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1 No ADS (.0) Cas Psc Cas CMa Gem Leo UMa Vir Boo Her 36 Oph Oph 70 Oph 1 Lyr 2 Lyr Cyg 61 Cyg Cyg Aqr (.0) (A) (B) (cm) 0 h 49 m h 29 m h 45 m h 18 m h 41 m h 51 m h 41 m h 15 m h 03 m h 05 m h 02 m h 34 m h 20 m h 44 m h 44 m h 45 m h 06 m h 44 m h 28 m ADS R. G. Aitken New General Catalogue of Double Stars Alan Hirshfeld and Roger W. Sinnott Sky Catalogue.0 Vol. 2 W. S. Finsen and C. E. Worley Third Catalogue of Orbits of Visual Binary Stars
2 A B, C W Catalogus 795 stllarum duplicium, Dorpat, , Cata-logus Novus Mcnsurae Micrometricae Positiones Mediae W Pulkowa Catalogue Otto Struve Catalogue of Eighty-one Double
3 Stars Discovered with Six inch Alvan Clark Refractor 1340 A General Catalogue of Double Stars within 121 of the North Pole, Carnegie Institution of Washington, R. G. New General Catalogue of Double Stars within 120 of the North Pole, Carnegie Institution of Washington, ADS m1, m2 m m1, m2, m J1, J2, J J1 J m1 J2 J m2 J J m J0 m 0 J J1 + J m m m2 m m1 2.5log{ (m1-m2) } 1 m m1 m2 m m1, m2 m1 m + 2.5log m
4 W. R D D cm T. Lewis 12.2 D D 41.9 D 91.4 D cm
5 P n T e a i P n 360 P T e a i t n 360 P M n ( t T ) E e sin E R a ( 1 e cos E ) tan ( v / 2 ) {( 1 + e ) / ( 1 e )}tan( E / 2 ) tan ( - tan ( v + ) cos i R cos ( v + ) sec ( - ) M R E v a a 3 P 2 G 4 2 ( M 1 + M 2 ) 3
6 p a p a a P 3 M 1 + M 2 p a a a a A.U. p M 1 + M 2 M 1 + M GP 2 a p 3 5 M 1 a 2, a a 1 + a 2 M 2 a 1 A B A B C C A B C,, A ( 0 ) ( ) x y B, C ( x, y ) ( x, y ) x cos ( - 0 ), y sin ( - 0 ) x cos ( - 0 ), y sin ( - 0 ) M B M 2 M A + M B M 1 + M 2 AB O x, y C C x x a 0 + a 1 ( t t 0 ) 6 y y b 0 + b 1 ( t t 0 ) a 0, a 1, b 0, b 1 t 0 t
7 ( x, y ) ( x, y ) 6 a 0, a 1, b 0, b 1 C i P T K 1 V 0 e a 1 sin i f(m 2, M 1 ) a i
8 P T a e Cas ADS 671 0h 49.1m i n Dorrit Hoffleit The Bright Star Catalogue Yale University Observatory, a a a AU p e a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a P M 1 + M 2 a 3 P
9 Paul Couteau A. H. Batten Observing Visual Double Stars 0.39 M 1 M 2 M M 1 + M 2 M M M i i
10 Cas T. J. J. See Researches on the Evolution of the Stellar Systems volume 1, P T a e i n
11 Psc ADS h 2.0m P T a e 720 i n BS p a a p AU a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P
12 Cas AB ADS h 29.1m P T a e 840 i n BS p a a 2.27 p AU 2.5 a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P
13 P T a e CMa ADS h 45.1m i n BS p a a p AU a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P M M
14 HR Russell, Dugan and Stewart Astronomy
15 HR 1920 G, K, M HR F. W C. H
16 1861 T. H A. G cm Why, father it has a companion! 1864 P T a e i T. J. J. See P T a e i n T, J, J, See Researches on the Evolution of the Stellar Systems vol. 1, 1896.
17 10 1 m p D M M m 5logD + 5 m + 5log p + 5 A, B M A log M B log W. S m F0 HR 10 10,000 10,000 1,000, , W. W A. S. F0 8, ,800km ,000gr/cm 3 V E km/sec V E M M
18 V E M M 2/3 1/3 R M R V E 20km/sec W. S m 1925 H + 26km/sec H km/sec + 4.3km/sec km/sec The Internal Constitution of the Stars 2,000
19 Te M vis R log R Te 5 M vis R ,000km 20,740km M R 3 V E V E 39,299 39, ,451g/cm 3 M km/sec R S. W. Burnham A General Catalogue of Double Stars part 2, 1906.
