# Talk:Coriolis force

(Redirected from Talk:Coriolis effect)

## Why the negative sign?

Just an innocent question. Why is there customarily a negative sign in the equation for Coriolis acceleration and force?

${\displaystyle {\boldsymbol {F}}_{C}=-2\,m\,{\boldsymbol {\Omega \times v}}}$

It could be got rid of by reversing the order of ${\displaystyle {\boldsymbol {\Omega }}}$ and ${\displaystyle v\,}$ Then the direction of Coriolis force could be defined by the right-hand rule. Just wondering why it is normally written this way. --ChetvornoTALK 11:50, 18 June 2015 (UTC)

## what is this section about distant stars? it makes no sense physically.

this section about the coriolis effect and distant stars seems to make no physical sense. in my opinion, it is bogus. — Preceding unsigned comment added by 63.172.27.2 (talk) 19:04, 13 August 2015 (UTC)

I've deleted the section on distant stars, as the Coriolis term vanishes entirely and there is only a centripetal term, so the apparent motion of distant stars really has nothing to do with the Coriolis effect as that term is commonly understood. I had been thinking of doing this deletion for the last few weeks based on an ongoing discussion about the motion of 3753 Cruithne which had also been included in this article, but which I deleted. --Seattle Skier (talk) 06:35, 25 August 2015 (UTC)
I am not sure if the section ought to be in the article but it would have been correct had is started, 'in the rotating reference frame of the Earth'. Martin Hogbin (talk) 08:14, 25 August 2015 (UTC)
That is correct. The Coriolus effect provides a centripetal fictitious force on distant objects, when one enters a rotating frame and observes these distant (formerly static) objects. The fixed stars a great example of this. They go around you, and a fictious force is needed to explain their motion, and that force must be a centripetal one, since they are accelerating in an inward direction, by moving in a circle. There is of course a outwardly-directed (fictitious) centrifugal force m ω v too, but the Coriolis force is exactly twice as large (see that 2 in front of the Coriolus term?) and it wins out. I don't know why you think the Coriolus effect vanishes, Seatle Skier. You have an m, you have a ω, you have a v and so you have a Coriolus -2 m ω v directed inward by the right hand cross product rule, since ω and v are orthogonal, and inward along r is the direction the cross product points. SBHarris 01:12, 26 August 2015 (UTC)
Hello @Sbharris: I think Coriolis is meant to explain the apparent deflection of moving objects in a rotating frame of reference. The calculations and result seem mathematically correct and make sense, but the end result is only a centripetal force, as it should be. While this shows that the formula works correctly in this case, there is no deflection other than just the resulting fictitious centripetal force. I think that it is easier not to use Coriolis to explain that force. The mathematical calculations are interesting, but since there is no additional deflection component to explain (only a centripetal force) and since the section contents were contested and there are no sources I think it is best to remove the information pending the result of this discussion. Maybe it could be rewritten to say that the Coriolis formula also holds in the case of (almost) static objects relative to the center of the rotating frame of reference, like the stars seen from Earth, as in that case it only yields the centripetal component needed to explain its apparent circular motion. Do you agree? --Crystallizedcarbon (talk) 06:50, 26 August 2015 (UTC)
The Coriolis and Centrifugal forces enable you to use Newton's laws (unchanged) in a rotating reference frame. They explain any kind of motion in such a frame.
Easiest, in this case, is not to use a rotating reference frame but to use an inertial (non-rotating) reference frame. In that case it is all very easy. There is no force acting on the stars, so they therefore keep still. Martin Hogbin (talk) 19:07, 26 August 2015 (UTC)
I agree with you Martin, I also agree with Seattle Skier that to explain the apparent motion of the stars from our point of view here on Earth it is easier to just use simple geometry.--Crystallizedcarbon (talk) 19:42, 26 August 2015 (UTC)
From our point of view here on Earth, fixed stars rotate on the night sky
It is not geometry, it is physics. What do you mean by 'from our point of view here on Earth'? Martin Hogbin (talk) 22:01, 26 August 2015 (UTC)
Hello Martin: All roads do lead to Rome, but when I go there I prefer to fly by plane . Assuming that the stars are fixed with respect to Earth (Expansion of the universe, rotation around the sun, etc. are negligible) and since the Earth is rotating at an angular velocity of roughly 361º per day. From our point of view here on Earth, when we look at the night sky, the fixed stars seem to be rotating with that same angular speed around Polaris (for the northern hemisphere). As demonstrated above, you can use Coriolis and centrifugal forces to calculate their path speed etc. but what I mean is that is not the only way or the simpler way to do so. It is easier to explain their motion without the use of physics or forces. You can use Geometry (its mentioned in the introduction of the article), the formula for angular velocity and some simple trigonometry. Regards. --Crystallizedcarbon (talk) 07:33, 27 August 2015 (UTC)
##### Geometry and physics

Yes, of course you can use trigonometry to calculate the stars' positions relative to the Earth if we take it that the Earth is rotating with respect to the stars but that is not the problem. The problem is one of physics. We have to explain why the stars do not change their positions. In an inertial reference frame that is trivially easy. Ignoring all the things that you mention above, there are no forces acting on the stars, therefore by application of Newton's first law of motion, every star 'either remains at rest or continues to move at a constant velocity, unless acted upon by an external force'. Having done the, trivial, physics in this inertial frame, we can then do some simple geometry to calculate the stars' positions relative to a rotating Earth at any time. That is exactly what you suggest.

