Total Effect of any Nearly-Diurnal Wobble of the Earth's Axis of Rotation in Latitude and Time Observations. Application to the Paris Astrolabe Observations from 1956.6 to 1973.8

Abstract

Summary The existence of a non-spherical ideal liquid core in the Earth's interior produces a free nearly-diurnal wobble of the Earth's axis of rotation. The effect of this wobble in latitude and time observations is more complex than has generally been considered before. In previous discussions only the variation of latitude and time due to the neglected wobble has been considered and not the errors arising from the complementary neglected nutation in space. We establish here the theoretical expression for the total effect and we show that the first effect is negligible in comparison with the second. This expression is compared with similar ones due to the diurnal wobble and the corresponding main terms of nutation in space. As an application we search for such expressions in the Paris astrolabe observations from 1956.6 to 1973.8 using several kinds of analysis. We first evaluate the amplitudes of errors in the main terms of nutation and secondly we show that the amplitude of a free nearly-diurnal wobble, if it exists, is at least 100 times lower than the one claimed by several authors.