A Study on Method for Detecting Radio Variables and Transients with the Use of Expectation Data

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A Study on Method for Detecting Radio Variables and Transients with the Use of Expectation Data

2014 _! 2

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2014 _/ 2

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2.1 O . . . 8

2.2 "@ . . . 8

2.3 2 >/!5$ . . . 16

2.3.1 2 >/!5$*Q . . . 16

2.3.2 2 >/!5$"@ . . . 18

2.3.3 <2L . . . 18

3 )*!%" &'$ 23 3.1 AO . . . 23

3.2 . . . 23

3.3 M@;:L . . . 25

3.3.1 0,9$. . . 25

3.3.2 C8R %D . . . 27

3.3.3 M@#F$. . . 42

3.3.4 . . . 44

3.3.5 1?KL . . . 45

3.4 M@NJGEH+B- . . . 46

3.4.1 "@=4Q . . . 46

3.4.2 JGI) . . . 50

3.4.3 OP 313 JG9(6 . . . 51

3.5 &T . . . 53

4 WJN &'$ 54 4.1 . . . 54

4.2 3P"@LWTFI)7' . . . 54

4.3 Rapid WTF Detection Technique . . . 56

4.3.1 <S%D . . . 56

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4.3.2 <.D4L%5 . . . 57

4.3.3 E3 . . . 59

4.3.4 F*1&G . . . 61

4.3.5 RWDT7BST . . . 62

4.4 RWDT M@ . . . 63

4.4.1 4?>(G . . . 63

4.4.2 (:WM . . . 64

4.4.3 @6M . . . 64

4.4.4 K) WTF 2@ . . . 65

4.5 'X . . . 68

!5 ) 70 $ (A "'& 74 A.1 V . . . 74

A.2 O!+HA%9T . . . 74

A.3 "$R8%5 . . . 76

A.4 U!,UI;JPN%5 . . . 79

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C.2 0/=#-CQ . . . 103

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1http://www.physics.purdue.edu/MOJAVE/

2https://dept.astro.lsa.umich.edu/datasets/umrao.php

2.2. QŠ-/17 11

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•63? P_n(θ) ). P_n(θ) θ ) 1 ¼”@H k€^{¹ &.

P_n(θ) = I

i=0

a_iθⁱ (3.3)

œW`” ¨ 0.99 )¬'…»63?)pf &. ±NUžbJ

¢, k€^{€œW`”)au(, 16~ k€ ¨)

¬&$, I = 16 .

3.3.2

¥ 29>21,&}o²’ 2›xRŠaUž'&®¡,ÁF

\7<«‘$ÌPθ,φ )au&. auÍ')“ 3.2. Ãa u¸Ê&½, UžAª(ÁF\Aª),Už¾g, Už}o, hCUž-3>/&. Ø,yg•63?lƒµ^{¨)vŽn

"iÎ, θ, φ 2 ¼”)əÅ)j, ¥ 1 9>21‡²’ 2 › xRŠa63?Už¨)vŽn θ (≤1.5^◦) 1 ¼”Ï. 4 3;+?5 n 7<«‘y®Z&Aª)«‘, &P°

¶B³Ÿr&®¡i7<«‘ÌP)θ_i[n],φ_i[n]&. Ø, T

§!θ_i[n],φ_i[n])Už}o tW” θ_i(t),φ_i(t)¹. ¥ 2Œ‡

#, Už}o t 43;+?5 n @HW`&.

t = t₀ +nΔt (3.4)

, t₀ , UžLw}o, Δt , 43;+?5VQ (0?9=?/VQ)

)¹. 1.5^◦ #%MÐC8.¨7<«‘¢q¤" 1/70

(-18 dB,ºÑA t‹)­°&!,®¡Ä„&CygnusÐC®šÐC

)ˆ, 1.5^◦ #%hÐC®¡‚[°)iδ'", *a

uE])#. , Cygnus A, ®šÐC®¡Ä„©£%, Â

28 ‚3l ¥{32*¦69;1OŽœ„aŸ D•

rŒ~|_'. (%*wX©'RbeIz'!, jE'.

'H{ŸU|_' i˜£Œ~CNŒ~H{,2:.$& '. A–‹Œ~ˆh”'f”žgKW0;-:4:;žg'X

%('³⁸⁾. Œ~H{,2:.h”r%r™ MHz ŠŽ€@’, 0;- :4:;žg$œt'X . ,Œ

›T€@’(,  "¤ƒ. , ‘p'H {h”r,2:.H{h”rr™ MHz<mE('n[#,LvH{n[

¥{32H{32]¢d'.