20 P T a e Gem ADS h 34.6m J. J i n BS p a a p AU 2.4 a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P
21 A, B AB C AB W.S Finsen and C. E. Worley Third Catalogue of Visual Binary Stars, Preliminary B 1896 A. Belopolsky Bb a 1 Gem A 1905 H. D. Curtis Aa a 2 Gem Aa, Bb Curtis Bb 2.85m A0 P T 2,416, JD K km/sec V km/sec e a 1 sin i km f(m 2, M 1 ) Aa 1.99m A ,416, JD 13.56km/sec +6.20km/sec km C 1920 W. S. Adams A. H. Joy Joy R. S. Sanford Cc 9.0m M1e P T 2,423, JD K km/sec K km/sec V km/sec e 0.0 a 1 sin i km a 2 sin i km M 1 sin 3 i 0.63 M 2 sin 3 i 0.57 van Gent a i i 86.4 a C c
22 Cc i 86.4 a 1, a 2, M 1, M 2 a km a km a a 1 + a km 0.018AU 3.88R M M MCc M 1 + M C, c R1, R2 a R R 0.76RR R 0.68R 1AU km R km Cc log M { M bol + 2 log ( Te 5200 ) 5.20 } M bol Te A, B A0 A, B log M B ( m A m B ) 0.12 ( ) M A M B : M A M A + M a 2.67M B + M b 2.03
23 Aa P a ( P M A + M a ) 2/3 ( ) 2/ AU Bb P a ( P M B + M b ) 2/3 ( ) 2/ AU i sin 3 i sin 3 i Aa f (M 2, M 1 ) M a 3 sin 3 i ( M A + M a ) M a M A + M a M A 2.27M a 0.40 Bb f (M 2, M 1 ) M b 3 sin 3 i ( M B + M b ) M b M B + M b M B 1.46M b 0.57 AB Cc AB p ABC Cc i 0 a ,000 AU P ( 1, ) 1/2 13,000 Aa /10AU Bb /20AU AB Aa Bb AU AC AB 1,000AU Cc 10,000
24 Cc Cc R R AU Cc Aa Bb
25 Leo ADS h 20.0m P T a e i n BS p a a p AU 3 a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P
26 P T a e UMa ADS h 18.2m i n BS p a a p AU a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P
27 UMa 6 UMa F. Savary UMa 1826 W. 2 T. J. J. See Researches on the Evolution of the Stellar Systems vol. 1, S. W. Burnham A General Catalogue of Double Stars part 2, 1906.
28 1905 N. E. Norlund 1923 W. H. van den Bos W. D. Heintz The Bright Star Catalogue Yale University Observatory, p W. H. Wright A Norlund Norlund 3 Wright 1908 Wright Norlund van den Bos UMa Aa UMa Aa 1966 W. D. Heintz 1928 W. H. van den Bos 4.32 m P T a e i Ursae Majoris Aa W. D. Heintz W.H. va den Bos G5V P T 2,418,582.0 JD K km/sec. e V km/sec. a 1 sin i km e i van den Bos UMa 1918 UMa B UMa Bb UMa Bb 1931 L. Berman 4.87 m P K km/sec. e 0.00 Ursae Majoris Bb L. Berman G0V T 2,425, JD V km/sec. a 1 sin i km
29 UMa M Aa + M Bb M A + M a + M B + M b 1.76 M Aa M Bb Berman 0.77 M Bb : M Aa 0.77 M A + M a 0.994M B + M b Aa A, a f ( M a, M A ) M a 3 ( M A + M a ) 2 sin 3 i ( ) K 3 1 P ( 1 e 2 ) 3/ ( ) 3/ MA + Ma i 86.3 M a ( sin 86.3 ) 3 ( ) M a 0.278M A a 1 p a 1 a p AU a 1 sin i i 86.3 a 1 sin i km AU a AU sin 86.3 M A + M a P a a a 1 + a 2 ( ) 1/ AU
