散乱特性から予想される直接衝突は起こらない
- 散乱の特徴から予想される直接的な衝突は、bi≧5およびbi≦1.5の場合に起こりません。なぜなら、このような場合、粒子はヒル球に入ることができないからです。
- 惑星と衝突する粒子の初期値は、図1(a)と(b)の上の直交軸に示されていますが、衝突するbiのすべての場合で直接衝突が必ずしも起こるわけではありません。
- バンドが分解されると、図3(a)で見られるように、微細構造が現れます。さらに、分解されたバンドにはより高い階層の微細構造もあります。
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和訳お願いします。
初めまして。なんとなくは分かるのですが・・・ 和訳お願いできますでしょうか。 As is expected from the features of the scattering, the direct collision with the planet never occurs for the cases |bi|≧5 and |bi|≦1.5, because in these cases a particle cannot enter the Hill sphere. The initial values of bi, with which a particle collides with the planet are marked on the upper abscissa of Figs. 1(a), and (b). However, for all the cases where bi lies in the collision band, shown in Fig. 1(a), the direct collision does not always occur. When the band is decomposed, the fine structure appears as seen in Figs. 3(a). Furthermore, the decomposed band is found to have also a fine structure of a higher hierarchy. 以上です、宜しくお願いします。
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拡散の特性から想像しうるに、地球との直接衝突は |bi|≧5 and |bi|≦1.5の場合決して起りえない、なぜならこういった場合において粒子はヒル球に入ることができないからである。粒子が地球に衝突する場合のbiの初期値については図1(a)および (b)の上部横座標上に示したとおりである。しかしながら、図1（a）に示してある、bi が衝突バンド上に位置するすべての場合において、直接衝突は常に起らない。バンドが分解される時、図3(a)で確認できるように、微細構造（※１）が現れる。さらに、分解されたバンドもより高い階層の微細構造を有することも発見されている。 ※1：原子物理学においては、原子のスペクトル線に現れる微細な分裂を指す http://ja.wikipedia.org/wiki/%E5%BE%AE%E7%B4%B0%E6%A7%8B%E9%80%A0_%28%E5%8E%9F%E5%AD%90%E7%89%A9%E7%90%86%E5%AD%A6%29
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- この和訳がわからず困っているので、教えてください
If |P(bi~,N1)-P(bi~,2N1)|≦0.05×P(bi~,N1), then P(bi~,N1) (or P(bi~,2N1)) is regarded as the collision probability, Pc(bi~). In Fig.10, Pc(bi~) is illustrated as a function of bi~ at the region near the orbit of the present Earth for the case ei~=4. As seen from this figure, a particle whose impact parameter, bi~, lies between 1.5 and 5.5, collides with the planet with certain probability. Especially, for |bi~|≒2 collisions occur frequently. よろしくお願いいたします。
- ベストアンサー
- 英語
- この文章の和訳をお願いします。
Now, Figs. 3(a) and (b) indicate that there seems to be several discontinuous spikes in the range of |bi| between 1.8 and 2.6, which hereafter is called the discontinuous band. In order to see the detailed features of the scattering in this region, we have calculated the particle orbits in a fine division of bi. The results, which are illustrated in Figs. 3(a) and (b), show that in almost all of the region ⊿b continues smoothly with respect to bi but there remain the fine discontinuous bands near bi=1.92 and bi=2.38. Again we have tried to magnify the range of bi between 1.915 and 1.925 and found that there are still finer discontinuities near bi=1.919(see Figs. 4(a) and (b)).
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- この文章の和訳をお願いします。
In the cases 1.5≦|b_i~|≦3, a particle comes near the planet and, in many cases, is scattered greatly by the complicated manner. Especially, as seen from Fig. 2, all particles with the impact parameter ｜b_i~| in the range between 1.8 and 2.5, of which interval is comparable, as an order of magnitude, to the Hill radius, enter the Hill sphere of the planet. Such a particle, entering the Hill sphere, revolves around the planet along the complicated orbit. After one or several revolutions around the planet it escapes out of the Hill sphere in most cases, but it sometimes happens to collide with the planet as described later. Fig.2. Examples of particle orbits with various values of b_i~ and with e_i~＝0. The dotted circle represents the Hill sphere. All the particles with 1.75＜b_i~＜2.50 enter the sphere. よろしくお願いします。
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These come from the fact that for small values of b~ and μ, as considered here, Eqs.(2・1) and (2.2) are approximately symmetric with respect to the y-axis. Now, we will see features of collision of a particle with the planet. It should be noticed that, as mentioned in §2, the radius of the planet changes with the distance between the Sun and the planet is assigned. Here we will concentrate on the collision near the orbit of the present Earth. よろしくお願いします。
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- 和訳していただけませんか。よろしくお願いします。
In this case we have a positive bf (see Fig. 5(b)). This shows clearly the reason why there exists the discontinuity in bf in spite of the bit difference in bi. Secondly, it is found that as long as we are concerned with the values such as <⊿b>_bi and <⊿e>_bi, averaged over the range of bi between 1.8 and 2.6, contributions from the fine spikes to the averages can be neglected within the error of about 1% when the division of bi is smaller than 10^-3, even if there exists an infinite hierarchy in the fine structure. In the range -1.5≦bi≦1.5, a particle turns back simply to the opposite side of the y-axis along the hair-pin curve, as seen from Fig. 2. Especially, in this case, we have remarkable features; that is, the relations bf=-bi and ef=0, (3.5) or, in other words, ⊿b=-2bi and ⊿e=0, (3.6) hold in a good accuracy.