( ², ²) i = 1 i = 2

ȓȸȠɶƷᩓඬเ ហኺ (J2000.0) ហዾ (J2000.0) ᩓඬࢍࡇ ( ) ( ) (mJy)

NVSS J010734+322006 01 07 34 32 20 06 112.2 NVSS J010730+322220 01 07 30 32 22 20 1757 NVSS J010725+322437 01 07 25 32 24 37 1106.5 NVSS J010725+322535 01 07 25 32 25 35 914.2

... ... ... ...

ȓȸȠɶ࣎Ʒហኺហዾ: ,

i i

Δ = − ⁱ, Δ = − ⁱ

ᚌុᩉ: ( ⁱ , ⁱ )

i

h m s ' "

θ φ

( θ φ¹, ¹) α δ S

α δ

α

α δ δ

θ φ

α^{( )n} δ^{( )n}

( )n ( )n ( )n ( )n

( )n ( )n ȓȸȠɶ࣎

i i

q 3.2: 'H{e\'H{ŸUS‰Ÿ . i58J('

Œ~˜Z*š. 58‡ouQ,u? (J2000.0) % Œ~

uQ, u?*jb', Œ~58‡o'y‹

FŽ(¨F)*M!'.

¡ª›‘pH{h”r 1.42 GHz±0.01 GHz P, 1.4 GHz ' wŒ/7+,2:.' NRAO VLA Sky Survey (NVSS) ,2:.*§¦

'⁶⁾. h”r€,2:., }" Ohio Survey ,2:."

§¦'B“'. š 3.1 CN 1.4 GHz €Y)(V@H{

$`s(,2:.'. , w,2:."uQŸUH{—>

00^h00^m00^s–24^h00^m00^s'.

¨F*Rb'!, ^i‘p 2 xcGkR=†H{e\ t %…Ÿ

3.3. ~d&$a]| 29 u 3.1: 1.4 GHz fF.5d$*!

North NVSS FIRST

O]s 1992 1993–1996 1998

5dme[ 31524 177348 946464 NXAW3o (Jy) 80×10⁻³ 2×10⁻³ 0.75×10⁻³ }/< Green Bank VLA VLA Nkb- −06^◦1952 −40^◦2551 −11^◦2356 NIb- +83^◦1515 +89^◦4909 +64^◦4100 PHxB ^{37) 6) 3)}

G_R Θ(t) :. mx>op> λ, \1R U(t) h{G_R Θ(t) SU:⁶³⁾,⁵⁹⁾.

Θ(t) = Θ₀(t) + (1 +ν)U(t) +λ (3.5) , ν (= 86400/86164−1)\1R62G_R62L, Θ₀(t)\1R 0 R!)'%"G_Ru. Θ₀(t)7Cc 4713 s 1 @ 1 r`E12 R jQr[u()#r J D(t) +0U?Q.

Θ₀(t) = 6 +38.0

60.0 +45.836

3600.0 +8640184.542

3600 T(t) + 0.0929

3600 T(t)² (3.6) T(t) = J D(t)−2451545.0

36525.0 (3.7)

J D =

−

14−M(t) 12

+Y(t) + 4800

× 1461 4

+

14−M(t) 12

×12 +M(t)−2

× 367 12

−

−[(14−M(t))/12] +Y(t) + 4900 100

×3 4 +D(t)−32075.5

(3.8)

U (3.6) – (3.8), [ ] #8J,^[vw. Y(t), M(t), D(t) 5dRK t s, r, @u. T(t) J2000.0 (()#r 2451545.0) r[ 100 ()#rg,u€.

SbqMt=hyMt=z4H. Z 3.3bqMt=, Z 3.4h yMt=l9T. hyMt=5dV,iDn. m;Y

30 >34 W;Y'HQI?0RS L δ = 90deg

α = 0h (ବЎໜ)

δ = -90deg ټƷҤಊ

᰾ᢊ

ٽᨗ

ហᢊ עྶ

ټྶ

α = 12h

ᩓඬเ (α,δ)

α δ

7 3.3: :J/M). @&B61E&5E<A :*, : 2 Q9YN. :JV δ = 0^◦ D$. :JJ,F (3OG) :* α= 0^h .

