Tidal friction and the ephemerides of the Sun and Moon

Abstract

Introduction In order to determine the value of Δ T from an eclipse observation, it is necessary to be able to calculate accurately the positions of the Sun and Moon at any selected epoch. By definition, the Sun has negligible acceleration on TT. However, the longitude of the Moon contains an appreciable quadratic term – part of which (owing to the reciprocal action of the tides) can only be determined empirically. Since many of the eclipses recorded in history are remote from the present-day, the effect of the lunar accelerative term on their calculated visibility is substantial. Furthermore, knowledge of the tidal component of this acceleration (usually denoted by ṅ), leads directly to a determination of the effect of the tides on the Earth's spin – see section 2.4. Consequently, it is important to investigate both the numerical value of ṅ and its constancy during the historical period. Each of these questions will be considered in the immediately following sections (2.2 and 2.3). Evaluation of the lunar tidal acceleration on TT As discussed in chapter 1, the gravitational component of the lunar acceleration (coefficient of T equal to 6″.05) is well established. Up to about 1970, all estimates of the non-gravitational lunar acceleration were based on analyses in a UT framework. Results for the secular acceleration of the Moon ( c ) and Sun ( c ′) on UT can be easily converted to ṅ using the formula: