( ) ,

II 2007 4

0. 0 1 0 2 ( ) 0 3 1 2 3 4, - 5 6 7 1

1 1 1 1) 2) 3) 4) ( ) () H 2.79 10 10 He 2.72 10 9 C 1.01 10 7 N 3.13 10 6 O 2.38 10 7 Ne 3.44 10 6 Mg 1.076 10 6 Si 1 10 6 S 5.15 10 5 Ar 1.01 10 5 Fe 9.00 10 5 2006 IAU 1 1) 2) 3) ( 1 2 or 1 ( 10 ) 2

H He H He H 2 O CH 4 NH 3 () (2006 ) ( km) (1221.5) Fe (3480.0) Fe (6350) Mg,Si,O (6371) Si,Al,Ca,O (6371) H,O (>6371) N,O 1 1-1 1 1) 2) H 2 O (1g/cc) H 2 O H 2 O 3) ( 8g/cc) 1-2 ( ) ( O 2 ) Si 4+ Mg 2+ Mg Si O 2:1:4 3

(a) 0.3871 AU 88.0 day 58.65 day <28 0.7233 224.7 243.01 177.3 1.0000 365.26 day 23 h 56 m 4 s 23.44 1.5237 687 24 h 37 m 23 s 25.19 5.2026 11.862 yr 9 h 50 m 30 s 3.1 9.5549 29.458 10 h 14 m 26.7 19.2184 84.022 17 h 17 m 97.9 30.1104 164.774 18 h 20 m 29.6 39.5399 248.534 6 h 9 m 118 (M) (R) (ρ) (g) (v e ) 332946 696000 km 1.41 g/cm 3 28.01 617.5 km/s 0.055 2439 5.43 0.38 4.25 0.815 6052 5.24 0.91 10.36 1 6378 5.52 1 11.18 0.107 3397 3.93 0.38 5.02 317.832 71398 1.33 2.37 59.57 95.16 60000 0.70 0.95 35.36 14.50 25400 1.30 0.89 21.33 17.22 24300 1.76 1.19 23.77 0.0021 1137 2.1 0.067 0.58 0.0123 1738 3.34 0.17 2.38 4

5

2. 2 1 H H 2 CO 2 N 2 O 2 H 2 O 2 2 T = σt 4 σ σ = 5.67 10 8 J s 1 m 2 K 4 T eq 4πR 2 σt 4 eq = πr 2 (1 A)F R A F 1AU F = 1370 J s 1 m 2 T e f f 4πR 2 σt 4 e f f = [ ] T s >> T eq, T e f f CO 2 T e f f > T eq T s > T eq, T e f f H 2 O CO 2 6

P(bar) 0.13 () 1.013 92 0.006 2 ( ) T s (K) 6430 () 280 750 240 134 ( ) (K)T e f f 5780 250 230 220 130 (K)T eq 256 227 216 98 (vol%) H (91.0) N 2 (78) CO 2 (96.5) CO 2 (95.3) H 2 (88.8) He (8.9) O 2 (21) N 2 (3.5) N 2 (2.7) He (11.1) O(78ppm) Ar (0.9) Ar (70 ppm) Ar (1.6) CH 4 (0.2) 2 3 < 3 Mm kt < G 2 R k G M m k = 1.38 10 23 J/K. v e 1 2 v2 e = G M R 3 2 kt < 1 2 mv2 e 2 2-1 - 2-2 0.3 256 K 2-3 2-4 7

3. 3 1 ( km) (1221.5) Fe (3480.0) Fe (6350) Mg,Si,O (6371) Si,Al,Ca,O (6371) H,O (>6371) N,O = 13.6 ev 1eV=1.602 10 19 J=1.727 10 4 K 3 2 P, T, ( ) ( ) 8

H 2 O 2 3 3 3 3 n A A (g) (l) P, T G(P, T, n g, n l ) = min. (3.1) 9

n g, n l G G = n g µ g (P, T) + n l µ l (P, T) = (n n l )µ g (P, T) + n l µ l (P, T) = nµ g (P, T) n l {µ g (P, T) µ l (P, T)} (n g = n, n l = 0) µ g < µ l P, T (n g = 0, n l = 0) µ g > µ l µ g = µ l G U + PV TS, µ i u + Pv T s (TS ) P, T µ g = µ l (3.2) (3.2) µ P T s = h µ g P δp + µ g T δt = µ l P δp + µ l δt (3.3) T = v, µ T = s v g δp s g δt = v c δp s c δt dp dt dp dt = s eq v = h eq T v - (3.4) (3.5) v v g = RT/P dp dt = h eq RT P (3.6) 2 h () 10

