DrZoidberg said:
It's easier to imagine with the sun instead of the moon. You have the sun's gravity that pulls on the Earth and you have the centrifugal force that pulls the Earth away from the sun. The two are cancelling each other. This is also the reason for why astronauts on the ISS are weightless even though the gravity of Earth is nearly as strong there as it is on the ground.
Aside: Using centrifugal force to explain why astronauts on the space station are feel "weightless" is fundamentally wrong. The reason is that you can't feel gravity.
Using centrifugal force to explain the tides is also fundamentally wrong. Every explanation I've seen of the tidal forces that invokes centrifugal force makes at least two errors, but with the happy result that two or more wrongs in this case do make a right. It's a terrible fudge.
Here are a couple of correct ways of looking at things. One is from the perspective of an inertial frame. Because gravity is a 1/r
2 force, the Moon pulls the water closest to the Moon away from the Earth and it pulls the Earth away from the water furthest from the Moon. This is exactly what Feynman wrote in
Six Easy Pieces:
Feynman said:
It actually works like this: The pull of the moon for the Earth and for the water is "balanced" at the center. But the water which is closer to the moon is pulled more than the average and the water which is further away from it is pulled less that the average.
Another valid way of looking at things is from the perspective of an Earth centered frame. From the perspective of this frame, the Earth as a whole accelerates towards the Moon due to gravity (and towards the Sun as well, and also Jupiter, Venus, etc.; these also induce (very small) tides). This Earth centered frame is an accelerating frame; this results in a constant inertial force at every point. Compare with the centrifugal force, which is not constant. It is instead varies linearly with distance from the axis of rotation. From this perspective, the tidal force is roughly a 1/
r3 force, where
r is the distance between the Earth and the Moon.
Both the inertial and Earth-fixed points of view yield valid explanations of the tidal forcing functions. They do not explain the tidal bulges for the simple reason that
Newton's tidal bulges do not exist. They can't exist for a number reasons:
- Newton's equilibrium theory of the tides dictate that high tide occurs when the Moon is closest to zenith / closest to nadir and that low tide occurs when the Moon is on the horizon. This happens only rarely, and it's sheer dumb luck when it does. One problem is that there are two huge north-south barriers to this supposed tidal bulge, the Americas and Africa/Eurasia. If Newton's equilibrium theory of the tides was correct, the timing and magnitudes of the tides at the Pacific and Atlantic sides of the Panama canal would be more or less the same. They're anything but. The tides on the Pacific side of the Panama canal are huge, over an order of magnitude larger than predicted by Newton's equilibrium theory of the tides. The tides on the Atlantic side are rather small, smaller even than the smallish tides predicted by the equilibrium theory. The tides on the Pacific and Atlantic sides of the canal also differ significantly in timing. The tides don't magically pick up where they would have been had Panama not existed.
Another place of interest is the North Sea. The North Sea is rather small; per Newton's equilibrium theory of the tides, high tide should occur more or less simultaneously across all of the North Sea. That's not what happens. Instead, regardless of time of day, you can always find some point in the North Sea where it's high tide. At the exact same time, you can also find some other point in the North Sea where it's low tide. The equilibrium theory of the tides cannot come close to explaining the tides in the North Sea.
- Suppose those continental barriers didn't exist, with the Earth covered everywhere by four kilometer deep oceans (the median depth of the oceans). You still wouldn't get Newton's tidal bulges. The problem is the Earth's rotation. The tidal bulges would be an ocean wave with a wavelength equal to half the circumference of the Earth. This wavelength is much, much greater than the four kilometer depth. The tidal bulge (if it existed) would be a shallow wave. Shallow waves travel at a speed of ##\sqrt gd##, or about 200 km/second in the case of a 4 km deep ocean. The tidal bulge on the other hand would need to travel at 465 km/second. The tidal bulge cannot exist even in a water world with oceans only 4 km deep.
- The oceans would have to be over 20 to 30 km deep to support Newton's tidal bulge, and even with that Newton's tidal bulge still wouldn't exist except near the equator. The problem this time is the coriolis effect. The tidal bulge can't exist as a world-wide phenomenon thanks to Kelvin waves. Any bumps in the bottom of this deep, deep ocean will eventually result in amphidromic systems forming, even in this very deep ocean.
The correct theory of the ocean tides started with Laplace, about 100 years after Newton's time, and culminated in the early 20th century with the works of George Darwin and A T Doodson. This dynamic theory of the tides accounts for the issues described above. There is no tidal bulge, at least not in the ocean tides. Newton's equilibrium theory does work (to some extent) for the Earth tides.