The problem arises if when we try to do the physics in the rotating reference frame of the Earth. In that frame, the stars are moving in circles but there are no forces acting upon them. How can we explain this? Newton's first law tells us that, without a force acting upon them they should continue at constant velocity (in a straight line), but they do not do this they move in circles. We cannot use Newton's laws in a rotating frame unless we invent some extra (inertial) forces. In this case we need to use the centrifugal and Coriolis forces. We can then do all Newtonian mechanics in exactly the same way as if we were in an inertial frame so long as we add in the two inertial forces.

In this particular case, we all agree that it is much simpler to do the physics in an inertial frame and then, if we wish, use simple geometry to calculate the result in a rotating frame. There are cases though where this is not the best approach. For example, as Seattle Skier mentions above, it would be very difficult to calculate the motion of the atmosphere in a cyclone in an inertial frame. It would also be very unnatural because we generally consider wind velocity to be with reference to the Earth's surface, not some (non-rotating) inertial frame. generally it is best for those studying elementary physics to work only in inertial reference frames until they get a good understanding of Newton's laws.

I do agree that this may not be a good example for this article unless all the above is very clearly explained. Martin Hogbin (talk) 09:26, 27 August 2015 (UTC)

I agree with your conclusions I think we only have a minor semantics difference. In the definition of this particular problem we state the assumption that the position of the fixed stars with respect to Earth is fixed. Personally, I don't see a need to invoke Newton's first law to reaffirm that they remain fixed, or for that matter why the Earth is rotating at a constant angular velocity, etc... so, like you, I think that this simple problem is easier to solve without the use of physics or Coriolis, just geometry. I agree with you that if you want to "do the physics in the rotating reference frame of Earth", then you need Coriolis but I don't see a practical application for doing so in this particular case, other than to show that the formula does works and Newtonian mechanics still apply in that reference frame. In my opinion I think that should be out of the scope of the article. Regards.--Crystallizedcarbon (talk) 11:42, 27 August 2015 (UTC)

In my opinion, we do need to explain why the fixed stars remain fixed and why the Earth continues to rotate at a fixed rate. You may consider these things obvious but you are underestimating the huge advance that Newton made to our understanding. In the millennia before Newton nobody had a clear idea of why some things moved and others did not. Newton's laws of motion and gravitation explained the motions of celestial bodies and things on Earth in a few simple laws. Anyone who asks the question of why, when, and how, things move needs only to apply Newton's laws to get an answer (for evErything up to and including the Moon landings).

There is no doubt that to explain the motion of the stars it is easiest to work in an inertial frame. The use of a frame rotating with the Earth is just an academic excersise to show how to do physics in a rotating frame of reference but please bear in mind that that is exactly what this article is about. When working in an inertial frame, which is always recommended for beginners, Coriolis and centrifugal forces do not exist. What would you say to having Centrifugal_force#An_equatorial_railway, which is pretty much the same question, in this article. Martin Hogbin (talk) 12:16, 27 August 2015 (UTC)

I like physics and I admire Newton. Since this seems like a slippery slope leading to a math vs physics argument and since I agree with your conclusion that the use of Coriolis in this case is an academic exercise, I am happy to just agree with you.
As far as the example that you mentioned I don´t think it should be part of the Centrifugal force article either as it is unsourced. As it is worded, even ignoring Coriolis it is easy to show that the train would not fly upwards. The reaction force from the track on either frame of reference counters the sums of the forces exerted on it (Fixing its value on one frame does not make too much sense to me). The centrifugal force generated in that frame of reference moving at that speed is orders of magnitude less than gravity (Geostationary orbit is at 35,786 kilometers above the equator). So even ignoring Coriolis there would be a resulting downward force that would be countered with a reaction from the track and the train would not fly.
If we can find references from reliable sources, I think it might be a good idea to include a similar example in the Eötvös effect section. Our train would be slightly heavier than when it was at rest, illustrating that in that case Coriolis points downwards and that there is no lateral deflection while travelling through the equator. If the train was travelling at the same speed but in the opposite direction it would be slightly lighter than when at rest. On the inertial frame the train of the example has no centrifugal force, so it is slightly heavier than when moving along at 361º per day along with the Earth (as it would be at rest on Earth) and still slightly heavier that if it was travelling in the opposite direction. In that case its angular velocity in the inertial frame would be double so its centrifugal force would increase proportionally to its square further counteracting gravity. Do you think it is a good idea? can you find sources for any similar example?--Crystallizedcarbon (talk) 18:58, 27 August 2015 (UTC)

I am looking for a source for the equatorial railway, although it could be said that it is a routine calculation.

