吉川 真

宇宙にある'ごみ'であるスペースデブリが近年非常に多くなってきており,今後の宇宙利用や宇宙開発にとって大きな障害になる懸念が広がってきている。このことは,GPSを利用したり,静止軌道の衛星を今後活用していこうとしている現在の航海技術にとっても他人事ではない。この報告では,このスペースデブリについてまずその現状を簡単にまとめてみることにする。次に,特に静止軌道付近にあるスペースデブリについてその軌道運動を解析した結果を報告する。

We investigated by numerical integrations the long-term orbital evolution of four giant comets or comet-like objects. They are Chiron, P/Schwassmann-Wachmann 1 (SW1), Hidalgo, and 1992AD (5145), and their orbits were traced for 100-200 thousand years (kyr) toward both the past and the future. For each object, 13 orbits were calculated, one for the nominal orbital elements and other 12 with slightly modified elements based on the rms residual of the orbit determination and on the number of observations. As past studies indicate, their orbital evolution is found to be very chaotic, and thus can be described only in terms of probability. Plots of the semi-major axis (a) and perihelion distance (q) of the objects treated here seem to cross each other frequently, suggesting a possibility of their common evolutionary paths. About a half of all the calculated orbits showed q- or a-decreasing evolution. This indicates that, at least on the time scale in question, the giant comet-like objects are possibly on a dynamical track that can lead to capture from the outer solar system. We could hardly find the orbits with perihelia far outside the orbit of Saturn (q>15 AU). This is perhaps because the evolution of the orbits beyond Saturn is so slow that substantial orbital changes do not take place within 100-200 kyr. © 1993 Kluwer Academic Publishers.

We systematically surveyed the orbits of short-period (SP) comets that show a large change of perihelion distance (q) between 1-2 AU (visible comets) and 4-5 AU (invisible comets) during 4400 years. The data are taken from Cosmo-DICE (Nakamura and Yoshikawa 1991a), which is a long-term orbital evolution project for SP comets. Recognizing that q is the most critical element for observability of comets, an invisibility factor (f), defined as the ratio of unobservable time span to observable span during 4400 years, is calculated for each of the large-q-change comets. A detection limit for each comet is obtained from the heliocentric distance at discovery and/or the absolute magnitude at recent apparitions. A mean f value for 35 SP comets with 2.9 ≤ J (J is the Tisserand's invariant) is found to be 19.8. This implies that for each visible SP comet of this J-range, at every epoch of time, there exist about 20 invisible comets near the capture orbits by Jupiter, under the assumptions of steady-state flux and ergodicity for the SP-comet population. © 1992 Kluwer Academic Publishers.

Motions of asteroids in mean motion resonances with Jupiter are studied in three-dimensional space. Orbital changes of fictitious asteroids in the Kirkwood gaps are calculated by numerical integrations for 10 - 10 years. The main results are as follows: (1) There are various motions of resonant asteroids, and some of them are very complicated and chaotic and others are regular. (2) The eccentricity of some asteroids becomes very large, and the variation of the inclination is large while the eccentricity is large. (3) In the 3:1 resonance, there is a long periodic change in the variation of the inclination, when (ω7 : Ω) is a simple ratio (ω7: longitude of perihelion, Ω: longitude of node). (4) In the 7:3 resonance, the variation of the inclination of some resonant asteroids is so large that prograde motion becomes retrograde. Some asteroids in the 7:3 resonance can collide with the Sun as well as with the inner planets. © 1992 Kluwer Academic Publishers. 5 6

