析说明了引起小行星光度变化的若干因素。第三章着重阐述了小行星形状和自转参数的研究方法，针对目前人们最常用的综合振幅和周期的方法所存在的问题——解的收敛问题，提出了一种解决的方法。第四章对小行星自转速率与直径的
关系进行了统计分析，选定了一批直径125公里左右的小行星进行观
测研究，给出了部分已处理完毕的小行星的自转周期、形状及自转轴
指向的结果。近年来，发现了越来越多的非单一周期光变的小行星，
对这类更特殊的小行星的观测分析可能会对小行星碰撞演化理论的
研究有着积极的推动作用。因此，在第五章中，针对2002年所观测
的一颗非单一周期光变的小行星(469)的情况，尝试利用小行星受迫
进动或双小行星运动理论，对(469)的光变曲线进行了解释。
目前，对直径125
究仅仅是一个开始，
公里左右的小行星的形状和自转参数的观测研
随着观测样本的不断扩充和反演方法的不断完
善，不难想象，这一工作的研究结果会让我们更好地理解小行星的碰
撞演化，甚至太阳系的演化。
According to the evolution theory of the solar system, the planets were formed from collapse of the planetesimal clouds. The asteroids, occupying the transition region between the rocky terrestrial planets and the outer gas giants with special configuration, underwent the collision evolution process. Thus, the physical parameters of the asteroids provide us with a blueprint about the conditions of the early solar system and the boundary conditions for the its evolution. Especially, the study of representative objects, can finish this task efficiently.
The photometric observation of the asteroids is an important way to study their physical parameters. The rotation and shape parameters of the asteroids derived from the lightcurves are necessary data for the evolution studies of the solar system and theirselves. In order to select the proper objects to observe and analyze, we made a statistic study on the rotational period, and selected the asteroids with diameter of about 125km as the objects. We had observed more than ten selected asteroids using 1-meter telescope in Yunnan Observatory during 2000 to 2002. The observational data of seven asteroids had been reduced and analyzed. We
have derived their synodic periods and estimated the shape and orientation of rotational axis for one asteroid.
In this thesis, several aspects were involved: (1) Why do we study the asteroids? (2) Based on two classical photometric models of the asteroids, the luminosity variation of the asteroids were introduced. There is significant difference between the luminosity variation due to the rotation surrounding a unique axis and the one due to rotation accompanying with the precession and the eclipse of binary asteroids. (3) We introduced the methods to estimate the shape and rotation of the asteroids with the lightcurves. With the improved NEWTON iteration method, we propose a method to solve the problem on the convergence of the iteration when the initial value is far from the real solution. (4) Before the presentation of results of our observations and analysis, the corrections for the CCD images and the methods to analyze the observational data were introduced. (5) In order to analyze the lightcurves of (469) with multi-periods, the theories about the precession of the asteroids and the eclipse of the binary asteroids were involved. By these basic theories, we give an explanation for the light variation of (469).
As long as the number of the samples is increased and the methods of estimation for the rotation and shape of the asteroids are improved continuously, this kind of research will help us to understand the evolution of the asteroids, and even the evolution of the solar system.
光电测光观测是研究小行星物理参数的主要手段之一，由小行星自转光变曲线推断出的小行星的形状和自转参数是以上两方面研究工作所必需的数据。在对现有自转速率的小行星进行统计分析时发现，直径在100—150公里之内的小行星的自转速率具有较为特殊的性质，这一特性与小行星的碰撞经历有关。为此，我选定了一些直径在125公里左右的小行星进行观测和分析；一方面，测定它们的自转周期，进行“角动量衰减”现象的研究，另一方面，对小行星形状和自转轴指向进行估算，为小行星碰撞演化研究提供更为有利的证据。
论文首先介绍了较为基础的有关小行星形状和自转参数的测定方法，然后描述了本人的研究工作内容。第一章说明了对小行星进行测光观测的意义。为了了解小行星的光度这个物理量，在第二章中介绍了两种经典的小行星光度模型，讨论了小行星光度随相位角的变化及冲效应对光度的影响，分析说明了引起小行星光度变化的若干因素。第三章着重阐述了小行星形状和自转参数的研究方法，针对目前人们最常用的综合振幅和周期的方法所存在的问题——解的收敛问题，提出了一种解决的方法。第四章对小行星自转速率与直径的
关系进行了统计分析，选定了一批直径125公里左右的小行星进行观
测研究，给出了部分已处理完毕的小行星的自转周期、形状及自转轴
指向的结果。近年来，发现了越来越多的非单一周期光变的小行星，
对这类更特殊的小行星的观测分析可能会对小行星碰撞演化理论的
研究有着积极的推动作用。因此，在第五章中，针对2002年所观测
的一颗非单一周期光变的小行星(469)的情况，尝试利用小行星受迫
进动或双小行星运动理论，对(469)的光变曲线进行了解释。
目前，对直径125
究仅仅是一个开始，
公里左右的小行星的形状和自转参数的观测研
随着观测样本的不断扩充和反演方法的不断完
善，不难想象，这一工作的研究结果会让我们更好地理解小行星的碰
撞演化，甚至太阳系的演化。
According to the evolution theory of the solar system, the planets were formed from collapse of the planetesimal clouds. The asteroids, occupying the transition region between the rocky terrestrial planets and the outer gas giants with special configuration, underwent the collision evolution process. Thus, the physical parameters of the asteroids provide us with a blueprint about the conditions of the early solar system and the boundary conditions for the its evolution. Especially, the study of representative objects, can finish this task efficiently.