3 4 () AB A B AB A B AB A + B (R3.1) G(P, T, n AB, n A, n B ) = min. (3.7) ξ AB n mol A+B ξ = n G G ξ = 0 (3.8) n AB ξ = 1, n A ξ = 1, n B ξ = 1 (3.9) G n AB + G n A + G n B = 0 (3.10) µ AB + µ A + µ B = 0 (3.11) µ i = µ i (P 0, T) + RT ln(p i /P 0 ) P A P B = P 0 exp ( ) µ AB µ A µ B RT P AB (3.11) = K(T) T x P A : P AB = x : 1 x (3.5) P = P AB + P A + P B x P = K(T) (3.12) 1 x2 T P ( ) ( ) 3 3-1 h (3.6) T T = T 0 P = P 0 3-2 100 C 1 100 C 2260 J g 1 0 C 350 C 11

4. 4 1 Pa=N/m 2 =J/m 3 (c.f. : 1 2 ρv2 + P + ϕ = const) ρ d g P P = ρgd (4.1) z dp dz = ρg (4.2) z r 4 2 ( ) ( ) ( ) 12

PV = NRT (4.3) N 1 mol µ N = Vρ/µ P = ρ RT (4.4) µ (4.4) (4.2) dp dz = µg RT P (4.5) ( P = P 0 at z = z 0 ) [ ] µg(z z0 ) P = P 0 exp RT (4.6) H = RT µg [ ] (z z0 ) P = P 0 exp H (4.7) (4.8) (4.7) H. 1/e (4.7) mgh = kt (4.8) m 1 R = N A k µ = N A m (N A ) (4.8) 1 dp P dz = 1 H(z) H(z) = RT(z) µ(z)g(z) H (4.9) (4.10) 13

4 3 (4.6) z P 0 P << l nσl = 1 (4.11) n σ l = H (4.12) ( ) 4 4 ktr 2GMm = v2 T > 1 v 2 esc ( ) 2 2kT v T = m m 1 ( )ϕ esc ϕ esc = v z f (u)d 3 u (4.13) u v esc,v z 0 f ( m ) 3/2 f (u) = n exp m(v2 x + v 2 y + v 2 z) (4.14) 2πkT 2kT 14

λ ϕ esc = n v T 2π 1/2 (1 + λ)e λ (4.15) λ = mv2 esc 2kT = v2 esc v 2 T 4 4-1 a) b) 1 km 10 K 500 hpa 1000 hpa 300 K 30 g mol 1 10 m s 2 4-2 R (1) r(< R) ρ r (2)(1) r (r = R) 0 (3) ρ c ρ m (ρ c > ρ > ρ m ) 4-3 (1) (4.15) ( ) (2) 1. a σ = 1 10 19 m 2 15

5. 5 1 da dt FdAdt F ( ) ( ) F cond = k dt (5.1) dl F cond l k J K 1 m 1 s 1 k 1 3 ρc pv T l. (5.2) ρc p (κ) ( ) () 5-2 16

0 K (T > 0) ( ) () ν ν + dν = 1 L n x, n y, n z ( nx πx ) ( ny πy ) ( nz πz ) sin sin sin e i2πνt. (5.3) L L L n x, n y, n z 1 2 ( 2 ) ν = c n 2L 2 x + n 2 y + n 2 z (5.4) c ν ν + dν (n x, n y, n z ) 2Lν/c n 2 x + n 2 y + n 2 z 2L(ν + dν)/c. (5.5) (n x, n y, n z ) 2Lν/c 2Ldν/c 1/8 4πL 3 ν 2 dν/c 3 L 8πν 2 dν/c 3. (5.6) 1 ν 1 0, hν, 2hν, 3hν, nhν, ( ) nhν exp ( nhν ) kt < ε ν > n=0 nhν exp ( ) nhν kt < ε ν >= n=0 exp ( ). (5.7) nhν kt 17