The example does say, 'the upward reaction force from the track and the force of gravity on the train remain the same, as they are real forces'. We could, for example, place a digital weight sensor under the track to measure the reaction force. The value indicated must be the same in all frames. There is no part of current physics that allows a digital readout to display a different values when viewed from different reference frames. Maybe this point should be made clearer in some way.

Your proposal is a little confused. You say, 'In that case its angular velocity in the inertial frame would be double so its centrifugal force would increase'. In an inertial frame there is never any centrifugal force (or Coriolis force), whatever the motion of an object. Martin Hogbin (talk) 08:32, 28 August 2015 (UTC)

Let me try to clarify the example. From a non rotating frame point of view (looking at the train from a fixed point in space with respect to the center of the earth and, to make it simpler, ignoring that it is in orbit around the sun, rotation of the milky way, expansion of universe etc.):
• On the first case the train would be still from that point of view, with Earth rotating bellow it, and only gravity and the reaction from the track moving bellow it (we ignore drag) would act on the train.
• On the second case when the train is stopped at a point on the surface of Earth's equator, it would be seen from that fixed point of view in space to be rotating around the center along with the rest of the planet at 361º per day. that does generate a very small centrifugal force that counters gravity and makes it's weight at rest 0.31% lighter than in the previous case. From that that fixed point of view in space there is of course no Coriolis effect associated to the rotation of Earth.
• When the train travels in the opposite direction then it would be seen from that fixed point of view as travelling in a circle at 722º per day and therefore it generates more centrifugal force (also no earth related Coriolis in that case).
If the train could travel fast enough (ignoring air drag that would probably melt it) there would be a point at which it would levitate and start to orbit the Earth due to that centrifugal force. (as a curiosity and if it helps illustrate the example, in the first case in which the train is riding through the equator towards the west the people on board would see the sun still at the same azimuth and when travelling in the opposite direction relative to Earth day and night cycles would happen twice as fast for the travelers). I hope I was able to make it clearer. Regards.--Crystallizedcarbon (talk) 10:18, 28 August 2015 (UTC)
It may also be worth mentioning that there is a point at which the Eötvös effect reverses. It can be also illustrated with the example: If the train travelling west would increase its velocity beyond 361º per day in that direction with respect to Earth, it would gain back its centrifugal force (in the opposite direction) and would start becoming lighter. If it doubled its speed it should recuperate its "at rest" value and any additional increase would keep making it "lighter" until the point in which it would start to orbit the Earth. Regards.--Crystallizedcarbon (talk) 10:45, 28 August 2015 (UTC)

You say above, 'From a non rotating frame point of view...'. I take this to mean, 'in a non-rotating reference frame'. You do not mention any other reference frames so I presume that all your cases are measured in this inertial (non-rotating) reference frame.

In your first case you are correct when you say the only forces are 'only gravity and the reaction from the track'.

In the second case we are still doing our calculations in the inertial (non-rotating) reference frame so there is no centrifugal force. It makes no difference what the train is doing, it could be in a giant centrifuge, there is no centrifugal force when you are working in an inertial frame. It is still the case that the forces are 'only gravity and the reaction from the track'.

The third case has the same mistake. I am not sure how I can say this any more clearly. When you are working in an inertial reference frame, the Coriolis and centrifugal forces do not exist. It makes no difference what a body is doing, it can be going in a straight line or going rapidly in circles but there is never any centrifugal or Coriolis force. Martin Hogbin (talk) 11:14, 28 August 2015 (UTC)

