96 32 VLBI (IAU International Astronomical Union) 1976 (1) IAU 5 (2) IAU 5 (3) IAU A4 (4) IAU B6 (5) IAU
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1 32 1 Vol. 32, No PROGRESS IN ASTRONOMY Jan., 2014 doi: /j.issn ( ) (IAU) N Brumberg-Kopeikin Damour-Soffel-Xu (1PN) IAU IAU IAU Brumberg-Kopeikin Damour-Soffel-Xu IAU2000 IAU P129, P132 A [1, 2] [3] ns [4] [5] [6 8] VLBI VLBI 10 µs VLBI [9] Gaia [10] ( ) wbhan@shao.ac.cn
2 96 32 VLBI (IAU International Astronomical Union) 1976 (1) IAU 5 (2) IAU 5 (3) IAU A4 (4) IAU B6 (5) IAU B B1.9 (6) IAU (Reference systems) IAU2000 (Reference frames ) N ( ) N Blanchet Damour 1989
3 1 97 B-D N N N Brumberg Kopeikin (BK ) [11 13] Damour-Soffel-Xu (DSX ) [14 17] 1PN IAU2000 [18] 2 IAU Brumberg-Kopeikin 4 DSX B-D 5 IAU2000 IAU IAU Pound-Rebka [19] Shapiro [20] [21] VLBI GPS 1976 IAU 10 IAU1991 ( ) [22] 2U(t, x) g 00 = O(4), c 2 g 0i = O(3), (1) ( ) 2U(t, x) g ij = δ ij O(4), c 2 U (t, x) U 2 U = 4πGρ. (2) IAU1991 (1) ( ) IAU 1991
4 98 32 N (1) U SI SI c = m s 1 T CB T CG T CB T CG = 1 c 2 [ t t 0 ( ) ] v 2 E 2 + U ext(x E ) dt + reυ i E i + O(4), (3) x i E υi E ri E = xi x i E xi BCRS U ext (x E ) (TT, ) (TAI ) s TAI ( JD= ) TT T CG T T T T = T AI s. (4) T CG T T = L G (JD ) , (5) JD TAI TDB ( ) T CB T DB = L B (JD ) (6) T CG T CB (3) ( ) T CB T CG = L C (JD ) r i Eυ i E/c 2 + P, (7) P [23] P = sin ( T ) sin ( T ) sin ( T ) sin ( T + 25 ) sin ( T ) +, T J [24] L B, L C L G IAU 1991
5 1 99 IAU1991 IAU1991 1PN B-K DSX IAU 3 Brumberg-Kopeikin Brumberg Kopeikin [11 13] (BRS) (GRS) BRS ( ) GRS GRS BRS 100 GRS Brumberg Kopeikin (1) (2) (3) BRS GRS BRS GRS Brumberg Kopeikin Brumberg Kopeikin η µν γ αβ µν = 16πG c 4 ( g)(t αβ + t αβ ) + χ αβµν µν, (8) (8) γ αβ χ αβµν γ αβ η αβ gg αβ, χ αβµν γ αβ γ µν γ αµ γ βν. (9) BRS GRS Brumberg Kopeikin GRS ĝ αβ (u, w)
6 [11] G 00 (T, X) = 1 + c 2(2) G 00 (T, X) + c 4(4) G 00 (T, X) + O(5), G 0i (T, X) = c 3(3) G 0i (T, X) + O(5), G ij (T, X) = δ ij c 2(2) G ij (T, X) + O(4), (2) G 00 (T, X) = 2ÛE(T, X) + 2Q (E) i X i + 3Q (E) ij X i X j + 5Q (E) ijk Xi X j X k + O(R 4 ), (2) (2) G ij (T, X) = δ ij G 00 (T, X), (3) G 0i (T, X) = 4Û i E (T, X) 4ɛ ijkc (E) jm Xk X m + O(R 3 ), (4) G 00 (T, X) = 2Û 2 E (T, X) 2ÛE(T, X)Q (E) i O(ÛER 3 ), Û E (T, X) = G E ÛE i (T, X) = G ρ (T, X ) X X d3 X + O(2), ν i (T, X) = dxi dt = ɛ ijk ˆω j E Xk. E ρ (T, X ) X X νi (T, X )d 3 X, ρ (T, X) = ρ(t, X)u 0 (T, X) G, X i 6ÛE(T, X)Q (E) ij X i X j + (10) (11) ÛE, ÛE i Brumberg Kopeikin Û E (T, X) = G ˆM E R + G 2R 3 Îij E ( δ ij + 3 R 2 Xi X j L 3 E ) + O(α E R ), 3 (12) ÛE i (T, X) = Gɛ ijk ˆω j X m EÎkm E R + O(α L 3 E 3 E R ), 3 ˆM E Îij E B-K GRS Q E i, Q E ij, Q E ijk, CE j, T (8) Q E i (Q E i = 0) B-K GRS [11] BRS
