On observability of the free core nutation

TL;DR

This paper discusses the limitations and uncertainties in measuring and interpreting the free core nutation using astronomical techniques like VLBI, highlighting the impact of model choices on the accuracy of nutation parameter estimates.

Contribution

It provides a detailed analysis of how the choice of nutation models affects the interpretation of VLBI measurements and the inherent uncertainties in isolating free core nutation.

Findings

Model choice influences nutation parameter estimates.

Separating different nutation components involves uncertain hypotheses.

Limits exist in inferring free core nutation from observational data.

Abstract

Neither astronomical technique, including VLBI, can measure nutation directly. Estimates of parameters of the nutation model are produced by solving the LSQ problem of adjusting millions parameters using estimates of group delay. The choice of the mathematical model for nutation used in the estimation process of analysis of group delays affects our ability to interpret the results. Ignoring these subtleties and using parameters of the nutation model either in the form of time series, or in the form of empirical expansion as "VLBI measurement of nutation", opens a room for misinterpretation and mistakes. Detailed analysis of the problem reveals that the separation of forced nutations, atmospheric nutations, ocean nutations, and the retrograde free core nutation requires invoking some hypotheses, and beyond a specific level becomes uncertain. This sets a limit of our ability to make an inference about the free core nutation.