Eclipses: A Brief History of Celestial Mechanics, Astrometry and Astrophysics.Solar and lunar eclipses are indeed the first astronomical phenomena which have been recorded since very early antiquity. The forthcoming American total solar eclipse of 8 April 2024 will be probably the eclipse with the largest mediatic impact of the history; we wish that also the scientific impulse toward solar physics and astronomy will be relevant, and the measure of the solar diameter with Baily's beads is indeed one of the topics significantly related to the Sun–Earth connections.