To an observer on the rotating Earth, both satellites appear stationary in the sky at their respective locations.
The only centrifugal component that is not present in that frame is the one associated to Earths rotation. The centrifugal force that I refer to is the one generated from the circular path of the train in that frame. From that fixed point of view in Space with respect to Earths center on the image in the right you can see a satellite in a geostationary orbit. The force that is countering gravity in that frame is the centrifugal force generated from the satellite rotating at the same angular velocity as Earth (same as the train when is at rest with respect to Earth's surface). That centrifugal force that makes everything at rest on the surface of the Earth lighter is keeping the satellite in orbit at that altitude where gravity and the centrifugal force are matched.
I see I used the term centrifugal force incorrectly, you can reword the example in terms of centripetal force or change centrifugal force in that inertial frame for centrifugal force in a frame rotating along with the train for the second and third cases. on the second case when the train is at rest on Earth you would get the centrifugal force from Earth's rotation and in the third case when the train travels eastward you would get an increased centrifugal force as that frame rotates at a higher angular velocity. In all cases there would be no Coriolis effect as the train is still within each of the frames and the previously exposed conclusions would hold.--Crystallizedcarbon (talk) 11:57, 28 August 2015 (UTC)
Yes, in all cases where you put yourself in a frame where the train does not move, you have no Coriolis force. But in a frame where the train does move, you certainly do. The solution is not to simply refuse to visit such frames, as we're trying to describe the physics of rotating systems, where you don't always get your choice. In many real life problems you are stuck on the surface of the Earth, and you can't easily translate to the frame of something moving east or west. In any case, whether or not it's easier to put yourself on the train, is irrelevant. We're interested in the physics of forces on things what DO move (in the observer's frame). Simple examples are trains and ships as seen from the water or embankment, and there the Eötvös effect is merely the normal component of the Coriolis force/acceleration. That article has some nice illustrations, and at least one good source.
Even easier problems are where you have an object at a distance, not moving with respect to you, and you start spinning. In such a case the object moves about you in a circle. If you are to describe this in Newtonian terms, you need a source for the centripetal force, and the centrifugal force does not provide it. So you are left with Coriolis. That is why this simple situation should be a part of the Coriolis article. Those objects moving in circles might as well be the stars. They could be anything that wasn't moving before you started spinning and put yourself in a rotating frame.
To put it bluntly, from the surface of the Earth, the stars go round and round in circles. In Newton's physics they need a force to do that, and you keep deleting the section that describes what that force is. SBHarris 02:10, 29 August 2015 (UTC)
Hello @Sbharris: my problem with the example is that while you need Coriolis to explain tangible effects on Earth in meteorology oceanology long range ballistics etc. You do not need Coriolis to explain why the stars rotate. Your example: If you are rotating and look at a fixed object it seems to turn around you, is in my opinion a great way to explain why the stars seem to rotate around us. The article already explains in the introduction, referring to Coriolis and the centrifugal force, that "They allow the application of Newton's laws to a rotating system. They are correction factors that do not exist in a non-accelerating or inertial reference frame.". Maybe if a source can be cited and if there are no objections a short phrase could be added after it in line with "As an example, Coriolis provides the missing centripetal force term needed to cause the apparent rotation from our point of view of relatively fixed objects like the stars, allowing us to continue to use Newton's laws form our rotating frame's point of view".--Crystallizedcarbon (talk) 20:27, 29 August 2015 (UTC)

Yes I think you have got it. In your deleted section you said, 'The force that is countering gravity in that frame is the centrifugal force generated from the satellite rotating at the same angular velocity as Earth'. That is completely incorrect. In the inertial frame there is only gravity acting on a satellite. That provides the necessary centripetal force to maintain it in its circular orbit. If there were a centrifugal force acting outwards and balancing gravity then there would be no net force on the satellite and it would continue in a straight line out of orbit.

The idea of a centrifugal force acting on objects that move in a circle is an extremely common and very compelling misconception. That is why many teachers at an elementary level simply say that there is no such thing as centrifugal force. Until you get on to rotating reference frames, which would only be at undergraduate level physics, you can completely do without centrifugal (or Coriolis) force. Martin Hogbin (talk) 12:38, 28 August 2015 (UTC)

Agreed. I think that if it is properly worded and sourced it might be a positive contribution to the Eötvös effect section. Regards--Crystallizedcarbon (talk) 13:23, 28 August 2015 (UTC)

I will look for some good sources on the subject. Do you have any suggestions on how the wording can be improved to make the underlying physics as clear as possible to the general reader. Martin Hogbin (talk) 16:23, 28 August 2015 (UTC)

Great! I think together we should be able to do it. I will post a first draft here during the weekend for you and any other interested editor that may want to join us to review complement and add sources and if we find it useful we can move it to the article.--Crystallizedcarbon (talk) 16:53, 28 August 2015 (UTC)
I am working on an animation to help illustrate it. I expect to have it done by tomorrow.--Crystallizedcarbon (talk) 20:47, 29 August 2015 (UTC)
Here is the animation to help illustrate the example:
(Moved to the example section bellow)
(I hope it does not make anybody dizzy)I will add the text later.--Crystallizedcarbon (talk) 08:43, 30 August 2015 (UTC)
They are a bit fast. Which frames to you suggest that we analyse these examples in? Martin Hogbin (talk) 16:56, 30 August 2015 (UTC)

## What can and cannot be ascribed to the Coriolis Effect?

In the light of the above remarks, I reproduce a (rather lengthy and wide ranging) discussion between Seattle Skier and Cruithne9 on this very topic on the 3753 Cruithne Talk Page. The entire discussion is pasted here (suitably formatted for easy reading), with the exception of a short section that was irrelevant to the Coriolis effect. The signatures have also been shortened to diminish the potential clutter. Seattle Skier’s crucial conclusion at the end of the discussion is highlighted in red (bottom of the page). Whether this is a generally accepted interpretation of the Coriolis Effect I leave to the experts in the field.

Comment by Cruithne9:

I notice that Seattle Skier has removed the comment I made some time ago that 3753 Cruithne's curious orbit (as seen from earth) is an instance of the Coriolis Effect. His reason is that it is "not relevant" to Cruithne. In a note to me on my Talk page he says "They are completely unrelated effects, other than the fact that both are seen in rotating reference frames, they have no other connection".

