Fabian Roosbeek

RDAN97: An Analytical Development of Rigid Earth Nutation Series Using the Torque Approach

New series of rigid Earth nutations for the angular momemtum axis, the rotation axis and the figure axis, named RDAN97, are computed using the torque approach. Besides the classical J2 terms coming from the Moon and the Sun, we also consider several additional effects: terms coming from J3 and J4 in the case of the Moon, direct and indirect planetary effects, lunar inequality, J2 tilt, planetary‐tilt, effects of the precession and nutations on the nutations, secular variations of the amplitudes, effects due to the triaxiality of the Earth, new additional out‐of‐phase terms coming from second order effect and relativistic effects. Finally, we obtain rigid Earth nutation series of 1529 terms in longitude and 984 terms in obliquity with a truncation level of 0.1 μ (microarcsecond) and 8 significant digits. The value of the dynamical flattening used in this theory is HD=(C-A)/C=0.0032737674 computed from the initial value pa=50′.2877/yr for the precession rate. These new rigid Earth nutation series are then compared with the most recent models (Hartmann et al., 1998; Souchay and Kinoshita, 1996, 1997; Bretagnon et al., 1997, 1998. We also compute a benchmark series (RDNN97) from the numerical ephemerides DE403/LE403 (Standish et al., 1995) in order to test our model. The comparison between our model (RDAN97) and the benchmark series (RDNN97) shows a maximum difference, in the time domain, of 69 μas in longitude and 29 μas in obliquity. In the frequency domain, the maximum differences are 6 μas in longitude and 4 μ as in obliquity which is below the level of precision of the most recent observations (0.2 mas in time domain (temporal resolution of 1 day) and 0.02 mas in frequency domain).

Considerations concerning the non-rigid Earth nutation theory.

This paper presents the reflections of the Working Group of which the tasks were to examine the non-rigid Earth nutation theory. To this aim, six different levels have been identified: Level 1 concerns the input model (giving profiles of the Earths density and theological properties) for the calculation of the Earths transfer function of Level 2; Level 2 concerns the integration inside the Earth in order to obtain the Earths transfer function for the nutations at different frequencies; Level 3 concerns the rigid Earth nutations; Level 4 examines the convolution (products in the frequency domain) between the Earths nutation transfer function obtained in Level 2, and the rigid Earth nutation (obtained in Level 3). This is for an Earth without ocean and atmosphere; Level 5 concerns the effects of the atmosphere and the oceans on the precession, obliquity rate, and nutations; Level 6 concerns the comparison with the VLBI observations, of the theoretical results obtained in Level 4, corrected for the effects obtained in Level 5.Each level is discussed at the state of the art of the developments.

Tidally induced surface displacements, external potential variations, and gravity variations on Mars

Abstract We have used and extended Roosbeek’s tidal potential for Mars to calculate tidal displacements, gravity variations, and external gravitational potential variations. The tides on Mars are caused by the Sun, and to a lesser degree by the natural satellites Phobos (8%, relative to the Sun) and Deimos (0.08%, relative to the Sun). To determine the reaction of Mars to the tidal forcing, the Love numbers h, l, and k and the gravimetric factor δ were calculated for interior models of Mars with different state, density, and radius of the core and for models which include mantle anelasticity. The latitude dependence and frequency dependence of the Love numbers have been taken explicitly into account. The Love numbers are about three times smaller than those for the Earth and are very sensitive to core changes; e.g., a difference of about 30% is found between a model with a liquid core and an otherwise similar model with a solid core. Tidal displacements on Mars are much smaller than on Earth due to the smaller tidal potential, but also due to the smaller reaction of Mars (smaller Love numbers). For both the tidal diplacement and the tidal external potential perturbations, the tidal signal is at the limit of detection and is too small to permit properties of Mars’s interior to be inferred. On the other hand, the Phobos tidally induced gravity changes, which are subdiurnal with typical periods shorter than 12 h, can be measured very precisely by the very broad band seismometer with thermal control of the seismological experiment SEIS of the upcoming NetLander mission. It is shown that the Phobos-induced gravity tides could be used to study the Martian core.

Analytical developments of rigid Mars nutation and tide generating potential series

In this paper, series of rigid Mars nutations for the angular momentum axis, the rotation axis and the figure axis, as well as series of rigid Mars tide generating potential (TGP) are computed. The method used is based on the calculation of the forces produced by the external bodies on the rigid Mars. We have included the direct effect of the sun, Phobos and Deimos. We have also included the indirect effects associated with these bodies and planets of the Solar System which are given at the level of the ephemerides. For the nutation series, with a truncation level of 0.1 mas (milliarcsecond), related to the present-day precision of the Martian precession constant, 24 terms in longitudes (Δ*****) and 10 terms in obliquity (Δ*****) are computed. The value of the dynamical flattening used is HD=(C−A)/C=0.00536, derived from the value pa=−7576±35 mas/yr for the precession rate. Our results show a perfect agreement with those of Bouquillon and Souchay (1996) to the truncation level of Bouquillon and Souchary (1 mas). For the TGP series, we have set the truncation level to 10−6 m2/s2 which corresponds to an effect on the vertical acceleration on Mars’ surface of about 10−12 m/s2=0.1 nanogal (1 nanogal=10−11 m/s2. With this truncation level, 134 terms are computed.