30 a 1 M a M A + M a a 1 a M a M A a 1 a M Bb f i M b M B UMa Aa MJD m
31 P T a e Vir ADS h 41.7m i n BS p a a p AU e a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P
32 Paul Couteau A. H. Batten Observing Visual Double Stars 0.49 M M T. J. J. See, S. W. Burnham, 1906.
33 P T a e Boo ADS h 51.4m i n Cas 70 Oph T. J. J. See, S. W. Burnham, 1906.
34 BS p a a p AU e a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P Paul Couteau A. H. Batten Observing Visual Double Stars 0.46 M 1 M 2 M M
35 P T a e Her ADS h 41.3m i n T. J. J. See, S. W. Burnham, 1906.
36 BS p a a p AU 1.4 e 0.47 a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P Paul Couteau A. H. Batten Observing Visual Double Stars 0.41 M 1 M 2 M M
37 36 Oph ADS h 15.3m P T a e i n BS a a p AU 2 e 0.90 a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P
38 P T a e Oph ADS h 03.1m i n T. J. J. See Researches on the Evolution of the Stellar Systems vol. 1, 1896.
39 P T a e 70 Oph ADS h 05.5m i n T. J. J. See, S. W. Burnham, Cyg 70 Oph 1950 K. Aa. Strand BS p a
40 a a p AU M A + M B a P Paul Couteau A. H. Batten Observing Visual Double Stars 0.42 M B 0.42 M A + M B M B , M A T. J. J. See Researches on the Evolution of the Stellar Systems vol. 1, Strand Dirk Reuyl Erik Holmberg Strand ,150 Strand
41 70 Oph AB
42 70 Oph Reuyl Holmberg a sin b ( t t 0 ) + c + ( t t 0 ) ( 1 ) ( b 2 /P ) c + ( t t0 ) Strand ( 1 ) a, b t 0 ( 1 ) a P t c a P t c C Oph p AU C A, B 61 Cyg A, B 0.15km/sec C 70 Oph M A 0.87 M B 0.63 C A AC P 17 M A + M C 0.87 M A + M C a 3 P 2 a (AC) 6.3AU a a
43 M C M A + M C M C AU 6.3AU M C C B M B + M C a 3 P 2 a a a (BC) 5.7AU M C M B + M C M C AU 5.7AU M C C Cyg C C A B C A B C 70 Oph 61 Cyg 70 Oph AC BC 6.3AU 5.7AU AB 22.6AU C
44 1 Lyr ADS AB 18h 44.3m P T a e i n , BS a a 2.78 p AU 3 e 0.19 a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P
45 2 Lyr ADS CD 18h 44.3m P T a e 585 i n BS a a 2.95 p AU 3 e 0.49 a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P
46 Cyg ADS h 45.0m P T a e i n BS a a p AU 2 e 0.30 a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P
47 61 Cyg ADS h 06.9m P T a e i n S. W. Burnham, 1906.
48 61Cyg J G. F. W. 2 61Cyg AB A. Auwers A B AB C. F. W. Peters 1885 P 782.6a 29.48e 0.17 S. W Cyg Oesten Bergstrand Cyg A, B B A 61Cyg 1910 F. Schlesinger D. Alter 61Cyg P. Baize (1927) Alan Fletcher (1931) Baise P 756 a 32.8e Fletcher P a e Cyg AU 2 61Cyg 1943 K. Aa. Strand 61Cyg C P 720 T 1690 a e 0.40
49 p M A + M B 1.12 A, B A, B C A, B C Strand P 4.9 T a e 0.7 A, B 5.57m, 6.28m K6, M0 0.80m, 1.2m p A, B M AV log m M BV log m 1/3 log M 1/3 los M A /3 log M B M A 0.58 M B M A + M B A, B 1 C C M C C 0.56 a ( ) ( MC ) P 4.9 M C M C 0.016
50 C A B a 0.70 ( a 2.4AU ) A B 1km/sec M C B ) Strand W. S. Finsen and C. E. Worley Third Catalogue of Vinary Stars BS p a a p AU 2 e a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P
51 Cyg ADS h 44.1m P T a e i n BS a a p AU Cyg e 0.58 a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P
52 P T a e Aqr AB ADS h 28.8m C i n Y BS a a p AU e a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P
53 S. W. Burnham A General Catalogue of Double Stars part 2, BS a a p AU 8.5 e a ( 1 e ) AU a ( 1 + e ) AU M 1 + M 2 a 3 P