< ε ν >= hν exp ( ). (5.8) hν kt 1 ν ν + dν U(ν, T)dν = 8π hν 3 c 3 exp ( ) dν. (5.9) hν 1 kt 5 3 da dω dt ν ν + dν I ν cos θdadωdtdν (5.10) θ da J m 2 sr 1 s 1 Hz 1 = J m 2 sr 1 I ν (radiation intensity) dω θ da da F = I ν cos θdωdν = F ν dν (5.11) F ν = I cos θdω dω u ν da cdt u ν dacdt. (5.12) dt da I ν dtda = u ν dacdt. (5.13) 18

I ν = u ν c (5.14) u ν I ν dω = 4πI ν I ν B ν (T) I ν = c U(ν, T) (5.15) 4π B ν (T) = 2 hν 3 c 2 exp ( ). (5.16) hν kt 1 ρ ds di ν di ν = κ ν ρi ν ds + ρ j ν ds (5.17) κ ν j ν ν ( ) j ν = κ ν B ν (T) (5.18) T di ν = κ ν ρi ν ds + ρ j ν ds = 0 (5.19) I ν = B ν (T) (5.18) - 100km 19

5 5-1 - π 4 15 0 x 3 e x 1 dx = 5-2 da dω dt λ λ + dλ I λ cos θdadωdtdλ (5.20) I λ = B λ (T) = 2hc 2 λ [ 5 exp ( ) ]. (5.21) hc λkt 1 5-3 T (5.21) 3000/T(K) µm 5-4 T = 250 K 6000 K 20

6. 6-1 ( V, A) d edv = F d A (6.1) dt V A e F F d A > 0 F d A < 0 c.f. F = dω dν cos θi ν (θ, ϕ) 6-2 ( 4 ) () ( ) di ν = κ ν ρi ν ds + ρ j ν ds (6.2) j ν = κ ν B ν (T) (6.3) I = I ν dν di = κρids + κρb(t)ds (6.4) 21

B(T) B(T) = σt 4 π (6.5) z τ(z) = z ρκdz. (6.6) (6.4) τ θ ds = dz/ cos θ (6.7) dτ = κρdz (6.4) κρds = dτ/ cos θ (6.8) cos θ di dτ = I B(T) (6.9) 2 (6.9) I τ 2 I (0 < θ < π/2) (π/2 < θ < π) I +, I F up = F down = dω(6.9) cos θ df up dω cos θi = πi + (6.10) dω cos θi = πi (6.11) 2 3 dτ = F up πb (6.12) 2 df down = F down πb (6.13) 3 dτ 22

τ τ + dτ 0 = [ ] [ ] = [F up (τ + dτ) + F down (τ)] [F up (τ) + F down (τ + dτ)] (6.14) F up (τ + dτ) F down (τ + dτ) = F up (τ) F down (τ) (6.15) F up (τ) F down (τ) = (6.16) (τ = 0) F down = 0 F up = F up (τ) F down (τ) = σt 4 e f f (6.12)+(6.13) (6.16) (6.12)-(6.13) 0 = F up + F down 2πB(T). (6.17) 2 d(f up + F down ) 3 dτ = σt 4 e f f. (6.18) F up + F down = 3 2 σt 4 e f f ( τ + 2 ) 3 (6.19) τ = 0 F up = σt 4 e f f, F down = 0 (6.17) πb(t) = σt(τ) 4 = 1 2 σt e f f ( ) 3 2 τ + 1 (6.20) = + σt 4 s = σt 4 e f f + F down(τ total ) (6.21) T s > T(τ total ) σt 4 s = 1 2 σt 4 e f f ( ) 3 2 τ + 2 (6.22) 23

6-3 dq = 0( ) 1mol µ V = µ/ρ P = ρrt/µ C v dt = PdV (6.23) C v dt = RTdρ/ρ (6.24) (5.24) dp dz = ρg (6.25) RdT + RTdρ/ρ = µgdz (6.26) (C v + R)dT = µgdz (6.27) dt dz = µg/c p (6.28) T = T s µg C p z 6 6-1 (1) 4/3 κ ν 1 10 m s 2 (2) 255 K (3) 24