The free core nutation period stays between 431 and 434 sidereal days

We determine the parameters of the Free Core Nutation (FCN) from the resonance induced in the forced nutations by a least-squares analysis of VLBI observations. By applying the procedure to consecutive observation series, we deduce the time evolution of the FCN period, and show that it varies only between 431 and 434 sidereal days. These bounds are within the limits of uncertainty arising from noise in the data. We therefore find no evidence for time variation of the FCN period.

Are the free core nutation parameters variable in time

Abstract The Free Core Nutation (FCN) is a normal mode of the Earth which induces resonance in the diurnal tides as well as in the nutations. This is particularly true for frequencies near the resonance frequency, i.e., for the retrograde annual nutation and the ψ1 tide. The paper aims at analyzing Very Long Baseline Interferometry (VLBI) data and superconducting gravimeter (SG) data in order to gain more information on the FCN period, damping, resonance strength and free mode amplitude. Section 2 deals with the variability as seen in precise tidal gravimetric observations from consecutive subsets of an SG located near Strasbourg (France). We will show that the apparent variations appearing in the eigenperiod, quality factor and strength are related to a variable noise level in the tidal gravimetric data. Section 3 is devoted to the analysis of the time variability of the VLBI series. In particular we show that the amplitude variations found in the forced nutational response of the Earth are not real but rather induced by a variable free mode excitation. We show that the eigenperiod is stable within a range of 3 days.

Time Transfer Experiments Using GLONASS P-code Measurements from RINEX Files

We have used GLONASS P-code measurements from different geodetic GPS/GLONASS receivers involved in the IGEX campaign to perform frequency/time transfer between remote clocks. GLONASS time transfer is commonly based on the clock differences between GLONASS system time and the local clock computed by a time transfer receiver. We choose to analyze the raw P-code data available in the RINEX files. This also allows working with the data from geodetic receivers involved in the IGEX campaign. As a first point, we show that the handling of the external frequency in some of the IGEX receivers is not suited for time transfer applications. We also point out that the GLONASS broadcast ephemerides give rise to a considerable number of outliers in the time transfer, compared to the precise IGEX ephemerides. Due to receiver clock resets at day boundaries, which is a characteristic of the R100 receivers from 3S-Navigation, continuous data sets exceeding one day are not available. Invthis context, it is therefore impossible to perform RINEX-based precise frequency transfer with GLONASS P-codes on a time scale longer than one day. Because the frequencies used by GLONASS satellites are different, the time transfer results must be corrected for the different receiver hardware delays. After this correction, the final precision of our time transfer results corresponds to a root-mean-square (rms) of 1.8 nanoseconds (ns) (maximum difference of 11.8 ns) compared to a rms of about 4.4 ns (maximum difference of 31.9 ns) for time transfer based on GPS C/A code observations.

Diurnal and Subdiurnal Terms in Rdan97 Series

In this paper, the series RDAN97 recently published (Roosbeek and Dehant, 1998) is completed by computing the diurnal and subdiurnal nutation terms. The method used is based on computing the torque induced by the external bodies on the rigid earth. The ephemerides used are analytical and based on celestial mechanics considerations. With a truncation level of 0.1 μas, 115 terms in longitude and 78 terms in obliquity have been computed. These terms correspond to the influence of the earths geopotential coefficients c2,2 and s2,2, c3,m and s3,m (for the interaction between the earth and the moon and the sun), and c4,m and s4,m (for the interaction between the earth and the moon). A comparison with the recent theories REN‐2000 (Souchay and Kinoshita, 1996, 1997) and SMART97 (Bretagnon et al., 1997, 1998) shows that our series is at a very high precision, better than the most recent VLBI campaigns.

The EUREF Permanent Network: Monitoring and On-line Resources

The EUREF Permanent Network (EPN) is a network of continuously operating GPS or GPS/GLONASS stations installed throughout the European continent. The EPN Central Bureau (CB), responsible for the daily management of the EPN, uses several monitoring procedures to verify the meta-data, latencies and quality of the observation data files in order to assess if the data meets the requirements of the analysis. In addition, several types of coordinate time series allow analysing the long-term stability of the site coordinates. All monitoring procedures result in regularly updated plots made available at the EPN CB website; they are created to be easily understood by all EPN station managers, even the non-specialists.