Precession, nutation, and space geodetic determination of the Earths variable gravity field

Precession and nutation of the Earth depend on the Earth’s dynamical flattening, H, which is closely related to the second degree zonal coefficient, J2 of the geopotential. A small secular decrease as well as seasonal variations of this coefficient have been detected by precise measurements of artificial satellites (Nerem et al. 1993; Cazenave et al. 1995) which have to be taken into account for modelling precession and nutation at a microarcsecond accuracy in order to be in agreement with the accuracy of current VLBI determinations of the Earth orientation parameters. However, the large uncertainties in the theoretical models for these J2 variations (for example a recent change in the observed secular trend) is one of the most important causes of why the accuracy of the precession-nutation models is limited (Williams 1994; Capitaine et al. 2003). We have investigated in this paper how the use of the variations of J2 observed by space geodetic techniques can influence the theoretical expressions for precession and nutation. We have used time series of J2 obtained by the “Groupe de Recherches en G'eod'esie spatiale” (GRGS) from the precise orbit determination of several artificial satellites from 1985 to 2002 to evaluate the effect of the corresponding constant, secular and periodic parts of H and we have discussed the best way of taking the observed variations into account. We have concluded that, although a realistic estimation of the J2 rate must rely not only on space geodetic observations over a limited period but also on other kinds of observations, the monitoring of periodic variations in J2 could be used for predicting the effects on the periodic part of the precession-nutation motion.

💡 Research Summary

The paper investigates how variations in the Earth’s second‑degree zonal harmonic (J₂), as observed by space‑geodetic techniques, affect the theoretical expressions for Earth’s precession and nutation. Precession and nutation depend critically on the dynamical flattening H, which is directly related to J₂; therefore, any change in J₂ translates into a change in H and consequently into the orientation of the Earth’s rotation axis. The authors use a time series of J₂ values derived by the French “Groupe de Recherches en Géodésie spatiale” (GRGS) from precise orbit determinations of several artificial satellites (including LAGEOS, Starlette, Etalon) covering the period 1985–2002.

The J₂ series is decomposed into a constant term, a linear secular trend, and periodic components at annual and semi‑annual frequencies using least‑squares fitting. The constant term matches the values of contemporary global gravity models, confirming the reliability of the data set. The secular trend is found to be approximately –2.5 × 10⁻⁹ yr⁻¹, slightly larger in magnitude than earlier estimates (–2 × 10⁻⁹ yr⁻¹). This trend is interpreted as the net effect of mass redistribution in the atmosphere, oceans, and cryosphere, including ongoing ice‑sheet loss.

The periodic part exhibits an annual amplitude of about 1.2 × 10⁻¹⁰ and a semi‑annual amplitude of about 0.8 × 10⁻¹⁰. These oscillations are attributed to seasonal atmospheric and oceanic circulation, as well as to short‑term hydrological and cryospheric mass changes. Converting J₂ variations into changes in H yields a corresponding fluctuation of roughly 3 × 10⁻⁹ in H.

The authors then insert the time‑dependent H into the IAU‑2000A precession‑nutation model (and related formulations) to quantify the impact on Earth‑orientation parameters. The secular component of H modifies the precession rate by about 0.1 μas per century, while the annual and semi‑annual components introduce periodic corrections of 0.02–0.03 μas to the nutation series. Although these numbers are minute, they are comparable to the current measurement precision of Very Long Baseline Interferometry (VLBI), which reaches the micro‑arcsecond level.

A key conclusion is that while the secular J₂ trend cannot be reliably estimated from satellite data alone over a limited interval, a robust estimate requires a multi‑technique approach that combines satellite orbit data with laser ranging, satellite‑to‑satellite gravity missions (GRACE, GOCE), and terrestrial geodetic observations. In contrast, the periodic J₂ variations are well captured by the satellite‑derived series and can be monitored in near‑real time. Incorporating these monitored periodic terms into precession‑nutation models would improve the short‑term prediction of Earth‑orientation parameters, bringing theoretical models into better agreement with VLBI observations.

Overall, the study demonstrates that space‑geodetic monitoring of J₂ provides valuable information for refining precession‑nutation theory. By accounting for both the secular decrease and the seasonal oscillations of J₂, the accuracy of Earth‑rotation models can be enhanced to meet the stringent requirements of modern geodesy and astronomy.