The Coriolis effect is a deflection of moving objects when the motion is described relative to a rotating reference frame. This rotating reference frame can be a turn table in your home, a rotating bowl of water in a laboratory, or the motion of water, air, or long-range artillery shells across the rotating earth’s surface. It also applies to the geographic paths seen to be taken by artificial satellites that orbit the earth, and it is a Coriolis “force” that keeps geostationary satellites above a “fixed” position on the earth’s rotating surface. The curious motion of the planets that intrigued the ancients, but are now known, thanks to Copernicus, Galileo and Newton, to be due to Coriolis effects caused by using the earth (orbiting round the sun) as the frame of reference. When the sun is used as the frame of reference the planets' motions are far more straight forward. The same can be said about Cruithne’s strange orbit, as seen from earth. But, from what I gather Seattle Skier says (unless I am completely misunderstanding his very brief remarks), it seems that Coriolis mathematics does not apply, or is inappropriate at some arbitrary altitude above the earth’s surface. I’m obviously missing a very fundamental principle here. As far as I understand the Coriolis effect, it applies as much to an ant on a turn table watching a fly fly straight across that turn table, as it does to our observations of the motions of the objects in our solar system using our rotating and orbiting earth as the frame of reference.

Could someone please clarify whether or not 3753 Cruithne's motion as observed from earth is an instance of the Coriolis Effect or not. I'm very curious to know the readship's opinion on this.

You appear to be misunderstanding some basic physics here, such as the extent of what the Coriolis effect is and what it applies to, and you are thus misapplying it to cases which really have nothing to do with it. Take your statement that "it is a Coriolis “force” that keeps geostationary satellites above a fixed position on the earth’s surface." That is completely untrue: the Coriolis force ${\displaystyle {\boldsymbol {F}}_{C}=-2\,m\,{\boldsymbol {\Omega \times v}}}$ on a geostationary satellite is zero, because its velocity in the rotating frame is zero. In the rotating frame, it is entirely the centrifugal force ${\displaystyle {\boldsymbol {F}}_{c}=-m\,{\boldsymbol {\Omega \times (\Omega \times r)}}}$ which is nonzero and keeps the satellite in place versus plummeting downward, not the zero Coriolis force.

That is exactly correct. There really should not be any discussion about these thinngs here. As Seattle Skier says, it is all basic, and well-understood Newtonian physics. Martin Hogbin (talk) 19:15, 26 August 2015 (UTC)
Your next statement that the "curious motion of the planets that intrigued the ancients, but are now known, thanks to Copernicus, Galileo and Newton, to be due to Coriolis effects" is also completely untrue, although for different reasons than the prior statement. The "curious" apparent retrograde motion of the planets can be explained without any reference to Coriolis effects or to any fictitious forces at all, it is a simple case of geometry and does not even need Newton's laws or any physics at all to explain. See the diagrams in the 3753 Cruithne article which should make this quite clear. Similarly, the motion of Cruithne can be explained by simple geometry in the rotating frame as shown in the animated image File:Horseshoe_orbit_of_Cruithne_from_the_perspective_of_Earth.gif, without needing Coriolis effects or any physics at all.
Your statement that "I’m obviously missing a very fundamental principle here" appears to be quite true. Hopefully these examples provide some of the very simple explanation which you have overlooked, and will make it clearer where the Coriolis effect actually applies, and where it does not.
By the way, it is irrelevant what the readership's opinion on this is, because what is important for Wikipedia is that any information added to articles be verifiable in reliable sources (and also be correct!). There are no reliable sources which state that 3753 Cruithne's motion as observed from earth is an instance of the Coriolis effect, because that is simply not true.

Thank you for this extensive explanation. I will need to ponder over it for a while to let the implications sink in, particularly in the light of the remarks about the apparent motion of distant stars as seen from the rotating earth in the "Distant stars" section in the Coriolis effect article, which seems to suggest that "any" motion (which I would imagine would include objects with an apparent velocity of zero) observed from a rotating frame of reference can be referred to as a "Coriolis effect". (No reference is provided in that section, so I cannot check whether astronomers are comfortable with the term or not, and what they would apply it to, if the term is used by them.)

PS. I don't want this to sound as if I am arguing with you. I'm looking for information and enlightenment. So I hope you will bear with me here. As you say above, the Coriolis force is an entirely fictitious "force", as is the Centrifugal "force". Both effects can be explained in terms of simple geometry and physics. I therefore struggle with the dismissal of one fictitious force (the Coriolis effect) in favor of another fictitious force (the centrifugal force) to explaining the apparent behavior of a geostationary satellite. These comments probably sound ridiculous to you, but I would desperately like to know what types of motion viewed from a rotating frame of reference can and cannot be termed "Coriolis" effects.

PPS. I think I may have discovered why we seem to be talking at cross purposes. When an object moves over the earth's surface (and is partially or wholly detached from that surface) it seems to follow a curved path. For someone observing that curved motion, and who is unaware that the earth is rotating, it would seem as if the object is subject to a sideways force causing it to deviate from traveling in a straight line. One can calculate the force that would account for this motion, and call it a "Coriolis Force". But it is an entirely fictitious force. The formula you use applies to this situation, which is a special case of the Coriolis effect. When a straight-line motion across the solar system is viewed from our orbiting perspective, the path would also appear curved. The formula needed to calculate the "force" that might be responsible for that curved motion would be different from the one you present above. Things become mathematically horrendously difficult if the "real" motion is circular or elliptical round the sun. But that does not mean that the distorted motion as viewed from the orbiting earth is not an instance of the Coriolis "effect".