The behavior of asteroids at the 5:2, 7:3, and 2:1 resonances with Jupiter is studied in the scheme of the elliptical restricted three-body problem. Following the previous study of Yoshikawa (1990, Icarus, 87, 78-102), the motions of asteroids are investigated by using semianalytical and numerical methods. In semianalytical models, the effect of the inclination of asteroids is taken into account. In numerical integrations, however, only planar cases are treated, but large parameter regions are investigated. The results are summarized as follows: (1) in the 5:2 resonance, the eccentricities of orbits of asteroids change greatly in most of the resonance region, (2) in the 7:3 resonance, the eccentricities of asteroids change greatly mainly in the central part of the resonance region, and (3) in the 2:1 resonance, the eccentricities of asteroids do not change greatly in most of the resonance region. This result for the 2:1 resonance is in agreement with Lemaître and Henrard (1990, Icarus 83, 391-409). Considering these results and the result of Yoshikawa (1990), we can say that the origin of the Kirkwood gaps at the 3:1 and 5:2 resonances can be explained by the scenario of collision with major planets, which was first proposed by Wisdom (1982, Astron. J. 87, 577-593). However, within the restriction of our study, the results obtained here do not support this scenario for the gaps at the 7:3 and 2:1 resonances. In order to reveal the formation mechanism of these gaps, we should study more general cases, that is, the motions of asteroids in three-dimensional space under the perturbation of several planets. © 1991.

The behavior of asteroids at the 3:1 resonance is studied in a large parameter region, and the various motions that these asteroids show are summarized. First, the motions of asteroids are investigated qualitatively using a semianalytical method, and the variations of (a, σ) and (e, ω) are obtained graphically for various values of the parameters (a = semimajor axis, σ = critical argument, e = eccentricity, ω = longitude of perihelion). Next, to know the motions of asteroids more quantitatively, the orbital changes in asteroids are calculated by numerical integrations in the scheme of a planar elliptical restricted three-body problem. The main results are as follows: (1) The variations in a and σ are rather complicated, and the variations in e and ω depend strictly on the behavior of these elements. (2) The region where the resonance occurs is obtained on the a-e plane, and almost all numbered asteroids avoid this region. (3) The eccentricities of most asteroids in the resonance region change markedly (Δe {greater-than or approximate} 0.2 or much larger), and these changes take place in a period of 10 -10 years. (4) In terms of the orbital changes of asteroids, the resonance region shows a complicated structure. © 1990. 4 5

この論文は国立情報学研究所の電子図書館事業により電子化されました。

The motions of asteroids in the mean motion resonances with Jupiter are investigated by a semi-analytical model. By using this model, it is found that eccentricities of asteroids may become very large when asteroids are in one of the resonances. These large increases in eccentricity are also confirmed by the numerical integrations. The gaps in the asteroidal belt can be explained by these large variations of eccentricities. It is known that asteroids show chaotic behavior when they are in the mean motion resonances. In this paper, the chaotic behavior of asteroids in the 7:3 resonance is shown.

The motions of asteroids in the secular resonance υ 6 are investigated by a simple analytical model. By using this model, it is found that eccentricities of asteroids may become very large (e ∼ 0.8) when asteroids are in or near this resonance. These large increases in eccentricity are also confirmed by numerical integrations. The strongly depopulated region in the asteroidal belt, which corresponds to the position of the secular resonance υ6, is explained well by this analytical model. © 1988.

When asteroids are in the secular resonance ν , the variation of the eccentricity becomes very large. In this paper, the dynamics of this secular resonance ν is investigated by a simple analytical model, in which the third degree terms of the eccentricity and inclination are taken into account. The eccentricity variations of asteroids located near this resonance are represented clearly by the diagrams of equi-Hamiltonian curves on the plane of {Mathematical expression} versus e ( {Mathematical expression} the longitude of perihelion of asteroids and Saturn, e: the eccentricity of asteroids). These diagrams predict that the eccentricity of these asteroids suffers a large increase or decrease, and that the secular resonance argument {Mathematical expression} librates about 0° and 180°. In order to confirm these predictions, numerical integrations are carried out over one million years. By these integrations, it is found that the eccentricity of secular resonant asteroids becomes more than 0.8, and that the libration about 0° also exists, as well as the libration about 180°. The strongly depopulated region in the asteroidal belt, which corresponds to the position of the secular resonance ν , is also explained well by this analytical model. © 1987 D. Reidel Publishing Company. 6 6 6

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