7 1 101 g 00 (t, x) = 1 + c 2(2) g 00 (t, x) + c 4(4) g 00 (t, x) + O(5), g 0i (t, x) = c 3(3) g 0i (t, x) + O(5), g ij (t, x) = δ ij c 2(2) g ij (t, x) + O(4), (2) g 00 (t, x) = 2U E (t, x), (2) g ij (t, x) = δ ij (2) g 00 (t, x), (3) g 0i (t, x) = 4UE i (t, x), (4) g 00 (t, x) = 2UE 2(t, x) + 2W E(t, x), (13) U(t, x) = U E (t, x) + Ū(t, x), U i (t, x) = UE i (t, x) + Ū i (t, x), W (t, x) = W E (t, x) + W (t, x), W E (t, x) = 3 2 υ2 EU E (t, x) + 3υEU i E(t, i x)g 1 2 χ E,00(t, x), (14) χ E (t, x) = G E ρ (t, x ) x x d 3 x, ρ (t, x) = ρ(t, x)u 0 (t, x) g, Ū(t, x) = A E W (t, x) = 3 2 GM A, Ū i GM A (t, x) = υa i, r A r A A E GM A υa 2 r A A E B A A E E ρ (t, x ) x x Ū(t, x )d 3 x G 2 M A M B + 1 GM A r A,00. r A r AB 2 A E U E, U i E, W E, χ E B-K BRS GRS BRS GRS g µν (t, x) =c 2 G 00 (T, X) T x µ T x ν + cg 0i(T, X) T x µ X i x ν + (14) (15) cg 0i (T, X) Xi T x µ x + G ij(t, X) Xi X j. (16) ν x µ x ν
8 BRS GRS T = t c 2 [S(t) + υe krk ] + c 4 [B(t) 1 2 υ2 EυEr k k + B k (t)r k + B km (t)r k r m ]+ O(c 4 r 3 ) + O(5), X i = r i + c 2 {[ 1 2 υi EυE k + F ik (t) + D ik (t)]r k + D ikm (t)r k r m } + O(4). (17) S, B, B k, B ij, F ij, D ik, D ikm GRS Q E ij, Q E ijm, Cij, E. [11, 12] B-K GRS BRS GRS Brumberg Kopeikin B-K GRS BRS 4 Damour-Soffel-Xu Damour Soffel Xu PN [14 17] DSX B-K 2000 IAU DSX [25] 4.1 N (ct, x i ) N N (ct A, XA a )(A = 1, 2,, N) ( A) N + 1 ( ) g 00 g ij = δ ij + O(4), G 00 G ab = δ ab + O(4). DSX DSX DSX PN (18) x µ (X α ) = z µ (T ) + e µ a(t )X a + ξ µ (X α ), (19) x µ X α z e ξ X a X a
9 1 103 e µ a, ξ µ [14] (2.36) w w i ( w µ ) γ ij γ ij = δ ij + O(4) 1PN g 00 = exp( 2w/c 2 ) + O(6), g 0i = 4w i /c 3 + O(5), g 00 = δ ij exp(2w/c 2 ) + O(4). 1PN (20) w µ = 4πGσ µ + O(4, 2), (21) η µν µ ν w µ σ µ (σ, σ i ) σ (T 00 + T ii )/c 2, σ i T 0i /c. (22) B-K DSX w µ w N µ + w N µ (21) wµ N ( ) w µ N ( ) DSX N ( ) w µ N = 0 w N µ 4.2 N A A X α A G 00 = exp( 2W A /c 2 ) + O(6), G 0i = 4Wa A /c 3 + O(5), G 00 = δ ab exp(2w A /c 2 ) + O(4). (21) W A α, (23) X W A α = 4πGΣ A α + O(4, 2), (24) Σ A α (Σ A, Σ A a ) (24) W α +A ( A )
