Precession In Longitude Research Articles

Precession of the non-rigid Earth: Effect of the mass redistribution

This research is focused on determining the contribution to the precession of the Earth’s equator due to the mass redistribution stemming from the gravitational action of the Moon and the Sun on a rotating solid Earth. In the IAU2006 precession theory, this effect is taken into account through a contribution of −0.960 mas cy−1for the precession in longitude (with the unspecific name of non-linear effect). In this work, the revised value of that second-order contribution reaches −37.847 mas cy−1when using the Love numbers values given in IERS Conventions, and −43.945 mas cy−1if those values are supplemented with the contributions of the oceanic tides. Such variations impose a change of the first-order precession value that induces relative changes of the Earth’s dynamical ellipticity of about 7.3 and 8.5 ppm, respectively. The corresponding values for the obliquity rate are 0.0751 and 0.9341 mas cy−1, respectively, in contrast to 0.340 mas cy−1considered in IAU2006. The fundamentals of the modeling have been revisited by giving a clear construction of the redistribution potential of the Earth through the corresponding changes in the Earth tensor of inertia. The dynamical problem is tackled within the Hamiltonian framework of a two-layer Earth model, introduced and developed by Getino and Ferrándiz. This approach allows for the achievement of closed-analytical formulae for the precession in longitude and obliquity. It makes it possible to obtain numerical values for different Earth models once a set of associated Love numbers is selected. The research is completed with a discussion on the permanent tide and the related estimation of the variation of the second degree zonal Stokes parameter,J2, and also the indirect effects on nutations arising from the relative change of the Earth’s dynamical ellipticity.

Changes of spin axis and rate of the asteroid (99942) Apophis during the 2029 close encounter with Earth: A constrained model

Context. The dramatic event of the 2029 close encounter between the Earth and the asteroid Apophis on April 13 2029 at a minimum distance of 38 400 km constitutes an opportunity to make investigations about the modeling of the rotational changes of the asteroid during the event. Aims. In this paper we deepen a previous study of the rotational changes of Apophis caused by gravitational effects during the close encounter, using important constraints on initial conditions brought by new recent observational data. We also evaluate the effects of the triaxial form of the asteroid on the motion of its axis of rotation in space, as well as the modifications of the spin rate due to tidal deformation. Methods. First we used more drastic constraints for the physical and geometrical parameters of Apophis, deduced from recent observational campaigns. Second we evaluated the disturbing potential due to the Earth depending not only on the asteroid flattening, but also on the component due to its triaxiality, to deduce the equations of motion and investigate the displacement of the spin axis. Third we estimated what should be the zonal deformation of the asteroid due to the tide exerted by the Earth during the close encounter and we measured the consequences on variations of the spin rate. Results. We show that the variations of obliquity and precession in longitude of Apophis during the 2029 close encounter can reach very large values, at the level of of respectiveley 1–10° and 10–40° depending on geometrical parameters. On the contrary, effects on the spin rate should be relatively small, leading to variations of the sidereal angle of rotation not exceeding 30 s. Conclusions. The tribute of this paper is to give a constrained model of the important rotational variations of Apophis during its 2029 close encounter with the Earth.

Improvement of the IAU 2000 precession model

The IAU 2000 precession consists of the IAU 1976 ecliptic precession (Lieske et al. 1977, AA the model is recalled in Tables 3−5. Due to the strong dependence of the precession expressions on the precession rates and of the precession in longitude (or equivalently the celestial CIP X coordinate) on the J2 rate model, we also provide a parameterized P04 solution for these quantities as functions of those parameters. The expressions include the quantities to be used in both the equinox-based and CIO-based (i.e. referred to the Celestial Intermediate Origin) transformations.

Effects of zonal deformations and the Earth's rotation rate variations on precession-nutation

Because of their importance in the accurate modeling of the Earth's orientation in space, some non-negligible predictable effects on precession-nutation are investigated. This paper considers the coupling effects between the axial and the equatorial components of the Earth's rotation vector in the dynamical equations, and the effects of the second order lunisolar torque due to the Earth's zonal deformations. Firstly, the coupling effects are shown to contribute for less than 0.1 μ as and are therefore negligible. Secondly, we demonstrate that the 0.7 mas contribution of the rotation rate variations due to zonal tides to the nutation in obliquity deduced by Bretagnon et al. ([CITE], Proc. IAU Coll., 180, 230; [CITE], Celest. Mech. Dyn. Astr., 80, 177) is an artefact which comes from an incomplete way of taking into account the effect of the rotation rate variations. The net contribution is shown to be negligibly small. Thirdly, for an Earth model with an elastic mantle and decoupled liquid core, the contribution of the second-order lunisolar torque due to the Earth's zonal deformations is shown to be 207.9 μ as and –9.7 μ as on the 18.6-year nutation respectively in longitude and in obliquity, and a correction of –4925.9 μ as/century on the precession in longitude.

