Tides question

In simple terms... the bit closest to the moon gets a bit more pull than the rest of the Earth, and so there is a hump towards the Moon.

The bit furthest away from the moon gets a bit less pull than the rest of the Earth, and so there is a hump away from the Moon.

Cheers -- Sylas

 

gravity and centrifugal force

 

What centrifugal force? In what rotating frame? Centrifugal forces only arise in rotating reference frames. You should be able to explain this phenomenon from any reference frame, and there is no centrifugal force in a non-rotating frame. Some phenomena (e.g., hurricanes) are much easier to explain in terms of a rotating frame than a non-rotating frame. This is not one of them.

IMO, the easiest frame to use as a basis for this explanation is an Earth-centered inertial frame. This is an accelerating frame, so a fictitious inertial force arises from the gravitational acceleration of the Earth toward the Moon. The apparent gravitational force exerted by the Moon at some point on the surface of the Earth is the gravitational acceleration toward the Moon at this point less the acceleration of the Earth as a whole toward the Moon. This apparent force is

• Directed toward the Moon (and away from the Earth) on the side of the Earth facing the Moon,
• Directed away from the Moon (and away from the Earth) on the side of the Earth opposite the Moon, with nearly the same magnitude as the apparent force at the sub-Moon point, and
• Directed toward the Earth (but at half strength compared to the sub-Moon point) at the points where the Moon is on the horizon.

The result: Bulges. Looking at just the sub-Moon and anti-Moon points omits what is happening elsewhere. The squeeze in the middle is just as important as those outward forces at the nodes.

 

gravity attracts the bodies toward one another and centrifugal force pushes them away from their center of mass (around which they orbit). there is an excess gravitational force on the moon side of the earth and an excess centrifugal force on the opposite side of the earth.

at the center of the earth the 2 forces are balanced.

 

http://www.scienceforums.net/forum/showthread.php?t=36766

http://www.coas.oregonstate.edu/research/po/research/tide/index.html [Broken]

 

In what rotating frame? Whenever you invoke centrifugal force you need to specify what your frame of reference is. There are no centrifugal forces in a non-rotating frame.

 

gravity attracts the bodies toward one another and centrifugal force pushes them away from their center of mass (around which they orbit/rotate).

 

This is the explanation I have found to be the most clarifying.

 

The Earth and Moon don't orbit in the rotating frame used to explain tidal effects from the perspective of centrifugal force. They are stationary in such a frame.

 

I dunno if you're beating him up excessively.

Inasmuch as centrifugal force can explain to the layperson why water stays in a swung bucket on a string, surely this is also an acceptable answer for the tides.

Not that I think it's the best explanation...

 

If you do the math properly, the Earth's ocean tides can be explained from the perspective of a Mars-centered, Mars-fixed reference frame. Just because it can be done doesn't mean it is the best choice. Explaining the tides from the perspective of a rotating frame is not the best (i.e., easiest) choice, either. If you pick a frame rotating with the Earth and Moon and with origin at the Earth-Moon barycenter, the sub-Moon point is a lot closer to the origin than is its antipodal point. If you pick a Moon centered or Earth centered frame, you have the fictitious inertial force plus the fictitious centrifugal force to deal with. Any way you cut it, the math is messy. There is no reason to invoke a rotating frame when a non-rotating frame gives a clearer and cleaner explanation.

 

I think he is not beating him up excessively. If anything, not enough.

The answer provided was simply "gravity and centrifugal force". Now, I think we can all agree that "gravity" by itself is a poor explanation. While gravity is the cause, the word "gravity" alone is not descriptive. So therefore, it is natural to conclude "and centrifugal force" means that centrifugal force plays a major role in the explanation. While it may be possible to twist things so this is technically correct, as an explanation, it's poor.

Russ' answer is, in my mind, the clearest. The moon's gravity pulls the near-side ocean away from the earth and the earth away from the far-side ocean.

 

I know some textbooks explain tides by centrifugal force with mass center of the two bodies.
But i myself agree with " The moon's gravity pulls the near-side ocean away from the earth and the earth away from the far-side ocean"

 

Here is what one of my profs has to say:

http://www.math.nus.edu.sg/aslaksen/teaching/tides.html

 

So, if the Earth and Moon were not rotating around a common center of gravity, and were stationary relative to one another, the oceans would still bulge out on the far side? What would cause this bulge?

 

The bulge occurs when the Earth, and its oceans, are all in freefall. If you actively hold the Earth stationary somehow, it's no longer the same situation.

 

The key is, if they were not rotating around each other, they would not be stationary relative to each other. They would accelerate toward each other. What would happen to the oceans in this case?

 

You'd still get the bulge, on both sides. Briefly. Then the ocean would be vaporized in the collision.

 

Russ is exactly right. The tides exist, so one had better be able to explain them from any frame of reference. Some choices are good in the sense that the explanation is clear and concise. Other choices, such as a frame with origin at the center of Mars and rotating with Mars' rotation rate (1 revolution per 1.026 days), are not so good in the sense that the explanation is anything but clear and concise.

From the link, a bit out of order,

Some argue in the same way as above, but in order to get an outward pointing force at the far side, they consider a centrifugal force caused by the Earth's rotation around the Earth-Moon center of mass. This is not correct.​

Hmm. That's just what Russ said.

This explanation seems to be popular among oceanographers. All the sites below use a centrifugal force.​

It appears oceanographers have been infected by a bad meme.

They argue that the centrifugal force is the same at every point of the Earth, and that it must be equal to the gravitational pull at the center of the Earth. I find it too much of a “coincidence” that the centrifugal force happens to equal the gravitational pull at the center (or the center of mass).​

This is an incredible hand-wave that is an aberration of the concept of centrifugal force. More below.

Some people, including Aslamazov and Varlamov in the book “The Wonders of Physics” use a centrifugal force, but they let the force depend on the distance from the center of rotation, which is clearly wrong. If we ignore the rotation of the Earth, then all points on the Earth describes circles with the same radius, but different centers, in the course of the month.​

I disagree with the author of that web site here. The centrifugal force on some object of mass m located at some point r from the origin of a rotating reference frame is defined as [itex]m{\boldsymbol{\omega}}\times{\boldsymbol r}[/itex]. If one insists on using a rotating frame, one should at least do it right.

The underlying assumption needed to arrive at the conclusion that "all points on the Earth describe circles with the same radius" is that the Earth is not rotating with respect to inertial space. This in turn means that the Earth is rotating with respect to the rotating Earth-Moon frame, and hence one has to consider Coriolis force as well as centrifugal force in explaining the tides. To make things worse, the authors of the sites erroneously use the term "centrifugal force" to describe what is really the sum of the centrifugal and Coriolis forces. Why do that when all one has to do is invoke the concept of tidal gravity and be done with it?

Personally I like tidal gravity (or gravity gradient) as the explanation. The explanation pops out clear and concise from the math, and this also explains why the squeeze at the middle. Words don't do as much for me as does mathematics.