10 W α A ( ) ( A ) 0 W α (X) (W, W a ) w µ (w, w i ) w = (1 + 2V 2 /c 2 )W + 4c 2 V a W a c2 ln(a 0 0A 0 0 A 0 aa 0 a) + O(4), (25) w i = υ i W + RaW i a c3 ln(a 0 0A i 0 A 0 aa i a) + O(2), V a Raυ i i R a(t i ) A µ α = x µ / X α w µ (x) = A µα (T )W α (X) + B µ (X). (26) A W α +A w A µ A ( A ) w A µ (x) = A A µα(t )W +A α (X) + O(4, 2), (27) wµ B (x) = A A µα(t ) W α A (X) + Bµ A (X) + O(4, 2). (28) B A σ A µ Σ A α σµ A (x) = X x AA µα(t )Σ A α(x) + O(4, 2). (29) BD B( A) ( ) 4.3 A x A U(x, t) = GM ( x z A GMi i x z A ( ) l l! L ( GML x z A ) + 1 ( ) 2! GMij ij + + x z A ) +, (30) M L M L (t) = d 3 X ˆX L ρ A (X, t). (31) A
11 1 105 Kip Thorne [26] ( (31)) ( ) (30) (31) (30) (31) Blanchet Damour 1989 [27] DSX [14] BD A X α (W, W a ) ( ) l W (T, X) = G L [R 1 M L (T ± R/c)] + 1 l! c 2 T (Λ λ) + O(4), (32) l 0 ( ) l W a (T, X) = G (ṀaL 1 L 1 R 1 + l l! l + 1 )ɛ abcs cl 1 bl 1 R 1 + l a(λ λ) + O(2), (33) λ(t, X) ( ) l 2l + 1 Λ 4G (l + 1)! 2l + 3 P L L R 1, P L (T ) l 0 A d 3 X ˆX bl Σ b (T, X). (34) M L (T ) d 3 X ˆX L 1 Σ + A 2(2l + 3)c N 4(2l + 1) 2 L P (l + 1)(2l + 3)c 2 L (l 0), (35) S L (T ) d 3 Xɛ ab<c l ˆXL 1>a Σ b (l 1), N L d X X 2 ˆXL Σ. (36) A ( (32) ) N L, P L ( (35)) ( (32)) ( (35)) λ = Λ DSX IAU ( (33)) ( (36)) A
12 ( [28 30]) ( [31]) Hartmann 1994 [32] 1 PN Tao [33] BD BD DSX G A (T ) W A (T, 0) + O(4), G A L (T ) [ <L 1ĒA al> (T, X)] X=0 + O(4), l 1 (37) HL A(T ) [ B <L 1 al> A (T, X)] X=0 + O(2), l 1 G A L l = 0 GA G A (37) λ(t, 0) = O(2) DSX H L A GA L W α A 4 Ē a a W + c W 2 T a, (38) B ab 4( a Wb b Wa ). W A 1 (T, X) = l! { ˆX L G A L(T ) + X 2 ˆXL GA L (T )/[2(2l + 3)c 2 ]}+ l 0 W A a (T, X) = l 0 c 2 T ΛA + O(4), 1 (l + 1)! [ 2l + 1 2l + 3 ˆX al Ġ A L(T ) ɛ abc ˆX bl 1 H A cl 1(T )] a ΛA /4 + O(2), (39) Λ A Λ A (T, 0) = O(2) ΛA X (T, 0) = O(2) DSX BD 1PN (STF) DSX N BD 1PN W α DSX N 1PN Brumberg-Kopeikin IAU2000 DSX
13 IAU 2000 IAU IAU IAU1991 (1) N Einstein-Infeld-Hoffmann [34] (1) Einstein-Infeld-Hoffmann IAU IAU IAU (B1.3 -B1.5 B1.9) N Brumberg-Kopeikin [11 13, 35] Damour-Soffel-Xu [14 17] 5.1 BCRS g 00 = 1 + 2w c 2w2 + O(5), 2 c 4 g 0i = 4 c 3 wi + O(5), ( g ij = δ ij 1 + 2w ) + O(4). c 2 (40) w, w i ( 1 ) 2 c 2 t w = 4πGσ + O(4), 2 w i = 4πGσ i + O(2). (41) σ, σ i T µν σ = 1 c 2 (T 00 + T ii ), σ i = 1 c T 0i. (42) ( ) w(t, x) = G d 3 x σ(t, x ) x x + G 2 2c 2 t 2 w i (t, x) = G d 3 x σi (t, x ). x x d 3 x σ(t, x ) x x, (43)
14 (41) N w(t, x) = N w A (t, x), w i (t, x) = A=1 N wa(t, i x). (44) ( ) A A (t, x) = GM A r A w = w 0 + /c 2 = A w i G(r A S A ) i = 2r 3 A A { 2υ 2 A + B A GM A r A + A A=1 + GM A r A υ i A, A (t, x), GM B + 1 [ ] } (r k A υa k )2 + r k r BA 2 r Aa k A 2 A + 2Gυk A (r A S A ) k ra 3 r BA A B a A 5.2 GCRS BCRS IAU2000 GCRS X a BCRS x i [11, 36] GCRS BCRS G 00 = 1 + 2W c 2W 2 + O(5), 2 c 4 G 0a = 4 c W a + O(5), 3 ( G ab = δ ab 1 + 2W ) + O(4). c 2 W α = (W, W a ) W α E (45), (46) (47) W α (T, X) = W α E (T, X) + W α ext(t, X). (48) (43) (T, X) W α ext W α ext = W α tidal + W α iner IAU2000 B-D [14, 27]
