Table 3: Effects of the second order contribution of the tidal potential (zonal tides contribution) on nutation angles ( $\mu$ as) and precession ( $\mu$ as/c) from different studies. MHB 2000Z: values of Mathews et al. (2002) including only the zonal tides contribution; SF99: Souchay & Folgueira (2000).
$\Delta\psi$ $\Delta\epsilon$

$\mu$ as $\mu$ as

l l' F D $\Omega$ sin cos sin cos

0 0 0 0 1

MHB 2000Z $^{\star}$ 101.3 - - $^{\star}$ -8.9

SF99 168.0 - - -9.0

This study 207.9 2.4 0.2 -9.7

0 0 0 0 2

MHB 2000Z - - - -

SF99 4.5 - - -2.8

This study 5.0 0.1 0.0 -3.2

0 0 2 -2 2

MHB 2000Z - - - -

SF99 3.2 - - 0.6

This study 4.0 0.0 0.0 0.4

Precession in longitude $\mu$ as/c

MHB 2000Z -

SF99 -

This study -4925.9

$^{\star}$ Note that revised values by Mathews (2004) are 194 $\mu$ as and -10 $\mu$ as for the 18.6-year
nutation in longitude and obliquity, respectively.

**Table 3:** Effects of the second order contribution of the tidal potential (zonal tides contribution) on nutation angles ( $\mu$ as) and precession ( $\mu$ as/c) from different studies. MHB 2000Z: values of Mathews et al. (2002) including only the zonal tides contribution; SF99: Souchay & Folgueira (2000).
	$\Delta\psi$	$\Delta\epsilon$
	$\mu$ as	$\mu$ as
l	l'	F	D	$\Omega$	sin	cos	sin	cos
0	0	0	0	1
MHB 2000Z	$^{\star}$ 101.3	-	-	$^{\star}$ -8.9
SF99	168.0	-	-	-9.0
This study	207.9	2.4	0.2	-9.7
0	0	0	0	2
MHB 2000Z	-	-	-	-
SF99	4.5	-	-	-2.8
This study	5.0	0.1	0.0	-3.2
0	0	2	-2	2
MHB 2000Z	-	-	-	-
SF99	3.2	-	-	0.6
This study	4.0	0.0	0.0	0.4
Precession in longitude	$\mu$ as/c
MHB 2000Z		-
SF99		-
This study		-4925.9

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