The IAU 2006 precession quantities with an improved Earth's $J_{2}$ long-term variation

Sat, 01 Nov 2025 00:00:00 +0000

Updating the long-term variation of Earth’s oblateness

The IAU 2006 precession model incorporates a linear trend in Earth’s gravitational coefficient $J_{2}$, which characterizes its oblateness. However, satellite laser ranging observations extending from 1976 to 2025 show that the long-term evolution of $J_{2}$ is better represented by a parabola.

We use these observations to determine an updated empirical model of $J_{2}$ and incorporate it into the integration of the precession equations. The resulting solution, named IAU $2006_{J_{2}}$, follows the framework of the IAU 2006 model while updating the polynomial expressions for the precession quantities.

Main results

A better-supported nonlinear trend: Nearly 50 years of satellite laser ranging data provide stronger evidence for a parabolic variation of $J_{2}$ than was available in earlier studies.
Revised precession quantities: The updated $J_{2}$ model mainly changes the quadratic and cubic terms of the precession in longitude, while the precession in obliquity remains close to the IAU 2006 solution.
Improved agreement with VLBI: Comparisons with the C04 and OPA2025a celestial pole offset series show that the updated model removes most of the residual curvature in $\mathrm{d}X$.
Smaller residuals before empirical fitting: The weighted root-mean-square values decrease from 179 to 130 microarcseconds for C04 and from 193 to 147 microarcseconds for OPA2025a.

Implications

The results provide observational support for updating the precession model within the IAU 2006 framework. The paper proposes the solution for consideration by the IAU/IAG CIERT working group and in a future revision of the IERS Conventions.

Further work on the corresponding nutation corrections is needed to ensure consistency between precession and nutation when the time variation of Earth’s dynamical flattening is taken into account.

C.-L. Huang | NJU Astrometry Group

The IAU 2006 precession quantities with an improved Earth's $J_{2}$ long-term variation

Updating the long-term variation of Earth’s oblateness

Main results

Implications