E<A,T(#;R-, #;2=8PR-R!R-A (K 0^◦, U180 ^◦),.HR- h (EC 0^◦) 2 Q9N.

:J/M5A:*,: α,δ , R-X+(L, M, N)

⎛

⎜⎝ L M N

⎞

⎟⎠=

⎛

⎜⎝

cosδcosα cosδsinα

sinδ

⎞

⎟⎠, (3.9)

%Q",

α δ

=

tan^−1M_L sin⁻¹N

(3.10)

3.3. H631G 31

El= 90deg ټ᪬

܇Ҝዴ

ᩓඬเ(Az,El)

᭗ࡇ

૾ˮᚌ Az = 0deg (Ҥ)

Az = 180deg (҅) ᚇยᎍ

0 3.4: 8D*A$. !6- (!6=) :/*A$. 8D5F&

(>0 ^◦,@FF 0^◦ .

B. F,F A, (>h B9F&I% (l, m, n)

⎛

⎜⎝ l m

n

⎞

⎟⎠=

⎛

⎜⎝

coshcosA

−coshsinA sinh

⎞

⎟⎠, (3.11)

"E ,

A h

=

tan^{−1 −m}_l sin⁻¹n

(3.12) . !6+) t 8D*A$4?*A$E ,;#.*A<

7 ,!6-;C> φ 8F'2+Θ(t) J,B

.

⎛

⎜⎝ l(t) m(t)

n(t)

⎞

⎟⎠=

⎛

⎜⎝

sinφ 0 −cosφ

0 1 0

cosφ 0 sinφ

⎞

⎟⎠

⎛

⎜⎝

cos Θ(t) sin Θ(t) 0

−sin Θ(t) cos Θ(t) 0

0 0 1

⎞

⎟⎠

⎛

⎜⎝ L(t) M(t)

N(t)

⎞

⎟⎠ (3.13)

32 l3b ‚i,+)ƒ-./*Dq}smX~:w

$A}<,

⎛

⎜⎜

⎜⎜

⎝

L(t) M(t)

N(t)

⎞

⎟⎟

⎟⎟

⎠=

⎛

⎜⎜

⎜⎜

⎝

cos Θ(t) −sin Θ(t) 0 sin Θ(t) cos Θ(t) 0

0 0 1

⎞

⎟⎟

⎟⎟

⎠

⎛

⎜⎜

⎜⎜

⎝

sinφ 0−cosφ

0 1 0

−cosφ 0 sinφ

⎞

⎟⎟

⎟⎟

⎠

⎛

⎜⎜

⎜⎜

⎝

l(t) m(t)

n(t)

⎞

⎟⎟

⎟⎟

⎠ (3.14) z'&. 0cLY#%, &[T, n|VyJ&€8E P&~P (~1;, Sq) $, htVyJ€8EZ]1o (hK,h2))B"& &. , WU, bsrQ….

\, =i,+gqPc"R WU, bs, v_NRULY~

`&.

‡{`&‚i,+LY, VyJ J2000.0 (&.

, J2000.0 )>ahKh2$k„, M5†$f '&I†?4

&uMWU, jˆe$5†7FnCOp@t'&?4

&ˆeWU$&3xWU!)Q…, |HhK, h2}<)Q&

(d 3.5).

ಊ᠆Ʒׅ᠃ ಊ᠆

ᐯ᠃

עྶ

d 3.5: WU6s. k„,M5†$f '&I†?4&uMWU, jˆe$5†7FnCOp@t'&?4

&ˆeWU#, G^9p (WU6s) f&.

3.3. J=;:H 33 9 3.6 , E₀,Q₀,P₀,X₀ EA "C,<C,I+,6EA, E(t), Q(t),P(t),X(t)EAT(t)-$/F,"C,<C, I+,6EA 5. M(t),N(t)&<C,&"C0A. , Y₀P₀M(t) = 90^◦ . , #'B?*.

ζ_A ≡ X₀P₀Y₀(t)

θ_A ≡ P₀M(t)P(t) = X₀M(t)X(t) z_A ≡ X(t)P(t)Y(t)

J2000.0 EA83, ζ_A(t),θ_A(t), z_A(t)

ζ_A(t) = 0.017998T(t)³+ 0.30188T(t)²+ 2306.2181T(t)

3600 (3.15)

θ_A(t) = −0.041833T(t)³ −0.42665T(t)²+ 2004.3109T(t)

3600 (3.16)

z_A(t) = 0.018203T(t)³+ 1.09468T(t)²+ 2306.2181T(t)

3600 (3.17)

.