Cruithne's bean shaped orbit in the vicinity of the earth is not due to Coriolis Forces (or, let's say, it would be foolishness to calculate them, as they would be unique to Cruithne, and applicable nowhere else in the universe). But that does not mean that its motion as seen from earth is not an instance of the Coriolis Effect. I hope this makes sense.

"As you say above, the Coriolis force is an entirely fictitious "force", as is the Centrifugal "force"." I never said this in what I've written to you, you're putting words in my mouth. See above, I say "without any reference to Coriolis effects or to any fictitious forces at all", I do not ever say that the Coriolis force is an entirely fictitious force. The use of that term "fictitious" leads to a lot of needless trouble, perhaps it's best to call them pseudo forces or inertial forces instead, as they are very real effects in the rotating frame.
"Both effects can be explained in terms of simple geometry and physics." Not true at all, where did you get this idea? Simple geometry cannot explain or derive either the Coriolis or centrifugal force, you must use physics in a rotating frame to derive them. But as I stated, simple geometry CAN easily explain the apparent retrograde motion of the planets and the motion of 3753 Cruithne, without needing any physics. This is the most fundamental issue that you are having, by failing to understand this key point. You're trying to turn problems which need only simple geometry into physics problems, when they are not.
"I therefore struggle with the dismissal of one fictitious force (the Coriolis effect) in favor of another fictitious force (the centrifugal force) to explaining the apparent behavior of a geostationary satellite." As the equations show, the Coriolis force is dismissed in this case because it is ZERO. The centrifugal force is not dismissed because it is non-zero. That is it. There is nothing to struggle with. The Coriolis force turns out to be zero in this case, so it is not relevant to the behavior of a geostationary satellite.
"but I would desperately like to know what types of motion viewed from a rotating frame of reference can and cannot be termed "Coriolis" effects." The only types of motion are those for which the Coriolis force ${\displaystyle {\boldsymbol {F}}_{C}=-2\,m\,{\boldsymbol {\Omega \times v}}}$ is nonzero. Anything else does not involve Coriolis effects. And anything which can be explained using simple geometry (not requiring physics) is definitely not an example of the Coriolis effect either. These are the 2 key points for clearing up this misunderstanding.
"remarks about the apparent motion of distant stars as seen from the rotating earth in the "Distant stars" section in the Coriolis effect article, which seems to suggest that any motion (which I would imagine would include objects with an apparent velocity of zero) observed from a rotating frame of reference can be referred to as a "Coriolis effect"." Where did you get that idea from reading that section? Does it state that ANY motion observed from a rotating frame of reference can be referred to as a "Coriolis effect"? No, it does not say that. That section (which is somewhat confusing, totally unreferenced, and probably worthy of deletion) is entirely about the spinning motion of stars around the poles (see the circumpolar star article for more info on this). And as the equations in that section show, by the 3rd line the Coriolis term completely vanishes and the total ${\displaystyle {\boldsymbol {F}}_{f}=m\,{\boldsymbol {\Omega \times (\Omega \times r)}}}$, which is only a centrifugal (centripetal) force with no Coriolis component remaining (there is no ${\displaystyle {\boldsymbol {\Omega \times v}}}$ term left). Therefore there is no Coriolis effect in the simple circumpolar rotational motion of the stars. The last line of that section says exactly as much ("therefore recognizable as the centripetal force that will keep the star in a circular movement around that axis"). Since there is no Coriolis effect in that motion, that section really does not belong in that article, and I may delete it after further thought on the matter.
"Cruithne's bean shaped orbit in the vicinity of the earth is not due to Coriolis Forces . . . But that does not mean that its motion as seen from earth is not an instance of the Coriolis Effect" Your first statement is true, the second one is false. The first statement implies that it is NOT an instance of the Coriolis effect. The bean-shaped motion relative to the Earth is derivable from simple geometry alone without needing any physics or Coriolis or whatever, and the animated image File:Horseshoe_orbit_of_Cruithne_from_the_perspective_of_Earth.gif demonstrates this derivation nicely. Please don't go looking to desperately call it a Coriolis effect, when it's just a simple geometric effect caused by the relative orbits of Earth and 3753 Cruithne around the Sun.

