The Sun is the closest star to our planet. The accurate knowledge of its physics is also knowledge of our living environment because of the strong energetic relationship with our climate. Most of the new physics of the XX century is involved in the study of the Sun: General Relativity, Nuclear Physics and Neutrino phase mixing physics. These three domains of modern physics considered the Sun a privileged laboratory. The secular variations of the solar diameter as well as the unexplicable great dimming of solar activity, known as Maunder minimun of 1645–1715 or the great maxima and minima identified in the past millenia [1], do not find a suitable predicting model.

2. Chaldean Astronomy

For millenia, mankind turned his gaze to the sky to admire and study its wonders. Of all the phenomena, solar and lunar eclipses are those that have influenced the mythology, religion and science of early civilizations the most. Chaldeans identified the periodic recurrence of lunar and solar eclipses, calculating a cycle of 18 years, 10/11 days, 8 h and 42 min, the Saros. Through prolonged and careful observations, the Chaldeans were not only able to predict the following eclipses; they also noted that the same eclipse occurred in the same place after 3 Saros, an Exeligmos cycle of 54 years and 34 days, as also described by Ptolemy in his writings ^[2][3][4][2,3,4]. It is safe to assume that the geometrical nature of the eclipses was already clear at that time. In general, the occultation of a body (the Sun, a star or a planet) by the Moon or an asteroid provides information on the shape of the darkening body itself and the relative distance between it and the darkened one (Figure 1). Also, the occultation of the Sun by the Earth produces, on the Moon, a shadow, which was called “defectus”, since the Moon is not occulted to our sight.

3. Occultation’S Astronomy

Figure 1 helps explain how occultations are related to celestial mechanics as it displays Venus’ occultation on 9 November 2023. The instant of the disappearance of Venus has been determined within ±0.01 s of accuracy, which allows for locating the Moon with s of accuracy, which allows for locating the Moon with ±10 m of space accuracy and 3 millarcsec of angular accuracy [5]. Asteroidal occultations are currently used to assess the asteroidal orbits with great accuracy and, in the case of some stars with large angular diameters like Betelgeuse (60 mas) and Regulus (1.7 mas), also their limb-darkening functions [6]. The eclipses of the Galilean satellite io by Jupiter offered the possibility to measure the speed of light by Roemer on his and Cassini’s data (1676) [7].

4. Eclipses’ Astronomy and Earth’s Rotation Rate

In the Sun–Earth–Moon system, two types of eclipses are recognized: lunar and solar. The first occurs when the Moon, whose orbital plane is inclined by 5.9° compared to the ecliptic, passes through one of the intersection nodes of the orbit in opposition to the Sun while being hit by the cone of shadow projected by our planet. These eclipses are visible from any point on the Earth’s hemisphere where the Moon is above the horizon. Solar eclipses, on the other hand, occur when the passage through one of the nodes occurs with the Moon in conjunction. The Moon projects its shadow on our planet, and due to the relative size and distances between the Sun, the Earth and itself, the shadow cone can vary in size and duration, giving information on the position of the three bodies in space. The most studied type of eclipse is the total solar eclipse, which is visible when the Earth–Moon distance is such that the angular diameter of our satellite is slightly greater than that of the Sun. This suggestive event has allowed also the first studies on the solar corona. The shadow cone generated during these phenomena covers a narrow band of the Earth’s surface, less than few hundreds of kilometers wide, where it is possible to observe a sudden and great variation in brightness of the sky (from 10 magnitudes to 10,000 times in intensity). Ptolemy reported in the Almagest (150 a.C.) the total solar eclipse recorded by the Chaldeans in 721 b.C. ^[8][9][8,9]. The occurrence of this phenomenon in Babylon tells us that the current Earth’s rotation rate changed during the last 27 centuries due to the ongoing post-glacial isostatic rebound of the continents ^[10][11][12][10,11,12].

5. Earth’s Axis Millennial Motions

The luni-solar precession (or “of the equinoxes”) is responsible for the double-conical movement of the Earth’s axis. With a period of approximately 25,700 years, the combined gravitational action of the Sun and Moon on the equatorial bulge tends to align the planet’s rotation axis along the direction perpendicular to the ecliptic plane. This gravitational pull is opposed by the rotational movement of the Earth, which keeps the angular momentum fixed. The resulting effect is a shift of the equinoxes by 20 arcminutes westwards [13]. Together with the precession of the equinoxes, and again due to the effect of the tidal forces deriving from the action of the Sun and the Moon, a second motion of our planet is observed: the nutation, which was discovered in 1737 by James Bradley. Nutation is characterized by a subtle wobble in the Earth’s rotation axis, which follows a cycle of approximately 18.6 years. The maximum amplitude of nutation in ecliptic latitude is 9 arcseconds. The Earth’s obliquity also variates in 42 Ky of ±2°. Since the dawn of observative astronomy, the Earth’s axis changed from about 24° to the present 23.42°.

6. Solar Astrometry: The Eclipse of Clavius

Another example of deducing changes in the properties of a celestial body using an eclipse is represented by the observation of the annular–total solar eclipse in Rome in 1567 AD by the Jesuit mathematician Clavius [14]. He personally observed the 1567 eclipse (9 May) and the eclipse of Coimbra in 1560 (21 August), and he reported, for the one in 1567, the presence of a clear disk of light around the Moon. Clavius deduced that the angular diameter of the Sun was greater than that of our satellite, which went against Ptolemy and medieval Arab astronomers. The nature of the ring of light observed by Christopher Clavius has been investigated by Kepler and by subsequent studies ^[15][16][15,16]. The occurrence of an annular eclipse in 1567 in Rome, instead of total, as predicted by the ephemerides for that day in Rome using current parameters, remains still intriguing. The solar diameter should have been 0.2% larger than expected, and the 1567 eclipse’s discussions gave birth to the studies on the secular variations of the diameter of the Sun [17]. It is therefore clear that not only do eclipses give important information on the celestial mechanics of the bodies involved, but they can also shed light on their properties and characteristics and how these influence our planet.