7>L,(=4)t <-,<!G1K.(L_m(t), M_m(t), N_m(t)) ,

⎛

⎜⎝ L_m(t) M_m(t)

N_m(t)

⎞

⎟⎠=

⎛

⎜⎝

p₁₁ p₁₂ p₁₃ p₂₁ p₂₂ p₂₃ p₃₁ p₃₂ p₃₃

⎞

⎟⎠

⎛

⎜⎝ L₀ M₀ N₀

⎞

⎟⎠ (3.18)

D. , (L₀, M₀, N₀) J2000.0 <-, <!G1 K.. ,%@2M:E p_ij ,

p₁₁ = cosζ_Acosθ_Acosz_A−sinζ_Asinz_A p₁₂ = −sinζ_Acosθ_Acosz_A−cosζ_Asinz_A p₁₃ = −sinθ_Acosz_A

p₂₁ = cosζ_Acosθ_Asinz_A+ sinζ_Acosz_A p₂₂ = −sinζ_Acosθ_Asinz_A+ cosζ_Acosz_A p₂₃ = −sinθ_Asinz_A

p₃₁ = cosζ_Asinθ_A p₃₂ = −sinζ_Asinθ_A p₃₃ = cosθ_A

(3.19)

34 F3A ZE\!#$1LUMG<WX+P

E⁰Ўໜ଺ƴƓƚǔ್ᢊ Q⁰Ўໜ଺ƴƓƚǔហᢊ P⁰Ўໜ଺ƴƓƚǔټƷ҅ಊ X⁰Ўໜ଺ƴƓƚǔବЎໜ Y⁰P(t)P⁰ǛᡫǔόԗƱQ⁰Ʒʩໜ

E(t)ᚇย଺t ƴƓƚǔ್ᢊ

Q(t)ᚇย଺t ƴƓƚǔហᢊ P(t)ᚇย଺t ƴƓƚǔټƷ҅ಊ X(t)ᚇย଺t ƴƓƚǔବЎໜ Y(t)P(t)P⁰ǛᡫǔόԗƱQ(t)Ʒʩໜ Q(t)

Q⁰ E⁰ E(t)

ټƷ҅ಊЎໜ଺

Ўໜ଺Ʊᚇย଺t Ʒ ហᢊƷʩໜM

҅ಊᚇย଺tP(t)

P⁰

Y⁰

Y(t) X⁰ X(t)

ټྶ

Ўໜ଺Ʊᚇย଺t Ʒ

᰾ᢊƷʩໜN'

ټƷҤಊЎໜ଺

B 3.6: ;9'MDO:Q4>.U*. SK>(ODO5

^, Y2K, @SK)I=0, -E>NUC

>./CR (t) . H0?J;9'M ,Y2W7U.

. T3D5, D%W7[6 J2000.0 D5, D5W7[6 U, 3.18 &VF 1 8]" #8] ,

⎛

⎜⎝ L₀ M₀ N₀

⎞

⎟⎠=

⎛

⎜⎝

p₁₁ p₂₁ p₂₃ p₁₂ p₂₂ p₃₂ p₁₃ p₂₃ p₃₃

⎞

⎟⎠

⎛

⎜⎝ L_m(t) M_m(t) N_m(t)

⎞

⎟⎠ (3.20)

R.

3.3. xb)(_^u 35

Xj, `kv/j"$Uqh1kYt3,`k1kEh5i

$1k?T5t3B%$⁵⁷⁾. Xj0;MKnV.

#, F{ZH, 10 l7Lcw10 fiDK_%$.

6bQI t $Xj'F{Uqh, `k'[Uqh, [`k

(\ 3.7). , Xj'F{, MK 'F{Uqh, `k%%s

<Uqh, s<`kC%$.

