Deep Dive into Tides

Guess what, everything you know about tides (statistically speaking) is wrong. Tell me if this sounds familiar. The gravitational pull of the moon on the Earth is stronger on the side of the Earth on which it is present and weaker on the opposite side. This difference in gravitational attraction causes ocean water to bulge out at opposite ends of the Earth. The Earth rotates in this bulge of water creating the phenomenon of tides. Simple and beautiful. Well this explanation, as we’ll see, is both correct for some reasons, and incorrect for others. Don’t feel bad if you thought this is how tides worked, by the way. I got to know about this today itself and I got so exited that I just had to make a blog post about it.

You are at the centre of the Earth. Imagine two points at opposite ends on the Earth along the Earth-Moon line. Your friend who is floating in outer space would see (if we ignore the gravity of the Earth) the point closest to the Moon accelerates the fastest, followed by you somehow in the centre of the Earth and then the point furthest from the Earth, which accelerates the slowest. From your perspective, however, our two points in question would seem to separate from the surface of the Earth as though they are being acted upon by some outward force. This force in fact is quite popular and even has a name. It’s called the tidal force. But like many famous people these days, this force is FAKE. It’s fake because it was measured from a non-inertial (that is accelerating) reference frame from the centre of the Earth. If you’ve read my article on General Relativity, you would know that in Newtonian mechanics, only those forces which are measured from non-accelerating reference frames are considered real. This fake, tidal force looks like anti-gravity to you but only along the Earth-Moon line.

How strong is the acceleration caused by this tidal force you might ask? Well, it’s extremely powerful, a whopping one ten millionth the acceleration due to gravity. A whole one micron per second squared. This acceleration is absolutely tiny, puny and negligible. You can’t lift an object by applying a force equal to one ten millionth its weight! But remember, the bulges in the ocean are real. So if the tidal force does not cause them, what does?

Well the key is to look at points which are not on the Earth-Moon line. If you look at a point which lies on a line perpendicular to the Earth-Moon line, you can see that the tidal acceleration is vertically down. The tidal force only looks like anti-gravity on the points situated along the Earth-Moon line. These acceleration vectors push the water on the Earth sideways toward the Earth-Moon line. Even though the acceleration due to Earth’s own gravity is ten million times bigger, the massive surface area of the oceans allow the tiny tangential tidal acceleration vectors to add up and nicely accumulate a respectably large body of water. This is precisely why you don’t see tides in small bodies of water, the surface area of the water must be huge. Think about it like tearing a piece of paper. The larger the piece, the easier it is to tear. If you’ve ever tried to tear a small piece of paper, you know how difficult it can be t break small things.

Tidal acceleration vectors

In summary, the water in the oceans is not being stretched by the gravitational deferential produced by the moon, instead it is being pushed toward the Earth-Moon line due to the tiny tidal acceleration vectors everywhere else.




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Shantanu Misra

Shantanu Misra

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