15 1 109 ( ( 1) l 1 W E = G M L L l! X + 1 ) 2c M 2 L L X + 4 c Λ + O(4), 2 l=0 ( WE a ( 1) l 1 = G Ṁ al 1 L 1 l! X + 1 ) l + 1 ɛ 1 abcs cl 1 bl 1 Λ,a + O(2), (49) X l=1 ( 1) l 2l + 1 Λ = G (l + 1)! 2l + 3 P 1 L L X, P L = Σ a ˆXaL d 3 X, l=0 M, S B-D Λ W E { W E = GM l ( ) l E RE 1 + P lm(cos θ)[c lm(t, X ) cos mφ+ X X l=2 m=0 } S lm (T, X ) sin mφ] V + O(4), (50) Clm(T, E X ) = Clm(T E ) 1 X 2 d 2 2(2l 1) c 2 dt 2 CE lm(t ), Slm(T, E X ) = Slm(T E 1 X 2 d 2 ) 2(2l 1) c 2 dt 2 SE lm(t ). (51) Clm E, SE lm GCRS Tao 1998 [33] WE a (49) Soffel [18] ṀaL 1 (Lense-Thirring ) WE(T, a X) = G (X S E ) a, (52) 2 X 3 S E S a W a E - W α ext X a X a W iner = Q a X a, W a iner = c 2 ɛ abc Ω b inerx c /4. (53)
16 Q a [ Q a = δ ai x w ] ext(x i E ) a i E, (54) w µ ext(t, x) = A E wµ A (t, x) Q a [37] [14] (6.30a) Winer a ( )GCRS Ω iner = Ω GP + Ω LTP + Ω TP, (55) Lense-Thirring Thomas Ω GP = 3 2c υ 2 E w ext (x E ), Ω LTP = 2 c w ext(x 2 E ), (56) Ω TP = 1 2c υ 2 E Q. 2 Thomas Lense-Thirring B-K GRS ( ) DSX IAU GCRS Damour 1992 [15] Klioner Voinov 1993 [35] G tidal ab 5.3 W tidal l=2 = 1 2 Gtidal ab X a X b, (57) [17] [38] GCRS BCRS GCRS BCRS x µ (T, X a ) X α (t, x i ) DSX x µ (T, X a ) [14 17] B-K [11 13, 35] x µ X α
17 1 111 T = t 1 [ ] A(t) + υ i c 2 E re i 1 [ + B(t) + B i (t)r c 4 E i + B ij (t)rer i j E + C(t, x)] + O(5), X a = δ ai {re i + 1 [ 1 c 2 2 υi Eυ j E rj E + w E(x E )re i + rea i j E rj E 1 ]} 2 ai ErE 2 + O(4), (58) Ȧ(t) = 1 2 υ2 E + w ext (x E ), Ḃ(t) = 1 8 υ4 E 3 2 υ2 Ew ext (x E ) + 4υEw i ext(x i E ) w2 ext(x E ), B i (t) = 1 2 υ2 EυE i + 4wext(x i E ) 3υEw i ext (x E ), (59) B ij (t) = υeδ i aj Q a + 2 x j wi ext(x E ) υ i E x w ext(x j E ) δij ẇ ext (x E ), C(t, x) = 1 10 r2 E(ȧ i ErE) i. GCRS BCRS x µ (X α ) = z µ (T ) + e µ a(t )X a + ξ µ (X α ), (60) z µ (T ) BCRS DSX e 0 0(T ) = c 1 ż 0 = 1 + O(2), e i 0(T ) = c 1 ż i, e 0 a(t ) = c 1 e i aż i + O(3), e 0 0(T )e i a(t ) = (1 + v 2 /2c 2 )(δ ij + υ i υ j /2c 2 )R i a(t ) + O(4), ξ 0 (X α ) = O(3), ξ i (X α ) = c 2 e i a(t )[A a X 2 /2 X a (A X)] + O(4), A a = R i a z i R i a(t ) BCRS w(t, x) w = w 0 + w L /c 2. (61) (45) w L l 1 TCB dτ dtcb = 1 1 c 2 (w 0 + w L + υ 2 /2) + 1 c 4 ( υ4 /8 3υ 2 /2w 0 + 4υ i w i + w 2 0/2 + ), (62)
