SpringerLink
Forum Springer Astron. Astrophys.
Forum Whats New Search Orders


Astron. Astrophys. 318, 639-652 (1997)

Previous Section Next Section Title Page Table of Contents

3. Terms of nutation coming from the sectorial parts C2,2 and S2,2 of the geopotential

A, B, and C being the principal moments of inertia of the Earth, the dimensionless coefficients [FORMULA] and [FORMULA] of the geopotential are characterzing the dynamical triaxiality of the Earth, by the way of the following equation:

[EQUATION]

Although the Earth is relatively close to an axisymetric body, with: [FORMULA], the influence of the difference [FORMULA] 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):

[EQUATION]

where [FORMULA], [FORMULA] and [FORMULA] are the geocentric distance, latitude and longitude of the perturbing body (Moon or Sun).

[FORMULA] is given by the following formula (Kinoshita 1977):

[EQUATION]

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 ([FORMULA]) is equivalent to the sidereal angle of rotation [FORMULA].

The [FORMULA] polynomials have the following expressions:

[EQUATION]

Notice that for the Sun, we can adopt the approximations: [FORMULA] and: [FORMULA]. 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):

[EQUATION]

Then, by the following partial derivatives:

[EQUATION]

The constant terms [FORMULA] and [FORMULA], which serve as a scaling factor respectively for the action of the Moon and of the Sun, are given by the following relationships:

[EQUATION]

where the value of the constant term [FORMULA] has been given in Sect. 2, when calculating the terms of the nutation due to [FORMULA], and where in a similar manner an accurate value of [FORMULA] has been recently calculated with an updated value of the general precession in longitude by Souchay & Kinoshita (1996), that is: [FORMULA]. We choose for the ratio [FORMULA] the same value as in (Hartmann et al. 1995) which is significantly different from the value in Kinoshita & Souchay (1990), that is to say: [FORMULA] instead of [FORMULA].

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 [FORMULA] in their argument. We have 34 coefficients up to 0.1 µas instead of the 7 coefficients up to 5 µas found by Kinoshita & Souchay (1990). A sign error has been detected in this last work, for the term of amplitude [FORMULA] as and argument [FORMULA]. Moreover, a big correction concerns the amplitude of the term of argument [FORMULA] which is [FORMULA] as instead of [FORMULA] as. Except this term all the other ones have been confirmed.


[TABLE]

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


Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998
helpdesk.link@springer.de