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この文章の和訳を教えてください。

It should be noticed that Λ_f is independent of both ei~ and R. In order to compare Λ_K with Λ_f clearly, we consider the ratio of these, that is, γ=Λ_K/Λ_f=3.0C_K(R/1AU)^1/2, (4・9) which is independent of the mass of the planet. The values of γare listed in Table I as well as those of C_K. As the parameter C_K is approximately proportional to R^-1/2 (see Fig.11), γ is almost independent of R and is 2.3 for ei~=0 and 1.4 for ei~=4. This indicates that, though the result is obtained in the limited framework of the two-dimensional particle motion, the collisional rate of Keplerian particles is enhanced by a factor of about 2.3 or 1.4 compared to that estimated in a free space formula, as long as we are concerned with the two cases of eccentricity. Furthermore, as seen from Table I, γ for the case ei~=4 is significantly smaller than that of the case ei~=0. This seems to confirm the conjecture that γ tends to unity in the high energy limit (i.e., ei~→∞), or in other words, the free space formula is right only in the high energy limit. お手数ではございますが、どうかよろしくお願いいたします。

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  • ddeana
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Λ_f がei~ と R双方と無関係であることに気づくべきである。 Λ_KとΛ_f を明確に比較する為に、我々はこれらの比率を以下のように見なす。 γ=Λ_K/Λ_f=3.0C_K(R/1AU)^1/2, (4・9) この公式は惑星の質量とは無関係である。 γの値に関してはC_Kの値同様、表1に記載されている。パラメーター C_K はほぼ R^-1/2に比例するので(図11参照のこと)γはRにほぼ依存しておらず、その値はei~=0の時には2.3で、ei~=4の時は1.4である。これは、二次元粒子運動の限られた枠組における結果であったとしても、ケプラー粒子の衝突速度は自由空間数式において予測されるものと比較して2.3もしくは1.4倍強められることを示している。更に表1で示した通り、ei~=4の場合のγはei~=0の場合よりも著しく小さい。これはγが高エネルギー限界(i.e., ei~→∞)で1になる傾向があるという推測を確かにするものであり、言い換えれば自由空間数式は高エネルギー限界領域においてのみ正解ということである。 「ケプラーの法則」は専門外なので不適当な訳があった場合はご容赦ください。

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  • これの和訳を教えてください。

    The evaluated values of C_K are shown in Fig. 11 and listed in Table I for the cases ei~=0 and 4, respectively. As is seen from Fig.11, C_K is approximately proportional to R~-1/2 and v_K also has the same dependence on R. Therefore, Λ_K is almost independent of R. On the other hand, the collisional rate for a free space, Λ_f is given by Λ_f=n_s2R_p(1+2θ)^(1/2)v(ei~), (4・7) where v(ei~) is the mean random velocity of an ensemble of particles with an eccentricity, ei~, and is given by √(5/8)ei~hv_K and θ is the Safronov number, which is defined as GM/v^2(ei~)R_p. For the cases ei~≦4, θ is much larger than unity, and then Eq.(4・7) is approximately rewritten as             Λ_f=(8GMR_p)^(1/2)n_s. (4・8)

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    The evaluated values of C_K are shown in Fig. 11 and listed in Table I for the cases ei~=0 and 4, respectively. As is seen from Fig.11, C_K is approximately proportional to R~-1/2 and v_K also has the same dependence on R. Therefore, Λ_K is almost independent of R. On the other hand, the collisional rate for a free space, Λ_f is given by Λ_f=n_s2R_p(1+2θ)^(1/2)v(ei~), (4・7) where v(ei~) is the mean random velocity of an ensemble of particles with an eccentricity, ei~, and is given by √(5/8)ei~hv_K and θ is the Safronov number, which is defined as GM/v^2(ei~)R_p. For the cases ei~≦4, θ is much larger than unity, and then Eq.(4・7) is approximately rewritten as             Λ_f=(8GMR_p)^(1/2)n_s. (4・8) よろしくお願いします。

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