᰾ᢊ

ჇƷហᢊ Δϕ

࠯רហᢊ

Δε ε

ε

ჇƷବЎໜ

࠯רବЎໜ

\ 3.7: Uqhp=1@XjΔψ,1k?5XjΔε. [Uqh,[

`k,6bQIt $Xj'F{Uqh,`k',s<U qh,s<`k,Xj'F{, MK 'F{Uqh,` k'o. Xj", 10l7w10 fiDK_%$.

aGAP", s<Uqh,s<`k&$!, [Uqh, [`k%%K Δψ, Δε #:!$$. JOgr|H (IAU, Internatiomal Astronomical Union) , Δψ, Δε ':!$!o3.3 R>]

o'mo$⁴⁷⁾. o9N%>]'yXjAP' IAU 1980 Xjz }. o 3.3 9N*,+( L, Γ, Γ, Ω, M_m , %%s<

Uqh8 s<1@,s<Uqh8 =ehs<1@, =ehs<1

@, s<Uqh#bs<WEh1@, s<1@'o$. 4*

,+(-2So%$. , d.i$.

36 .3+ 9-: !$162/)78#4 L = 280.466457 + 0.98564735800624d+ 0.0003032T²

Γ = 282.937348 + 0.00004707624d+ 0.0004569T² Γ = 83.353243 + 0.11140352394d−0.0103217T²

Ω = 125.044555−0.05295376227d+ 0.0020756T² M_m = 218.316646 + 13.17639647564d−0.0014664T²

(3.21)

, d J2000.0 3,

d = J D−2451545.0 (3.22)

T ,

T = d

36525 (3.23)

. 5 3.3 , <(5 3.2 5. '

L Γ Γ Ω M_m Δψ Δε

a b c d e A B

5 3.2: +2&*5 1 '

Δψ, Δε "0

Asin(aL+bΓ +cΓ+dΩ +eM_m) Bcos(aL+bΓ +cΓ+dΩ +eM_m) .

5 3.3: IAU 1980 +2;=%,5

Δψ Δε

L Γ Γ Ω M_m Coef. () Coef. ()

1 -17.1996 -0.01742T +9.2025 +0.00089T

2 -1.3187 -0.00016T +0.5736 -0.00031T

2 +0.2062 +0.00002T -0.0895 +0.00005T 1 -1 +0.1426 -0.00034T +0.0054 -0.00001T

3.3. 37

Δψ Δε

L Γ Γ Ω M_m Coef. () Coef. ()

3 -1 -0.0517 +0.00012T +0.0224 -0.00006T 1 1 +0.0217 -0.00005T -0.0095 +0.00003T

2 -1 +0.0129 +0.00001T -0.007

2 -2 +0.0048 +0.0001

2 -1 +0.0046 -0.0024

2 -2 -0.0022

2 -2 +0.0017 -0.00001T

4 -2 -0.0016 +0.00001T +0.0007

1 -1 1 -0.0015 +0.0009

-1 1 1 -0.0012 +0.0006

-2 2 +0.0011

-2 2 1 -0.0006 +0.0003

1 1 -1 -0.0005 +0.0003

2 -2 1 +0.0004 -0.0002

3 -1 -1 +0.0004 -0.0002

1 -1 +0.0004

2 -0.0003 +0.0001

1 -1 -0.0003

2 -1 -0.0002 +0.0001

-2 3 +0.0001

3 -1 -2 +0.0001

-2 3 +0.0001

-1 -1 2 -0.0001

1 -1 2 +0.0001

-1 1 1 +0.0001

3 -1 -2 -0.0001

2 -0.2274 -0.00002T +0.0977 -0.00005T -1 1 +0.0712 +0.00001T -0.0007

-1 2 -0.0386 -0.00004T +0.02

-1 3 -0.0301 +0.0129 -0.00001T

2 -1 -1 -0.0158 -0.0001

1 1 +0.0123 -0.0053

-1 1 1 +0.0063 +0.00001T -0.0033

-2 2 +0.0063 -0.0002

38 3

Δψ Δε

L Γ Γ Ω M_m Coef. () Coef. ()

