So, it is interesting to begin with how Galileo viewed the phenomenon of the tides in the context of the time and with respect the main controversy that he was involved in, i.e., the motion of the Earth around the Sun.
"Cardinal Bellarmine had written in 1615 that the Copernican system could not be defended without "a true physical demonstration that the sun does not circle the earth but the earth circles the sun". Galileo considered his theory of the tides to provide the required physical proof of the motion of the earth. This theory was so important to him that he originally intended to entitle his Dialogue on the Two Main World Systems, the Dialogue on the Ebb and Flow of the Sea. The reference to tides was removed by order of the Inquisition.
For Galileo, the tides were caused by the sloshing back and forth of water in the seas as a point on the Earth's surface sped up and slowed down because of the Earth's rotation on its axis and revolution around the Sun. He circulated his first account of the tides in 1616, addressed to Cardinal Orsini (Discourse on the Tides). His theory gave the first insight into the importance of the shapes of ocean basins in the size and timing of tides; he correctly accounted, for instance, for the negligible tides halfway along the Adriatic Sea compared to those at the ends. As a general account of the cause of tides, however, his theory was a failure.
If this theory were correct, there would be only one high tide per day. Galileo and his contemporaries were aware of this inadequacy because there are two daily high tides at Venice instead of one, about twelve hours apart. Galileo dismissed this anomaly as the result of several secondary causes including the shape of the sea, its depth, and other factors."[1]
"Galileo dismissed the idea, held by his contemporary Johannes Kepler, that the moon caused the tides."[1]
"Discourse on the Tides does not include gravitational forces in its theory to explain the Earth's orbit and does not consider the relation between the ocean and cosmic gravitational forces, like that of the moon. Occurring invisibly, gravity was far too mystic for Galileo's consideration. Galileo did end the Discourse on the Tides with reservations that his theory may be incorrect and the hope that further scientific investigation will confirm his proposal."[2]
This stance towards gravitation and the notion of action at a distance without mediators that Newton introduced was common at the time.
"Descartes' book of 1644 Principia philosophiae* (Principles of philosophy) stated that bodies can act on each other only through contact: a principle that induced people, among them himself, to hypothesize a universal medium as the carrier of interactions such as light and gravity—the aether. Newton was criticized for apparently introducing forces that acted at distance without any medium."[3]
Newton's law of universal attraction:
$$\large\vec{F}=-G\frac{m_1 m_2}{r^2}\hat{r}$$
yes we have tex
Beyond that, the theory was widely accepted and there was also a controversy between Newton and Hook regarding who was the father of the theory. It seems that Halley, Wren, De Moivre, and the Royal Society had some part to play in the controversy until in the end Clairaut settled the matter.[3]
In addition, there is this paper on the ArXiv that discusses the issue, titled: "The reception of Newton's Principia"
"Newton's Principia, when it appeared in 1687, was received with the greatest admiration, not only by the foremost mathematicians and astronomers in Europe, but also by philosophers like Voltaire and Locke and by members of the educated public. In this account I describe some of the controversies that it provoked, and the impact it had during the next century on the development of celestial mechanics, and the theory of gravitation."[5]
So, this was more or less the state of things at that time with respect to the notion of action at a distance and the tides. Let me wish a safe journey to this blog with this first step outside the door in the roads of the Blogoshpere**.
* In Principia Philosophiae one can also find the introduction of Newton's first law of motion, while foundational work on dynamics can be found in Galileo's book Dialogo sopra i due massimi sistemi del mondo (Dialogue on the two main world systems).
** “It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien, The Lord of the Rings.
References:
[1] Wikipedia: Galileo, Kepler and theories of tides in Galileo Galilei
[2] Wikipedia: Discourse on the Tides
[3] Wikipedia: Historical context in Philosophiæ Naturalis Principia Mathematica
[4] Galileo's Big Mistake
[5] "The reception of Newton's Principia", arXiv:1503.06861 [physics.hist-ph]
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