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2008MI021

dm, F = m dv
dt + c dt
,.

,,3.

[1]

F =0,,2.

v

,cdv
=−dm
m.

,3.

.

,,v = −c log m + A (A).

P,m1v=0.

,(1 − ε)m1.
A,γ, Me,Re, a = h + Re,mh,,,.
m1
εm1 (0 < ε < 1) ,.
m = m1 + P,0 = −c log(m1 + P ) + Av = −c log

γmM ea2v

mv /a.

γmM e
mv 2=a2av=

β = mP1,h γM e i 12h + Re).εcP,0.8m11,β100
1 : 100v.

100km,γ = 6.7 ×10−11 ,M e = 6 × 1024 ,h + Re = 100 + 6378 = 6478,(2).(β3.0kms−1.
,v ' 7.8kms−1m i
m1 + P,m = (1 − ε)m1 + Phε iv = −c log 1 −1+β2,hv1 ' 4.7kms−1(1)

.

,.

,.

,.

δt
δmpuv

m1 , m2m,,.

v

P,2.1.

,2,[(m − δmp)(v + δv) + δmp(−u)] − mv
δtδv
δmp δmp= lim m − (u + v)
−δv
δt→0δtδtδtdv
dmp= m − (u + v)
dt
dt

F = limδt→0,c = u + v,,2.

dmp/dt

dm, dmpdt = − dt

m2P.

m1,(2),1h−c log 1 −(2)2 +P,β = mm1i
εm1
m1 + m 2 + P(1),2h−c log 1 −εm2 i
m2 + P(2)U^4)_041:3þ5 T% °±*M Î 5 U0J5&K)MLNKMB ^C &T % °±/~ O<¦ Î ¶äKMP/í_¦#] Î ¶ S KVÕ(]2,2.

v2 = −c log 1 −εm1εm2 i− c log 1 −m1 + m 2 + P
m2 + P

m1 = m 21,β = 100h¶¦#]V¶Vih

5 c?Á¯W#5BK Sý T ¶_WV]YC<q=M.
~?Ô2C¦ËeY^w~,¶¶mWY]SfpïVM dM(4)x, ydv3dv3dx = 0, dy = 0
y < x < 100,v3.

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v
KYB] Î ¶?~ d ]V¶
x = 17.03, y = 3.65,m = m1 + m2 + m3 = 100P

P1=m1 + m 2100,

m1 = 79.3P, m2 = 17P, m3 = 3.7P, m1 = m2 = 50P.
,,c = 3.0kms−1 , ε = 0.8, β =.

1/100(5).
(3)
3.0, ε = 0.8

m1 = 79.3P, m2 = 17P, m3 = 3.7P, c =v3 ' 8.9kms−1v2 ' 6.1kms−1,.

,,,.

(4) = F,,D(x, y) = Fxx (x, y)Fyy (x, y) − Fxy (x, y)2.

,

1,2,3.

,D(a, b) > 0, Fxx (a, b) < 0,m1 , m2 , m3.3,,iP3hεm1v3 = −c log 1 −m3 + m 2 + m 1 + P
hεm3 i−c log 1 −m3 + Phiεm2−c log 1 −m3 + m 2 + P, F (x, y)(a, b)(6).(5)x, y,D(x, y) = 1.6 × 10−4Fxx (x, y) = −0.3 × 10−2,

(6)

.
.
,,x = 17, y = 3.5.

,(3)

(4)

,(5)

x, y(4)v = 8.90100.
1,β = 100

m1 , m2 , m3y580

P1=
m1 + m 2 + m 3100

Î }A 2
~2Z[}v~[`<\ZIRP¦#]V¶

60

¶?W#]

640,m1 = m2 = m3 = (100/3)P. c =3.0kms , ε = 0.8, m1 = m2 = m3 = (100/3)P8.8−1720

8.5002040860r 1 ^ (4) 5+8Ä&pv3 ' 6.92kms−180x100

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YväZR\C S (Â#5"*~ù ] Î ¶ K T% °±5(º9Y~T (Â SY{ A0/8A8­vm\*85:¶Ò¦<] é U^4)_0V1#3-B]# ¢Rî#5m (Â¶[W<] { A |?~ V4g Z¶ <K*» M_X²C ³R´# Sµ °BU± ^2)02143h5 T ~bñ:Ô:W_C(¦ ÂeÎ" ¶[MRK:ÕEW ¶5/¶Õ¶bW­ ² ³°/±m~VÔCI¦h
im¶
WXC´<µz|{~}
0+þo1 b+ <G WN o #+ hG Q Ä   "  Ë ^#K_Á G :~:·  ¡o¢£¤6,,1. P/m = 100
100P.

,1,2,3,m = m1 + m2 + m3 =,m2 = xP, m3 = yPhε(−yP − xP + 100P ) i
v3 = −c log 1 −101Ph
εyP i−c log 1 −yP + Phi
εxP−c log 1 −yP + xP + Pv ' 7.8kms.
,3m3 = 79.3 : 17 : 3.7
v3 ' 8.9kms−1.
−1

[1]

(4)/)

 ¥¦ 1990.

m1 : m2 :,(/