*Astron. Astrophys. 318, 639-652 (1997)*
## 3. Terms of nutation coming from the sectorial parts *C*_{2,2} and *S*_{2,2} of the geopotential
*A*, *B*, and *C* being the principal moments of
inertia of the Earth, the dimensionless coefficients
and of the geopotential
are characterzing the dynamical triaxiality of the Earth, by the way
of the following equation:
Although the Earth is relatively close to an axisymetric body,
with: , the influence of the difference
on the nutation of the Earth is not negligible.
It was calculated firstly by Kinoshita (1977) for the 3 biggest terms
and by Kinoshita & Souchay (1990), up to 0.005 milliarcsecond
(mas). The expression of the luni-solar potential related to the
triaxiality can be expressed as follows (Kinoshita 1977):
where , and
are the geocentric distance, latitude and
longitude of the perturbing body (Moon or Sun).
is given by the following formula (Kinoshita
1977):
*h*, *l* and *g* are the canonical variables in
Kinoshita (1977) theory. Three planes are involved in order to define
these variables. *h* is defined along the ecliptic of the date
from the mean equinox of the date to the intersection with the plane
perpendicular to the angular-momentum vector. *g* is the angle
from that intersection along the angular momentum plane and its
intersection with the equator. And *l* is from that last
intersection to the prime meridian. Thus the sum
() is equivalent to the sidereal angle of
rotation .
The polynomials have the following
expressions:
Notice that for the Sun, we can adopt the approximations:
and: . The coefficients
of the nutation due to the triaxiality can be calculated starting from
the determining function, by integrating the potential as given by
(9):
Then, by the following partial derivatives:
The constant terms and
, which serve as a scaling factor respectively
for the action of the Moon and of the Sun, are given by the following
relationships:
where the value of the constant term has
been given in Sect. 2, when calculating the terms of the nutation due
to , and where in a similar manner an accurate
value of has been recently calculated with an
updated value of the general precession in longitude by Souchay &
Kinoshita (1996), that is: . We choose for the
ratio the same value as in (Hartmann et al.
1995) which is significantly different from the value in Kinoshita
& Souchay (1990), that is to say: instead
of .
The results of the computations are listed in Table 2. Notice
that all the terms have a quasi semi-diurnal period, because of the
presence of in their argument. We have 34
coefficients up to 0.1 *µ*as instead of the 7 coefficients
up to 5 *µ*as found by Kinoshita & Souchay (1990). A
sign error has been detected in this last work, for the term of
amplitude as and argument
. Moreover, a big correction concerns the
amplitude of the term of argument which is
as instead of as. Except
this term all the other ones have been confirmed.
**Table 2.** Coefficients of rigid Earth nutation coming from the Earth triaxiality. Comparison of new results (this paper) is made with results of Kinoshita & Souchay (1990), both in longitude and in obliquity
© European Southern Observatory (ESO) 1997
Online publication: July 8, 1998
helpdesk.link@springer.de |