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1 40 (1959 1999 ) (IMO) 41 (2000 ) WEB 1 1959 1 IMO 1 n, 21n + 4 13n + 3 2 (x + 2x 1) + (x 2x 1) = A, x, (a) A = 2, (b) A = 1, (c) A = 2?, 3 a, b, c cos x a cos 2 x + b cos x + c = 0 cos 2x a = 4, b =
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ac b 0 r = r a 0 b 0 y 0 cy 0 ac b 0 f(, y) = a + by + cy ac b = 0 1 ac b = 0 z = f(, y) f(, y) 1 a, b, c 0 a 0 f(, y) = a ( ( + b ) ) a y ac b + a y
01 4 17 1.. y f(, y) = a + by + cy + p + qy + r a, b, c 0 y b b 1 z = f(, y) z = a + by + cy z = p + qy + r (, y) z = p + qy + r 1 y = + + 1 y = y = + 1 6 + + 1 ( = + 1 ) + 7 4 16 y y y + = O O O y = y
第Ⅰ章
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II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R
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II Karel Švadlenka 2018 5 26 * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* 5 23 1 u = au + bv v = cu + dv v u a, b, c, d R 1.3 14 14 60% 1.4 5 23 a, b R a 2 4b < 0 λ 2 + aλ + b = 0 λ =
(1) D = [0, 1] [1, 2], (2x y)dxdy = D = = (2) D = [1, 2] [2, 3], (x 2 y + y 2 )dxdy = D = = (3) D = [0, 1] [ 1, 2], 1 {
![(1) D = [0, 1] [1, 2], (2x y)dxdy = D = = (2) D = [1, 2] [2, 3], (x 2 y + y 2 )dxdy = D = = (3) D = [0, 1] [ 1, 2], 1 {](/thumbs/94/118399854.jpg "(1) D = [0, 1] [1, 2], (2x y)dxdy = D = = (2) D = [1, 2] [2, 3], (x 2 y + y 2 )dxdy = D = = (3) D = [0, 1] [ 1, 2], 1 {")
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０４年度LS民法Ⅰ教材改訂版.PDF
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vol.31_H1-H4.ai
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[ ]. lim e 3 IC ) s49). y = e + ) ) y = / + ).3 d 4 ) e sin d 3) sin d ) s49) s493).4 z = y z z y s494).5 + y = 4 =.6 s495) dy = 3e ) d dy d = y s496).7 lim ) lim e s49).8 y = e sin ) y = sin e 3) y =
広報さっぽろ 2016年8月号 厚別区
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001 ) g 20 g 5 300 g 7 002 720 g 2 ) g 003 0.8 m 2 ) cm 2 004 12 15 1 3 1 ) 005 5 0.8 0.4 ) 6 006 5 2 3 66 ) 007 1 700 12 ) 008 0.315 ) 009 500 g ) kg 0.2 t 189 kg 17.1 kg 010 5 1 2 cm 3 cm )km 2-1 - 011
[1.1] r 1 =10e j(ωt+π/4), r 2 =5e j(ωt+π/3), r 3 =3e j(ωt+π/6) ~r = ~r 1 + ~r 2 + ~r 3 = re j(ωt+φ) =(10e π 4 j +5e π 3 j +3e π 6 j )e jωt
![[1.1] r 1 =10e j(ωt+π/4), r 2 =5e j(ωt+π/3), r 3 =3e j(ωt+π/6) ~r = ~r 1 + ~r 2 + ~r 3 = re j(ωt+φ) =(10e π 4 j +5e π 3 j +3e π 6 j )e jωt](/thumbs/101/152334931.jpg "[1.1] r 1 =10e j(ωt+π/4), r 2 =5e j(ωt+π/3), r 3 =3e j(ωt+π/6) ~r = ~r 1 + ~r 2 + ~r 3 = re j(ωt+φ) =(10e π 4 j +5e π 3 j +3e π 6 j )e jωt")
3.4.7 [.] =e j(t+/4), =5e j(t+/3), 3 =3e j(t+/6) ~ = ~ + ~ + ~ 3 = e j(t+φ) =(e 4 j +5e 3 j +3e 6 j )e jt = e jφ e jt cos φ =cos 4 +5cos 3 +3cos 6 =.69 sin φ =sin 4 +5sin 3 +3sin 6 =.9 =.69 +.9 =7.74 [.]
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x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y)
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2018_センター試験速報_数2B.indd
08 年度大学入試センター試験解説 数学 Ⅱ B 第 問 60 80 ア = 80 = 80 44 = 80 44 = 4 5 イ, ウ = 80 = 45 エオカ sin + 5 - cos + 0 = = + 5 = - 5 sin - cos { - 5 + 0 } = sin - cos - = キ 6 cos - 6 = cos cos 6 + sin sin 6 = cos + sin
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