-2 1 3 -0.0059 +0.0026

1 1 -1 -0.0058 -0.00001T +0.0032

-1 -1 3 -0.0051 +0.0027

-2 4 -0.0038 +0.0016

-2 4 -0.0031 0.0013

2 -1 1 +0.0029 -0.0012

-2 2 +0.0029 -0.0001

-2 2 +0.0026 -0.0001

1 -1 1 +0.0021 -0.001

-2 1 1 1 +0.0016 -0.0008

2 -1 1 -1 -0.0013 +0.0007

-2 1 -1 3 -0.001 +0.0005

-2 -1 5 -0.0008 +0.0003

1 -1 2 +0.0007 -0.0003

-1 1 2 -0.0007 +0.0003

-2 -1 4 -0.0007 +0.0003

3 -1 -1 -1 -0.0007

2 -2 2 +0.0006 -0.0003

-2 1 2 -0.0006 +0.0003

2 -1 -1 1 +0.0006 -0.0003

-2 -1 3 +0.0006

2 1 -2 -0.0005 +0.0003

-2 -1 4 -0.0005 +0.0003

-1 1 -1 1 +0.0005

3 -1 -2 -0.0004

-1 2 -1 +0.0004

-1 1 -0.0004

-1 1 -1 3 -0.0003 +0.0001

-3 1 1 3 -0.0003 +0.0001

-3 5 -0.0003 +0.0001

-3 1 4 -0.0003 +0.0001

1 -1 -1 1 -0.0003

-1 -2 3 +0.0003

2 1 -2 -0.0002 +0.0001

3.3. 39

Δψ Δε

L Γ Γ Ω M_m Coef. () Coef. ()

1 -1 -1 3 +0.0002 -0.0001

2 1 1 -1 -0.0002 +0.0001

-2 1 2 +0.0002 -0.0001

-1 2 1 -0.0002 +0.0001

-1 3 +0.0002 -0.0001

-4 1 5 -0.0002 +0.0001

-3 3 +0.0002

1 2 -1 +0.0001 -0.0001

-2 2 2 +0.0001 -0.0001

3 -1 -1 1 +0.0001 -0.0001

-2 -1 -1 5 -0.0001 +0.0001

-4 2 4 -0.0001 +0.0001

2 -2 2 +0.0001 -0.0001

4 -1 -3 -0.0001

4 -2 -2 -0.0001

1 -2 3 +0.0001

1 1 -1 -1 +0.0001

-2 -2 6 -0.0001

-2 -1 1 3 -0.0001

2 -2 2 +0.0001

2 -3 3 +0.0001

2 -1 -2 1 -0.0001

1 -1 -1 2 +0.0001

-3 1 1 1 1 +0.0001

3 -2 -0.0001

1 1 -0.0001

-1 -1 2 -0.0001

2 -1 2 -3 -0.0001

-1 1 -1 2 -0.0001

3 -1 -1 1 -1 -0.0001

-2 -1 2 1 -0.0001

-2 -2 4 +0.0001

-4 6 -0.0001

-1 1 +0.0001

40 R3E aN)($b+-/'7X^ZSA_`3\

H 3.8 , VPYc!<L SE _>G% !. BT6E E Z !,< SE _>Yc9!. S E G,&*.$ c, 5NC E E G_>,&*.

$ v !. c=|c|, v =|v| ""<OX, T6=WOX$#. , 5NCQ!<MQ1Z, c−v , #, SE _>,&

*.!. , H 3.8 , VPF_> SEF $ θ, _>

SEF $ θ !!, ESE =θ−θ !. J:Ud , v

sin(θ −θ) = c sinθ

!,

sin(θ−θ) = v c sinθ,

, v/c1 !, θ −θ ]D4!. , sin(θ −θ) = sin 1·(θ−θ)

= v csinθ

!,

θ −θ = v

csin 1 sinθ

!. ,θ = θ ,

θ−θ = v

csin 1 sinθ

= κsinθ

["!. κ <?@UI!. T6=WOX 29.785 km/s, <OX 299792.458 km/s !, κ

κ = v

csin 1 sinθ

= 20.5 , ;@K8,K02"!.

3.3. lV%$SQj 41

S

E v E' F

c

θ θ'

θ'-θ

P 3.8: bK=@F. Y7 E , E _.

UALGf:Hij"n, k/8')ZO\W4o1"

:Hij"L. , J (3.5) "n, 3VIE t 0^%$(

#*& n Yi?RI":H.

Yi?RI;[, 3Vi,1 A, B] h \g.] φ "J (3.18)X a,%$(#*& n T9, T.i>m<6 . J (3.20)"n, ^0i>m<"J2000.0 i>m<h2.

,J(3.10)Xa, k/8')ZOJ2000.0>

i>T9, T.(α[n],δ[n]) !. (α[n], δ[n]) "ZO3V d-`\W5 "c[,5 ND, ')ZO>

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