PDF《SOFA software support for IAU 2000》

by the end of the century it will have drifted only as far as αICRS = 0h 00m 00s.0046. ? The CEO can be thought of as "a kinematically defined place on the celestial equator close to where the ICRS prime meridian crosses". AAS

2004 Denver,

2004 May

31 What is precession? ? Astronomers have traditionally talked of "the precession of the equinoxes" and also have distinguished between luni-solar precession, planetary precession and general precession. ? Lay people just talk about what the pole does. ? Indeed, precession can simply be regarded as the slow component of the motion of the Earth's axis;

this is the IAU

2000 picture. ? In IAU 2000, the clean separation between the pole's motion and Earth rotation makes things clearer and reduces "cross-talk" effects. AAS

2004 Denver,

2004 May

31 Precession-nutation, old and new A ωA ?ψ A ε + ? ε χA A+? χ χ ?ψ1 mean equator of epoch mean equator of date ψ - ' ζ A

90 ο + zA

90 ο ωA γ

1 θA Q εA ? ε1 + equator of date γ o f e p o c h fixed ecliptic GST εO O γ ? instantaneous origin of longitude m γ e c l i p t i c o f d a t e γ

1 (TEO) 90° + E Σo α( ) σ 90° + moving equator Σ N d s γ equinox σ CEO stellar angle θ ? E celestial reference plane CRS Classical: equinox-based New: CEO-based ? Precession of the equator ↑ Precession of the ecliptic ? nutation of the equator ?Precession-nutation of the equator AAS

2004 Denver,

2004 May

31 So what happened to the ecliptic? ? The ecliptic remains important in a qualitative and descriptive sense… ? …and is part of constructing a precession model… ? …but is no longer needed to define the zero point of right ascension. ? The ecliptic is in any case a rather slippery concept: ? Is the ecliptic defined by the EMB's path, or the orbital angular momentum vector? n.b. Difference ~ 0.1 arcsec. ? Does it go through the Sun? Solar system barycentre? Earth- Moon-Sun barycentre? ? What about long-period nutation terms? ? There is no "IAU

2000 ecliptic" in the SOFA software. AAS

2004 Denver,

2004 May

31 Precession-nutation matrix, new method R(t )=R3(-E) ・ R2(-d) ・ R3(E + s - θ) = Q(t) ・ R3(-θ) X = sin d cos E, Y = sin d sin E, and Z = cos d where a = ? + (X2 + Y2)/8 ( ) ( ) s R Y X a -

1 Y - X - Y aY -

1 aXY - X aXY - aX -

1 Q(t)

3 2

2 2

2 ? ? ? ? ? ? ? ? ? ? ? + = AAS

2004 Denver,

2004 May

31 Direct models for CIP X,Y X = - 0. "016617 + 2004."191743 t - 0."4272190 t2 - 0."1986205 t3 - 0."0000460 t4 + 0."0000060 t5 + Σi [(as,0) i sin(ARGUMENT) + (ac,0) i cos(ARGUMENT)] + Σi [(as,1) i t sin(ARGUMENT) + (ac,1) i t cos(ARGUMENT)] + Σi [(as,2) i t2 sin(ARGUMENT) + (ac,2) i t2 cos(ARGUMENT)] + … Y = - 0."006951 - 0."025382 t - 22."4072510 t2 + 0."0018423 t3 + 0."0011131 t4 + 0."0000099 t5 + Σi [(bc,0)i cos(ARGUMENT) + (bs,0)i sin(ARGUMENT)] + Σi [(bc,1)i t cos(ARGUMENT) + (bs,1)i t sin(ARGUMENT)] + Σi [(bc,2)i t2 cos(ARGUMENT) + (bs,2)i t2 sin(ARGUMENT)] + ... (Capitaine, Chapront, Lambert, Wallace 2003, A&A 400) precession;

bias effect;

nutation;

cross terms precession * nutation AAS

2004 Denver,

2004 May

31 X,Y from classical precession-nutation matrix vGCRS = B ・ P ・ N ・ vTRUE = R ・ vTRUE B = frame bias matrix (GCRS ? mean J2000) = R3(-?α0)・R2(-?ξ0)・R1(?η0) P = precession matrix = R1(-ε0) ・ R3(ωA) ・ R1(ψA) ・ R3(-χA) N = nutation matrix = R1(-εA) ・ R2(?ψ) ・ R1(εA+?ε) R = classical precession-nutation matrix = B・P・N (X,Y)CIP = matrix elements R(1,3) and R(2,3) AAS