The photometric observation of the asteroids is an important way to study their physical parameters. The rotation and shape parameters of the asteroids derived from the lightcurves are necessary data for the evolution studies of the solar system and theirselves. In order to select the proper objects to observe and analyze, we made a statistic study on the rotational period, and selected the asteroids with diameter of about 125km as the objects. We had observed more than ten selected asteroids using 1-meter telescope in Yunnan Observatory during 2000 to 2002. The observational data of seven asteroids had been reduced and analyzed. We
have derived their synodic periods and estimated the shape and orientation of rotational axis for one asteroid.
In this thesis, several aspects were involved: (1) Why do we study the asteroids? (2) Based on two classical photometric models of the asteroids, the luminosity variation of the asteroids were introduced. There is significant difference between the luminosity variation due to the rotation surrounding a unique axis and the one due to rotation accompanying with the precession and the eclipse of binary asteroids. (3) We introduced the methods to estimate the shape and rotation of the asteroids with the lightcurves. With the improved NEWTON iteration method, we propose a method to solve the problem on the convergence of the iteration when the initial value is far from the real solution. (4) Before the presentation of results of our observations and analysis, the corrections for the CCD images and the methods to analyze the observational data were introduced. (5) In order to analyze the lightcurves of (469) with multi-periods, the theories about the precession of the asteroids and the eclipse of the binary asteroids were involved. By these basic theories, we give an explanation for the light variation of (469).
As long as the number of the samples is increased and the methods of estimation for the rotation and shape of the asteroids are improved continuously, this kind of research will help us to understand the evolution of the asteroids, and even the evolution of the solar system.
引文
[1] Binszel, R. P., An overview of the asteroids, 1989, In Asteroids Ⅱ,3-18
[2] Kepler, J. Mysterium Cosmographicm, 2nd ed., 1621, (Frankfurt: G. Tampachii.)
[3] Kant, Ⅰ. Allgemeine Naturgeschichte und Theorie des Himmels, 1755, (Konigsberg and Leipzig: J.F. Petersen), PP 18ff—163ff
[4] Chladni, E.F.E., ber den Usprung der von pallas gefundenen und anderer ihr hnlicher Eisenmassen (Riga: J.F. Hartknoch), 1794, pp. 56-59, Rpt. 1974, Meteoritical Society, with introduction by J.T. Wasson.
[5] Proctor, R.A.,Other world than ours, (New York: D. Appleton),pp220-229.
[6] Schmidt, O. Yu.,Meteortic theory of the origin of the Earth and planets Doklady Acad. Nauk 45: 229-233.
[7] Chamberlin, T.C., Fundamental problems of geology. Carnegie Inst. Of Washington Year Book 3:195-258.
[8] Safronov, V.S., Evolution of the protoplanetary cloud and formation of the Earth and planets (Moscow: Nauka),1969, In Russian, Trans. NASATT F-667,1972
[9] Safronov, V.S., On the origin of asteroids. ,1979, In Asteroids, ed. T. Gehrels (Tucson: Univ. of Arizona Press),pp 975-993
[10] Wisdom, J., Meteorites may follow a chaotic route to Earth. Nuture 315, 731-733.
[11] Wetherill,G W., A steroidal source of ordinary chondrites. Meteoritics 20:1-22.
[12] Mcfadden, L.-A. Physical properties of Atens, Apollo and Amor asteroids., 1989, In Asteroids Ⅱ, ed. Binzel, R.P., et al., Tucson: Univ. of Arizona Press, 442-467
[13] Binzel, R.P., et al., Asteroid rotation rates: Distribution and statistics. 1989, In Asteriods, pp.416-441
[2] Kepler, J. Mysterium Cosmographicm, 2nd ed., 1621, (Frankfurt: G. Tampachii.)
[3] Kant, Ⅰ. Allgemeine Naturgeschichte und Theorie des Himmels, 1755, (Konigsberg and Leipzig: J.F. Petersen), PP 18ff—163ff
[4] Chladni, E.F.E., ber den Usprung der von pallas gefundenen und anderer ihr hnlicher Eisenmassen (Riga: J.F. Hartknoch), 1794, pp. 56-59, Rpt. 1974, Meteoritical Society, with introduction by J.T. Wasson.
[5] Proctor, R.A.,Other world than ours, (New York: D. Appleton),pp220-229.
[6] Schmidt, O. Yu.,Meteortic theory of the origin of the Earth and planets Doklady Acad. Nauk 45: 229-233.
[7] Chamberlin, T.C., Fundamental problems of geology. Carnegie Inst. Of Washington Year Book 3:195-258.
[8] Safronov, V.S., Evolution of the protoplanetary cloud and formation of the Earth and planets (Moscow: Nauka),1969, In Russian, Trans. NASATT F-667,1972
[9] Safronov, V.S., On the origin of asteroids. ,1979, In Asteroids, ed. T. Gehrels (Tucson: Univ. of Arizona Press),pp 975-993
[10] Wisdom, J., Meteorites may follow a chaotic route to Earth. Nuture 315, 731-733.
[11] Wetherill,G W., A steroidal source of ordinary chondrites. Meteoritics 20:1-22.
[12] Mcfadden, L.-A. Physical properties of Atens, Apollo and Amor asteroids., 1989, In Asteroids Ⅱ, ed. Binzel, R.P., et al., Tucson: Univ. of Arizona Press, 442-467
[13] Binzel, R.P., et al., Asteroid rotation rates: Distribution and statistics. 1989, In Asteriods, pp.416-441