18 υ i BCRS TCB TCG { t [ ] } [ υ T CB T CG =c 2 2 E 2 + w 0,ext(x E ) dt + υer i E i + c 4 t 0 c 4 { t t 0 3w 0,ext (x E ) + υ2 E 2 [ υ4 E υ2 Ew 0,ext (x E ) + 4υ i Ew i 0,ext(x E ) w2 0,ext(x E ) ] ] υ i Er i E } dt. IAU1991 T T T CG T CB 3 d T T/d T CG = 1 L G, < T CG/ T CB >= 1 L C, < T T / T CB >= 1 L B, <> 1 [18] (63) (64) 1 L C, L G, L B [18] IAU 1991 IAU 2000 IAU 2000 Constant /s s 1 /s s 1 /ms a 1 L C L G L B L C + L G L C L G BCRS GCRS W E (T, X) = w E (t, x)(1 + 2υE/c 2 2 ) 4 c 2 υi EwE(t, i x) + O(4), W a E (T, X) = δa i [w i E (t, x) υi E w E(t, x)] + O(2), w E (t, x) = W E (T, X)(1 + 2υE/c 2 2 ) + 4 c δ iaυew i E(T, a X) + O(4), 2 we i (t, x) = δi awe a(t, X) + υi E W E(T, X) + O(2). (65) 6 IAU2000 IAU2000 IAU 10 IAU
19 1 113 Gaia IAU2000 Klioner 2003 Gaia (GREM) [38] IAU2000 β, γ de Felice RAMOND [39 41] master RAMOND IAU BCRS RAMOND 1 BCRS 0.1 (VLBI) IAU2000 [42, 43] IAU2000 IAU2000 B-K DSX (PPN) Will BCRS 10 [44] JPL DE 2000 Klioner Soffel [45] 2004 Kopeikin Vlasov [46] IAU DSX 1PN BCRS (Klioner 0.1 [38] ) 0.1 GCRS 1PN 1 2PN GCRS Xu DSX 2PN [47] DSX IAU2000 B-D B-D Tao Huang DSX B-D [33] Klioner [48 50] DSX IAU BCRS GCRS ( ) [51, 52] IAU BCRS
20 GCRS DSX IAU [53] ( ) BCRS GCRS ( ) [54] Kopeikin [55, 56] Turyshev Toth N [57] DSX (1) (2) (3) IAU (, +, +, +) 2. c G 3. α β γ µ ν λ a b c i j k L i 1 i 2... i l, T L T i1i 2...i l, L 1 i 1 i 2... i l 1, T L 1 T i1i 2...i l 1 ; 6. Einstein S L T L i 1i 2...i l S i1i 2...i l T i1i 2...i l 7. ( ) 8. (STF) ˆT L T <L> STF(T L )
21 T (ij) (T ij + T ji )/2, S [i T j] (S i T j S j T i )/2 ; 10. δ ij Kronecker ɛ ijk Levi-Civita 11. g µν G αβ ( BCRS) ( GCRS) (ct, x i ) (ct, X a ) i / x i a / X a 12. O(n) O(c n ) A µ = O(m, n) A 0 = O(m), A i = O(n) B µν = O(m, n, p) B 00 = O(m), B 0i = B i0 = O(n), B ij = O(p) m, n, p > 0 [1]. ( ) 2002 [2] : 288 [3] Murphy T W. Space Science Review, 2009, 148: [4] Manchester R N. AIP Conference Proceedings, 2011, 1357: 65 [5] [6] Pearlman M, Noll C, Dunn P, et al. Journal of Geodynamics, 2005, 40: 470 [7] Gurtner W, Noomen R, Pearlman M R. Advances in Space Research, 2005, 36: 327 [8] Exertier P, Bonnefond P, Deleflie F, et al. Comptes Rendus Geosciences, 2006, 338: 958 [9] IERS / IVS Working Group. IERS Technical Note, 2009: 35 [10] [11] Brumberg V A, Kopeikin S M. Nuovo Cimento, 1989, 103B: 63 [12] Kopeikin S M. Celes. Mech., 1988, 44: 87 [13] Brumberg V A. Essential Relativistic Celestial Mechanics, Bristol: Adam Hilger, 1991: 15 [14] Damour T, Soffel M, Xu C. Phys. Rev. D, 1991, 43: 3273 [15] Damour T, Soffel M, Xu C. Phys. Rev. D, 1992, 45: 1017 [16] Damour T, Soffel M, Xu