Conventional astronomical standards are applied to a wide range of applications, many of which do not require state-of-the-art precision. Stability of the standards is of great importance, although there is a trend by some in the astronomical community to promote frequent revision of the values of astronomical constants. It is possible to employ stable standards and to differentially correct them by use of the IERS formulation when very precise observations require such action.

The IERS formulation for the transformation from a fixed frame to an of-date frame involves precession and nutation along with two parameters δψ and δ which can represent modifications to the standard precession and nutation formulation. The transformation from the mean-of-date frame to the true-of-date frame in the IERS formulation using rotation matrices is rtrue = NrMean where

N = R1(−εm − Δε − δε) R3 (−ΔΨ − δΨ) R1(ε)m

where εm is the mean obliquity, ΔΨ and Δε are the nutations in longitude and obliquity, and where δψ and δε are IERS parameters which allow for changes to the IAU system. They are tabulated in the IERS reports and are generally thought of as observationally-determined values, but the IERS formulation can be used to introduce corrections of an arbitrary nature.