Jheri asked a good question about the tides. First you need to watch Henry Reich's piece on the subject. (His goal is to move quickly so you might have to stop every now and again and rewatch a segment.)

Basically differential gravity - the water on the side of the Earth closest to the Moon is attracted to the Moon. So is the Earth, but the Earth acts as a solid body so you can abstract it as a mass at it's center. Since the center of the rigid Earth is farther from the Moon than the near-side water, the whole Earth moves a bit less towards the Moon than the near-side water. In other words the water level closest to the Moon rises. The water away from the Moon is even further away than the center of the Earth, so the Earth is effective moved closer to the Moon than the water. This gives the tidal bulges on either side. Henry goes on with some other things including the tidal effect of a black hole (known as in the trade as spaghettification:)

Jheri's question gets at something deeper. "Why aren't there tides on ponds and lakes? Or in my coffee cup?"

That's a great observation - one that never occurred to me until I was working on a homework problem in college. There were three parts - describe the effect in simple terms, derive a formula for the tidal gravitational potential, and finally calculate the average high tide in the center of the ocean. I answered the first part like Henry did. The second part wasn't difficult - it was just Newtonian physics and I thought I did it properly. Then the third part.. the numbers just didn't make sense. I was getting sub-millimeter sized tides, but I couldn't find the flaw.

Finally the answer came. The expression I derived was correct, but the my model wasn't. Jheri is right.. If the Earth is rigid why wasn't the coffee in a cup rising? Why wasn't I rising? I'm not going to do the model here, but the trick is considering each point on the oceans and integrating the vector components of the forces.

Imagine the Earth covered with water and the Moon orbiting over the equator. A glob of water at the poles would be attracted to the center of the Moon. Draw lines from the center of the Moon to these globs and you see they form an angle. If you work out the vector components every glob of water not on the equator would have a small force pointed towards the equator. If you add up all of these forces - do the integral - the total force is substantial. Since water is fluid it is getting squeezed a bit. Although each bit is small, the oceans are huge and all of those little bits add up to the tides we observe.

The same squeezing happens on the solid Earth, but our planet is rigid enough that the effect is small. A tide exists in the coffee in a cup, but the total force is small enough to make them microscopic. A large lake like Lake Michigan might build a few centimeters of tide, but you don't notice it with normal waves and wind.

The example in the video is sort of right - there really is differential gravity. The problem is it's about ten million times weaker than the surface gravity on Earth. It's also an example of failure when a model is too simple and seems to be good enough. Fortunately people like Jheri notice something's wrong which means you need a better model.

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