C. Phys. Rev. D, 1993, 47: 3214 [17] Damour T, Soffel M, Xu C. Phys. Rev. D, 1994, 49: 618 [18] Soffel M, Klioner S A, Petit G, et al. AJ, 2003, 126: 2687 [19] Pound R V, Rebka Jr G A. Phys. Rev. Lett., 1959, 3 (9): 439 [20] Shapiro I I. Phys. Rev. Lett., 1964, 13 (26): 789 [21] Shapiro I I, Ash M E, Ingalls R P, et al. Phys. Rev. Lett., 1971, 26 (18): 1132 [22] IAU XXIst General Assembly, Resolution, Buenos Aires, Argentina, 1991: A4 [23] Seidelmann P K, Fukushima T. A&A, 1992, 265: 833 [24] Fairhead L, Bretagnon P, Lestrade J-F. Proc. of the the IAU Symposium, 1988, 128: 419 [25]. 1999: 6 [26] Thorne K S. Rev. Mod. Phys., 1980, 52: 299 [27] Blanchet L, Damour T. Ann. Inst. Henri Poincaré A, 1989, 50: 377 [28] Anderle R J. Rev. Geophys. & Space Phys., 1979, 17: 1421 [29] Lerch F J. Rev. Geophys. & Space Phys., 1985, 21: 560 [30] Reigber C, Balmino G, Miiller H, et al. J. Geophys. Res., 1985, 90: 9285 [31] wgs84.html, 2013 [32] Hartmann T, Soffel M H, Kioustelidis T. Celes. Mech., 1994, 60: 139
22 [33] Tao J H, Huang T Y. A&A, 1998, 333: 1100 [34] Einstein A, Infeld L, Hoffmann B. Annals of Mathematics, 1938, 39: 65 [35] Klioner S A, Vionov A V. Phys. Rev. D, 1993, 48: 1451 [36] Klioner S A, Soffel M. A&A, 1998, 334: 1123 [37] Kopeikin S M. Manuscripta Geod., 1991, 16: 301 [38] Klioner S A. AJ, 2003, 125: 1580 [39] de Felice F, Bucciarelli B, Lattanzi M G, et al. ApJ, 2004, 607: 580 [40] de Felice F, Vecchiato A, Crosta M T, et al. ApJ, 2006, 653: 1552 [41] Crosta M, Vecchiato A. ApJ, 2010, 509: A37 [42] Eubanks T M A. Proc. of the USNO workshop on Relativistic Models for Use in Space Geodesy, Washington, 1991: 60 [43] McCarthy D D, Petit G. IERS Conventions, IERS Technical Report, 2003: 32 [44] Will C M. Theory and experiment in gravitational physics, Cambridge: Cambridge Univ. Press, 1993: 86 [45] Klioner S A, Soffel M H. Phys. Rev. D, 2000, 62: [46] Kopeikin S A, Vlasov I. Phys. Rep., 2004, 400: 209 [47] Xu C, Klioner S A, Soffel M, Wu X. IAU Joint Discussion 7: Space-Time Reference Systems for Future Research at IAU General Assembly, Beijing, 2012 [48] Klioner S A, Soffel M. Proceedings of Journées, Paris: Paris Observatory, 2007: 139 [49] Klioner S A, Soffel M. Proceedings of the Journées Systèmes de référence spatio-temporels, Soffel M and Capitaine N eds. Lohrmann-Observatorium and Observatoire de Paris Paris, 2008: 3 [50] Klioner S A, Gerlach E, Soffel M. Proc. of the IAU Symposium, 2010, 261: 112 [51] Kopeikin S M, Xie Y. Acta Phys.Slov., 2010, 60: 393 [52]. 