What are tides and how are they produced?

This is a few months old question and perhaps you have found or figured out the answer by now. However, it might be worth it to go a little deeper into it because the explanation is slightly more complex than what most people thinks.

We all know that the bulge, of a few centimeters up to several meters, that develops twice a day on the surface of the seas or oceans is due to the attraction of the Moon. Not only do we know this, but we have known it for a long time. Dante, 300 years before Galilei and Newton, wrote that “Turning without rest, the Moon covers and discovers the sea shores”. The question that nobody asked in his days was : how could that be? Neither Dante nor Galilei had any notion of Gravity.

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Galilei, who was more scientifically inclined than Dante, thought of the centrifugal force. The oceans had to be pushed outwards by the spinning Earth. It was not a bad idea and it lasted until Newton demonstrated the existence of the force of gravity: from then on, tides were due to the attraction of the mass of the Moon and that was it. Galilei was posthumously scorned and derided for centuries.

This was because the world did not know at the time a most relevant fact: the watery bulge as observed at certain hours of the day in Europe when the Moon is at Zenith position, concurs exactly, on the opposite side of the Earth, where the Moon is at Nadir position (see the picture). How is that possible? The Moon and the bulge at opposite sides? Gravity could not explain such absurdity. Was Galilei right after all?… Well, partly. But for a big part.

In fact three factors (at least) concur in creating tides and the Moon’s Nadir bulge. One is gravitational, and two are centrifugal.

1) Gravitational: the Moon’s pull on the Earth diminishes with the inverse cube of the distance. While the Zenith bulge is obvious, the Nadir side of the needs some explaining. Relative to the Moon, it is further away (twice the Earth’s radius) from its satellite than the Zenith side is. This represents nearly 3.5% of the total average Earth-Moon distance which, to the denominator and to the power 3, is a sizable figure. In other words, the Nadir side of the Earth with respect to the Moon is pulled less energetically inwards, than the Zenith side is pulled outwards. The former is therefore actually “left behind” with respect to the latter that is pulled up. The water surface is accordingly deformed. Hence the Nadir bulge . 2) Centrifugal 1 : this is simply what Galilei thought, the away push of the week water surface due to the rotation of the Earth (The Coriolis force is another such effect). However if you do the math, which I didn’t, this is rather a small number.

3) Centrifugal 2. It is the most important one and I left it for the end. Here is the scoop: the Moon does not only revolve around the Earth; they also both revolve around each other (the Moon moving considerably faster) and the couple system is centered about a point in space located on the plane of the ecliptic closer to the Earth. That is to say: Earth and Moon form a rotating couple whose gravity centre sits between the two. The rotational arm of such couple is therefore not just the Earth’s radius, but a stretched arm at least 20 times longer; the total distance between Earth and Moon being of approx. 500.000 km. Hence its ensuing centrifugal force acting on either side of the Earth is much, much stronger than mere gravity would suggest. Again I didn’t, and do not intend to do the math.

The resulting outward push on the water surface, Zenith and Nadir bulges, are therefore the result of all three forces: one pulling and two outward pushing in opposite directions. I made this answer a little longer than I wanted to, but I had an old and respectable countryman to vindicate.

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