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However, from a number of orbital calculations, the following two points are made clear. At first, it becomes easy to understand qualitatively the reason why there exist many fine spikes in the scattering pattern of bf. An example of a particle orbit is shown in Fig. 5(a) for the case bi=1.91894, which belongs to the region of a discontinuous band. Here, after the particle revolves around the planet many times, it gets out of the Hill sphere through the gate of the L1-point, and has a negative bf in the final stage. But by just a little bit of difference of the initial value of bi (for example, bi=1.91898), then a particle happens to escape from the Hill sphere through the gate of the L2-point.
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- この文章の和訳をお願いします。
When |b_i~| is relatively large (e.g., |b_i~|≧5), a particle passes through the region far from the Hill sphere of the planet without a significant influence of the gravity of the planet. As seen from Figs. 1(a) and (b), both the impact parameter, b_f~, and the eccentricity, e_f~, at the final stage are not so much different from those at the initial, i.e., a particle is hardly scattered in this case. When 3≦|b_i~|≦5, as seen from Fig. 1(a) and (b), a particle is scattered a little by the gravity of the planet and both |⊿b~| and |⊿e~| increase gradually with the decrease in |b_i~|, where ⊿b~=b_f~－b_i~ (3・1) and ⊿e~=e_f~－e_i~. (3・2) よろしくお願いします。
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We have two kinds of the final stage of the particle orbit: One is the scattering case and another is the collisional case. For the scattering case, after the passage near the planet a particle orbit settles again to the Keplerian at the region far from the planet. The final orbital elements (b_f~, e_f~, ε_f, δ_f), of course, are different from the initial owing to the gravitational interaction with the planet. On the other hand, we regard the case as the collision of the particle with the planet when the distance between the particle and the center of the planet becomes smaller than the planetary radius, r_p, which is given in the units adopted here by r_p=R_p/R=(3M/4πρ)^(1/3)/R, =4.57×(10^－3)h/(R/1AU), (2・12) where R_p and R are the radius of the planet in ordinary units and the distance between the planet and the Sun, respectively. どうかよろしくお願いします。
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- この和訳をおしえて下さい。
In order to see qualitatively the collision frequency, we will define the collision probability, Pc(bi~) as follows. For a fixed value of bi~, orbital calculations are made with N's different value of δ, which are chosen so as to devide 2π(from -πto π) by equal intervals. Let n_c be the number of collision orbits, then P(bi~, N)=n_c/N gives the probability of collision in the limit N→∞. In practice, however, we can evaluate the value of Pc(bi~) approximately, but in sufficient accuracy in use, by the following procedures; i.e., at first for N=N1(e.g., N1=1000), P(bi~,N1) is found and, next, for N=2N1, P(bi~,N) is reevaluated. よくわからないのでよろしくお願いします。
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- この文章の和訳をお願いします。
For the cases where |b_i~| is smaller than about 5.7, a particle with δ*=0 can enter the Hill sphere. The same as for the case e_i~=0, a particle which enters the Hill sphere revolves around the planet and after the complicated motion it escapes from the Hill sphere. As a result of this, the particle has quite different osculating orbital elements at the final stage from the initial. At the same time, a particle sometimes happens to be able to collide with the planet during the revolution. As |b_i~| decreases, the region of δ*, with which a particle experiences a large angle scattering or a direct collision, propagate on both sides around δ*=0 as seen from Fig.7. We can also see from this that the region of |b_i~| where a particle is largely scattered or collides with the planet, is shifted outward (i.e., to the side of large values of |b_i~| in comparison with that for the case e_i~=0). This is due to the fact that a particle has a finite eccentricity in this case and it can come close to the Hill sphere near the perigee point even if the impact parameter |b_i~| is relatively large. Fig.7. The change of the eccentricity ⊿e~ versus the parameter δ*, for particle orbits with various values of b_i~ and with e_i~=4. As b_i~ decreases from 6.0 to 2.0, the regions where a large scattering occurs spread to both sides of δ*=0. For b_i~=1, particles return half way to an opposite side of b_i~=0, conserving the initial eccentricity. 長文になりますが、どうかよろしくお願いします。
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