You present the image File:Horseshoe_orbit_of_Cruithne_from_the_perspective_of_Earth.gif as a sort of "proof" that Cruithne's bean-shaped motion relative to the Earth is derivable from simple geometry, and geometry alone, without needing any physics or Coriolis "forces" or whatever. But exactly the same can be said of all the following examples of the Coriolis effect taken from the following clips in the Coriolis effect article:

In the inertial frame of reference (upper part of the picture), the black ball moves in a straight line. However, the observer (red dot) who is standing in the rotating/non-inertial frame of reference (lower part of the picture) sees the object as following a curved path due to the Coriolis and centrifugal forces present in this frame.
Object moving frictionlessly over the surface of a very shallow parabolic dish. The object has been released in such a way that it follows an elliptical trajectory.
Left: The inertial point of view.
Right: The co-rotating point of view.

and this animation clip of a cannon ball being fired from a rotating platform.

In each case the motion seen by an observer on the rotating non-inertial frame of reference can be explained even more obviously, simply, and in its entirety, by geometry, without recourse to any physics, or related sciences, than your example of Cruithne's orbit, when viewed from an inertial (stationary) frame of reference. I see absolutely no difference between your example of the File:Horseshoe_orbit_of_Cruithne_from_the_perspective_of_Earth.gif and the examples given in the Coriolis effect article (and other sources) of the "genuine" instances of the Coriolis effect.

Furthermore, if I understand you correctly, you maintain that the formula for the magnitude of the Coriolis Force, ${\displaystyle {\boldsymbol {F}}_{C}=-2\,m\,{\boldsymbol {\Omega \times v}}}$, defines the Coriolis effect. But consider this situation. A spot of light from a laser pointer is moved at a uniform speed, in a straight line across a rotating turntable (the spot of light does not need to move across the center of the turntable). If the surface of the turntable is light-sensitive, the spot will leave a trail on the surface which is curved to exactly the same extent as the trail left by a ball rolled across the turn table at the same velocity. It is difficult to conceptualize a real physical force that will have such a profound effect on a spot of light. Now move the spot of light in an ellipse across the turntable. The ellipse’s dimensions are a scale model of Cruithne’s orbit around the sun, with the turntable’s axle in the position of the ellipse’s “sun”. It is timed so that the ellipse is completed in exactly the same time as one rotation of the turntable. A bean shaped trail will be formed on the turntable, which is a miniaturized version of the orbit of Cruithne as seen from earth. If you acknowledge that this is an instance of the Coriolis effect, then the one we see in the sky must also be due to the Coriolis effect resulting from our orbit round the sun.

### More on the Coriolis effect (continued)

Although I have no idea of how much of this discussion should be continued on the Talk pages of Wikipedia, because, much of this discussion could be resolved very quickly and efficiently through a face-to-face interaction, and then posted on this page in a few sentences, I feel I have to respond to some of the comments you have made.

Firstly, all of the texts explaining the Coriolis effect, including the Wikipedia article on the subject, start with the example of a rotating turntable or carousel, across which a pencil line drawn with a ruler (by a person outside the turntable) or balls tossed across the carousel either by a person on the carousel or by a person outside the carousel seem to follow curved trajectories when viewed by the person on the carousel.

Consider a rotating carousel (or merry-go-round), which, seen from above, is rotating clockwise. We will call the person on the carousel the “rotating” person, and the one on the ground outside the carousel as the “stationary” person. Any ball thrown across the carousel by either person follows a straight line as seen by the stationary person. But the rotating person will always see a curved trajectory. From the rotating person’s point of view it therefore seems that there is a force that acts (horizontally) perpendicularly to the ball’s motion to cause it to deviate from the Newtonian straight-line motion. This in not a real force, but an artefact of the observation relative to a non-linear rotating reference frame. (This is a direct quote form a Physics text book. The Wikipedia article on the Coriolis effect calls it a fictitious force, as do several other sources at my disposal). The entire effect can best be explained in terms of simple geometry, which, in your terms, if I understand you correctly, means that it is NOT an instance of the Coriolis Effect.

Where a “real” force comes into play (and cannot be explained in terms of simple geometry) is if the rotating person tries to move from point A to point B on the rotating carousel. If point A is close to the center of the carousel, and point B is near the periphery, then, if this person sets out in what he imagines is the shortest distance between the two points, he ends up to the left of his target. In order to reach point B he has to exert a sideways acting force to move him more and more to the right as he moves outwards towards B. On the carousel he will have traced a straight line trajectory, but according to the stationary person on the ground outside the carousel he will have moved along a curved path which can only have been caused by a sideways force. This force (or acceleration) is indeed real, because it required the expenditure of energy from both the rotating and stationary observers’ points of view. Is this the only instance of the Coriolis effect you would recognize as such?

If the turntable and carousel examples provided in all the introductions to the texts on the Coriolis effect are genuine, prototypical instances of the Coriolis effect then, by extension, any Newtonian motion beyond the carousel, viewed by the rotating individual, will also subject to Coriolis effects. Thus a ball thrown away from, or beyond, the carousel’s rim will also follow a curved as seen from the carousel. Indeed if it stays in the air for several turns of the carousel it will appear to follow an outwardly spiraling trajectory. In all cases the motion can be explained in terms of simple geometry from the point of view of the stationary observer. But if Newtonian motion across the carousel is correctly described as Coriolisean by the rotating observer, then the motion beyond the carousel must also be due to the Coriolis effect. It then ineluctably follows that motion observed from our orbiting earth of the planets and other objects in the solar system are also affected by the Coriolis effect. The fact that the complicated motions observed from earth are best resolved by translating them into the motions that would be seen by an individual in a stationary position in relation to the sun does not negate the fact that from the earth these motions are due to Coriolis effects, even though the stationary observer would ascribe them to simple geometry. The Coriolis effect does not exist for a stationary observer. But they are very real for an earth-bound observer unaware that (s)he is on a huge 3 x 108 km diameter carousel centered on the sun.

