Expresssions for the difference between the IAU 2006 and IAU 2000A
expressions for X and Y, Dpsi and Deps
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The non-polynomial part of each expression (ARG being for various combination of
the fundamental arguments of the nutation theory) is written as:
Sum_i[D_{s,0})_i * sin(ARG) + D_{c,0})_i * cos(ARG)]
+ Sum_i)j=1,4 [D_{s,j})_i * t^j * sin(ARG) + D_{c,j})_i * cos(ARG)] * t^j]
The Tables below provides the values for D_{s,j})_i and D_{c,j})_i
The expressions for the fundamental arguments appearing in columns 4 to 8
are those of the IERS Conventions 2003
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1) Difference between the IAU 2006 and IAU 2000A expressions for X and Y
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1-1 X_IAU 2006 - X_IAU2000A = polynomial part + non-polynomial part
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Polynomial part (unit microarcsecond)
155. t - 2564.0 t^2 + 2.20 t^3 + 53.63 t^4
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Non-polynomial part (unit microarcsecond; cutoff: 0.1 microarcsecond)
Note that, according to Eq. (16) of Chapter 5,
D_{s,j})_i is for the difference in a_{s,j})_i,
D_{c,j})_i is for the difference in a_{c,j})_i,
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i D_{s,j})_i D_{c,j})_i l l' F D Om
-----------------------------------------------------------------
j = 1 Nb of terms = 5
1 18.75 -0.04 0 0 0 0 1
2 1.44 0.00 0 0 2 -2 2
3 0.25 0.00 0 0 2 0 2
4 -0.22 0.00 0 0 0 0 2
5 -0.17 0.00 0 1 0 0 0
j = 2 Nb of terms = 1
6 -0.02 -0.80 0 0 0 0 1
-----------------------------------------------------------------
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1-2 Y_IAU 2006 - Y_IAU2000A = polynomial part + non-polynomial part
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Polynomial part (unit microarcsecond)
- 0.2 - 514. t - 23.7 t^2 + 58.31 t^3 - 0.53 t^4 - 0.85 t^4
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Non-polynomial part (unit microarcsecond; cutoff: 0.1 microarcsecond)
Note that, according to Eq. (16) of Chapter 5,
D_{s,j})_i is for the difference in b_{s,j})_i,
D_{c,j})_i is for the difference in b_{c,j})_i,
-----------------------------------------------------------------
i D_{s,j})_i D_{c,j})_i l l' F D Om
-----------------------------------------------------------------
j = 1 Nb of terms = 4
2 -0.03 -25.57 0 0 0 0 1
3 0.00 -1.59 0 0 2 -2 2
4 0.00 -0.27 0 0 2 0 2
5 0.01 0.25 0 0 0 0 2
j = 2 Nb of terms = 1
6 -0.59 0.00 0 0 0 0 1
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2) Difference between the IAU 2000_R06 and IAU 2000A nutation expressions
2-1: Nutation in longitude, Dpsi
Note that, according to Eq. (35) of Chapter 5,
D_{s,0})_i is for the difference in A_i, D_{c,0})_i is for the difference in A"_i
D_{s,1})_i is for the difference in A'_i, D_{c,1})_i is for the difference in A"'_i
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Dpsi(IAU 2000A_R06 - IAU 2000A)
(unit microarcsecond; cutoff: 0.1 microarcsecond)
------------------------------------------------------------------
i D_{s,j})_i D_{c,j})_i l l' F D Om
--------------------------------------------------------------
j = 0 Nb of terms = 4
1 -8.08 0.00 0 0 0 0 1
2 -0.62 0.00 0 0 2 -2 2
3 -0.11 0.00 0 0 2 0 2
4 0.10 0.00 0 0 0 0 2
j = 1 Nb of terms = 8
5 47.78 -0.01 0 0 0 0 1
6 3.66 0.00 0 0 2 -2 2
7 0.63 0.00 0 0 2 0 2
8 -0.58 0.00 0 0 0 0 2
9 -0.41 0.00 0 1 0 0 0
10 -0.20 0.00 1 0 0 0 0
11 0.14 0.00 0 1 2 -2 2
12 0.11 0.00 0 0 2 0 1
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2-2: Nutation in longitude, Deps
Note that, according to Eq. (35) of Chapter 5,
D_{s,0})_i is for the difference in B"_i, D_{c,0})_i is for the difference in B_i
D_{s,1})_i is for the difference in B"'_i, D_{c,1})_i is for the difference in B'_i
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Deps(IAU 2000A_R06 - IAU 2000A)
(unit microarcsecond; cutoff: 0.1 microarcsecond)
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i D_{s,j})_i D_{c,j})_i l l' F D Om
--------------------------------------------------------------
j = 0 Nb of terms = 4
1 0.00 -25.57 0 0 0 0 1
2 0.00 -1.59 0 0 2 -2 2
3 0.00 -0.27 0 0 2 0 2
4 0.00 0.25 0 0 0 0 2
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