Over the past decade the analysis of sedimentary cyclic rhythmites of tidal origin, i.e., stacked thin beds or laminae usually of sandstone, siltstone, and mudstone that display periodic variations in thickness reflecting a strong tidal influence on sedimentation, has provided information on Earth's paleorotation and the evolving lunar orbit for Precambrian time (before 540 Ma). Depositional environments of tidal rhythmites range from estuarine to tidal delta, with a wave-protected, distal ebb tidal delta setting being particularly favorable for the deposition and preservation of long, detailed rhythmite records. The potential sediment load of nearshore tidal currents and the effectiveness of the tide as an agent of sediment entrainment and deposition are related directly to tidal range (or maximum tidal height) and consequent current speed. Hence the thickness of successive laminae deposited by tidal currents can be a proxy tidal record, with paleotidal and paleorotational values being determined by analysis of measured records of lamina and cycle thickness. The validity of the findings can be investigated by testing the primary, observed values for internal self-consistency through application of the laws of celestial mechanics. Paleotidal and paleorotational values provided by late Neoproterozoic (~620 Ma) tidal rhythmites in South Australia are validated by these tests and indicate 13.1+/-0.1 synodic (lunar) months/yr, 400+/-7 solar days/yr, a length of day of 21.9+/-0.4h, and a relative Earth-Moon distance a/a0 of 0.965+/-0.005. The mean rate of lunar recession since that time is 2.17+/-0.31cm/yr, which is little more than half the present rate of lunar recession of 3.82+/-0.07cm/yr obtained by lunar laser ranging. The late Neoproterozoic data militate against significant overall change in Earth's moment of inertia and radius at least since 620 Ma. Cyclicity displayed by Paleoproterozoic (2450 Ma) banded iron formation in Western Australia may record tidal influences on the discharge and/or dispersal of submarine hydrothermal plumes and suggests 14.5+/-0.5 synodic months/yr and a/a0=0.906+/-0.029. The combined rhythmite data give a mean rate of lunar recession of 1.24+/-0.71cm/yr during most of the Proterozoic (2450-620 Ma), suggesting that a close approach of the Moon did not occur during earlier time. Concentrated study of Precambrian tidal rhythmites promises to illuminate the evolving dynamics of the early Earth-Moon system and may permit the lunar orbit to be traced back to near the time of the Moon's origin.