2010: 5 [53] Xu M H, Wang G L and Zhao M. A&A, 2012, 544: A135 [54] Kopeikin S M. Proc. of the IAU Symposium, 2009, 261: 7 [55] Kopeikin S M. Phys. Rev. D, 2012, 86: [56] Kopeikin S M. Phys. Rev. D, 2013, 87: [57] Turyshev S G, Toth V T. arxiv: , 2013 Review and Prospect of the Relativistic Astronomical Reference System HAN Wen-biao 1, TAO Jin-he 1, MA Wei 2 (1. Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai , China; 2. School of Economics and Management, Tongji University, Shanghai , China) Abstract: The International Astronomical Union (IAU) released two important resolutions about the relativistic astronomical reference systems at the year 1991 and 2000 respectively. Especially the resolutions in the year 2000, based on two equivalent theories of multi-reference systems of relativistic N-body system: Brumberg-Kopeikin formalism and Damour-Soffel-Xu formalism, the resolutions constructed theoretically rigorous and consistent local reference system and global reference system with first order post-newtonian (1PN) level, and gave
23 1 117 out the coordinate-transformation rules between the two reference systems. During the more than ten years after the publication of the IAU2000 resolutions, it has begun to be used in some data-processing models of the highly accurate astrometry. But the engineerization of the IAU2000 resolutions is still not widely implemented, especially, there is almost no application of the resolutions to astronomical observations and space explorations in China. Therefore, it is necessary to introduce the IAU s relativistic theory of astronomical references in details. Firstly we introduce the simple resolutions on relativistic reference systems given by IAU in 1991; And the Brumberg-Kopeikin and Damour-Soffel-Xu formalisms are discussed in detail in the chapter 3 and 4; Then, we give out the details of the IAU2000 resolutions about the relativistic reference-system theory. Finally, we try to give some discussions of the engineerization of the IAU2000 resolutions, theoretical progress of the relativistic reference systems in the recent ten years, and prospects for the future. Key words: celestial mechanics; astrometry; general relativity; astronomical reference system
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年 月总第 8 期 数学方法与数学思想 编辑点评 数学与哲学都是研究最普遍的事物的 但是研究的角度 目的 方法 过 程和成果并不一样 所以两者之间有联系也有区别 该文通过对像 先有鸡 还是先有蛋 这样一些通俗又典型的例子 说明数学家与哲学家对于同一 个问题思维和处理的方式如何不同 便于读者形象地理解文中的论点 文 章的论述比较恰当 准确 深刻 写作也通顺流利 是一篇可读性较强的 文章 值得读者体会和学习
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