Astronomical determination of the Earth's dynamical flattening using VLBI observations and IAU 2006/2000 Precession-Nutation Model

Thu, 21 May 2026 00:00:00 +0000

Background and method

The Earth’s dynamical flattening, $H_{\mathrm d}$, describes the distribution of its principal moments of inertia and is a fundamental parameter in precession-nutation theory:

$$ H_{\mathrm d}=1-\frac{A+B}{2C}, $$

where $A$ and $B$ are the equatorial principal moments of inertia and $C$ is the axial moment.

We estimate this parameter directly from celestial intermediate pole (CIP) coordinates obtained by combining the IAU 2006/2000 precession-nutation model with VLBI celestial pole offsets. The analysis considers four individual analysis-centre series and the IERS C04 combined series, with free core nutation removed before fitting.

The method explicitly accounts for the dependence of several precession-rate contributions and the main nutation term on $H_{\mathrm d}$, while incorporating additional theoretical corrections. This provides a consistent determination of dynamical flattening within the precession-nutation framework.

Main results

The estimated dynamical flattening is $H_{\mathrm d}=0.00327380936\pm5\times10^{-11}$, with the quoted uncertainty being formal. This differs from the IAU 2006 adopted value by approximately 4.54 ppm.
The simultaneously estimated frame-bias components are $\delta X=-16603\pm8,\mu\mathrm{as}$ and $\delta Y=-7033\pm8,\mu\mathrm{as}$, in good agreement with the IAU model.
A separate analysis using 15-year sliding windows with a 2-year step estimates long-term changes in $H_{\mathrm d}$ and converts them to changes in the Earth’s second zonal gravity coefficient, $J_2$, under the adopted relationship.
The VLBI-derived $J_2$ variations show a broadly parabolic long-term trend, generally consistent with smoothed satellite laser ranging results, although differences remain for some windows.

These results demonstrate the value of VLBI precession-nutation observations as an independent probe of long-term changes in the Earth’s dynamical figure and provide observational constraints for further refinement of Earth-rotation models.

Dynamical Flattening | NJU Astrometry Group

Astronomical determination of the Earth's dynamical flattening using VLBI observations and IAU 2006/2000 Precession-Nutation Model