A precise modeling of Eros 433 rotation

Thanks to the recent data obtained from the NEAR space probe, we calculate in this paper, with a precision never reached so far for an asteroid, the precession and the nutation of Eros 433. In a preliminary step, we show that Eros obliquity has a remarkable value of 89.0° which tends to align its figure axis along the orbital plane. This very specific obliquity has some consequences on the motion of the axis of figure: one is the very small amplitude of the precession in longitude, for which we get the value ψ ̇ =2″.84/ y . Moreover, we calculate Eros nutation for the figure axis due to the Sun, after developing the perturbing potential at the 4th order of the eccentricity. We show that the figure axis undergoes very large oscillations in the direction perpendicular to Eros orbital plane, due to the nutation in obliquity. Peak to peak, these oscillations reach 55″, which is far larger than the amplitudes of the nutations of the Earth due to the Sun (of the order of 2″). Moreover, we give the analytical developments of Δ ψ and Δ ε, both for the axis of angular momentum, and the axis of figure.

A New Precession Formula

We adapt J. G. Williams' expression of the precession and nutation using the 3-1-3-1 rotation to an arbitrary inertial frame of reference. The modified formulation avoids a singularity caused by finite pole offsets near the epoch. By adopting the planetary precession formula numerically determined from DE405 and by using a recent theory of the forced nutation of the nonrigid Earth by Shirai & Fukishima, we analyze the celestial pole offsets observed by VLBI for 1979-2000 and determine the best-fit polynomials of the lunisolar precession angles. We then translate the results into classical precession quantities and evaluate the difference due to the difference in the ecliptic definition. The combination of these formulae and the periodic part of the Shirai-Fukishima nutation theory serves as a good approximation of the precession-nutation matrix in the International Celestial Reference Frame. As a by-product, we determine the mean celestial pole offset at J2000.0 as 0 = -(17.12 ± 0.01) mas and 0 = -(5.06 ± 0.02) mas. Also, we estimate the speed of general precession in longitude at J2000.0 as p = 50287955 ± 00003 per Julian century, the mean obliquity at J2000.0 in the inertial sense as (0)I = 8438140621 ± 000001 and in the rotational sense as (0)R = 8438140955 ± 000001, and the dynamical flattening of Earth as Hd = (3.2737804 ± 0.0000003) × 10-3. Furthermore, we establish a fast way to compute the precession-nutation matrix and provide a best-fit polynomial of an angle to specify the mean Celestial Ephemeris Origin.

Lunisolar torque on the atmosphere and Earth's rotation

The atmospheric effect on Earth's rotation is classically computed from atmospheric angular momentum (AAM) series by considering that the whole AAM variations are transmitted to the solid Earth. In fact, such a procedure is an approximation because it ignores that the atmosphere exchanges also angular momentum with the moon and the sun. The computation of the lunisolar gravitational torque on the atmosphere is the core of the present study. It is derived analytically and then estimated from pressure data over the period 1975–2000. The mean surface pressure is the main contributor, at the level of 10 17 N m for the equatorial component, 10 16 N m for the axial one, whereas the thermally driven pressure variations provide about 10% of the variance. This torque plays a significant role in the budget of the atmospheric angular momentum, but does not account for the inconsistency between the present series of the atmospheric angular momentum and the interaction torque between the solid Earth and the atmosphere. From the tidal waves of this torque we derive accurately the contribution of the atmosphere to the lunisolar precession–nutation of the Earth ( 0.31 marcsec/year for the precession in longitude, 46 microarcseconds for the nutation in 18.6 years).

Expressions for Precession Formulae

In 1976, the IAU recommended for the value of the precession constant 50".290 966 per Julian year and, since 1984, most of the ephemerides have used the formulas of Lieskeet al.(1977). In this paper, the motion of the ecliptic was based on Newcomb’s theory. The ecliptic was defined with an accuracy of 0".3 over 1000 years and of 6 mas over one century around J2000. For several years, new determinations of the precession constant have showed that this value is too high by about 3 mas per year. For instance, Williamset al.(1991) give 50".2882 per year. From this value and from the mean elements defining the ecliptic given by Simonet al(1994), we have built new expressions for precession formulae. The motion of the mean ecliptic is described through variablesqandp:wheretis the time reckoned in thousands Julian years from J2000. This solution has an accuracy of 1 mas over several thousands years and 0.1 mas over one century around J2000. The variations of the equator are obtained by integration of the differential equations of the precession in longitude and of the obliquity in Kinoshita (1977) and Kinoshita and Souchay (1990). The dynamical ellipticity is determined in order to obtain (dP/dt) = 50 288".2 att= 0 asHd= 0.003 273 7752. From this value forHd, we can integrate the differential equations forPand ε:

The evolution of adopted values for precession

A survey of values of the speed of general precession in longitude is presented from the time of Bessel to the adoption of the new value by the IAU in 1976 for use in the FK5 and the J2000 reference system. The important contributions of Walter Fricke to this area of fundamental astronomy are outlined.

Long-term variations of caloric insolation resulting from the earth's orbital elements

A contribution to a global a priori model of climatic changes for the Quaternary Ice Age is tentatively proposed. Special emphases are put on the astronomical problem and on the insolation available in the assumption of a perfectly transparent atmosphere. It is shown that for these two steps an accurate solution can be obtained, limiting the cumulative effect of computational approximation and allowing input to a climatological model to be of real value. For the earth's orbital elements, the proposed solution includes terms dependent to the second degree on disturbing masses, to third degree on planetary eccentricities and inclinations and, for the obliquity and the annual general precession in longitude, also to the second degree on earth's eccentricity. Improvements introduced by this solution upon the insolation computed through the Milankovitch series are deduced from the differences between Vernekar's results and present ones. The relative agreement between results clearly shows that the new astronomical solution is probably close to the ideal one from a paleoclimatological point of view.