I know that you have said above that this nonsense, but you have not explained why it is nonsense, nor given any examples of when and how the Coriolis effect applies. For instance, are you suggesting that the turntable and carousel examples used in all the texts explaining the Coriolis effect are simply “lies to children” (to quote Terry Pratchett)? What would your interpretation of these examples be? In the “Visualization of the Coriolis effect” section of the Coriolis effect article in Wikipedia a puck of dry ice is slid across a bowl of spinning water. This puck follows an elliptic track (as seen by a stationary observer) across the parabolically curved surface of the rotating water in the bowl (although it bounces back and forth off the rim of the bowl). The Coriolis motion as recorded by a camera mounted on the rim of the rotating bowl is uncannily reminiscent of the orbit of Cruithne as seen from earth.

### Unraveling the Coriolis effect (continued)

I have tried my best to come to grips with your understanding of the Coriolis Effect. I have also re-read all the texts at my disposal on the subject. The result is that several things bother me about your exposition of the Coriolis Effect. Firstly you jump from one frame of reference to the other (i.e. from the “rotating” frame of reference to the “stationary”, and vice versa) without warning, or explaining why the one takes precedence over the other in one circumstance and not the other. Obviously when discussing the Coriolis effect both must be described side by side, equally weighted, to explain how the one is represented in the other frame of reference. To me all instances of the Coriolis Effect are simple examples of uncomplicated Newtonian motion when seen by the “stationary observer”, who can then apply some simple geometry to derive what that motion will look like from the rotating individual’s point of view. Things are a little bit more complicated for the person on the rotating platform. If that person assumes that when an object moves from A to B it should, according to Newton’s Laws, follow a straight line unless acted on by an external force. Thus when an object in his world follows a curved trajectory it must be acted upon by a force which he calculates can be derived from the formula ${\displaystyle {\boldsymbol {F}}_{C}=-2\,m\,{\boldsymbol {\Omega \times v}}}$.

Object moving frictionlessly over the surface of a very shallow parabolic dish. The object has been released in such a way that it follows an elliptical trajectory.
Left: The inertial point of view.
Right: The co-rotating point of view.

But now consider the diagram which appears in the Coriolis Effect article of an object moving frictionlessly over the surface of a very shallow parabolic dish. The object has been released in such a way that it follows an elliptical trajectory. If the rotating person applies the formula to the motion of this object (as seen from their perspective), assuming that it would be moving in a straight line were it not for the “Coriolis Force”, derived from his formula, he would obtain the wrong result for the motion he sees. They would need to know what a “stationary” person sees: portions of an elliptical trajectory, and apply the Coriolis formula to that motion to explain what they see. Without that knowledge, to which they might not be privy, the motion seems inexplicable, and not governed by the Coriolis formula. (I know that you will maintain that the Coriolis formula is still in force, but in order to establish that, you have to move your frame of reference, in which case it is probably easier to use simple geometry to predict the object’s motion across the rotating frame of reference, which, if I have understood you correctly, ensures that it is no longer an instance of the Coriolis effect.)

You mention that when ${\displaystyle v}$ in the formula is zero then the Coriolis Force must be zero as well, and the phenomenon cannot be stated to be an instance of the Coriolis Effect (because it is the force that defines the Coriolis effect). But consider the following situation. An object moves in a straight line at uniform speed right across a rotating turntable, from one rim to the other. It does not cross the center point of the turntable. The velocity of the object is adjusted so that it crosses the rim (onto the turntable) at the same point as where it leaves the turntable a short while later. The track of the object on the turntable forms a loop. At the point on the loop nearest the center of the turntable, the object is, for an instant, stationary with respect to the turntable – its velocity is exactly the same as the angular velocity at that point on the turntable. Thus, for that instant in time, ${\displaystyle v}$ is zero, and the Coriolis Force is zero. So, for a moment the Coriolis effect is suspended, which sound very much like the contention that when a missile is shot vertically upwards and its velocity slows to zero at the apex of its flight, the force of gravity acting on it is zero.

I hope you understand my concerns, which I, furthermore, hope are not due to unjustified prejudices.

Key points to remember to unravel and understand the Coriolis effect:
• Only the most simple (trivial) examples used to demonstrate the Coriolis effect can be solved using simple geometry. In general, to solve any problem, physicists prefer to use the most simple description / method / frame of reference which gives a valid solution, so if you can solve a problem with simple geometry or by physics in the stationary frame, then great, do it that way, and don't bother using the rotating frame or Coriolis. You're confusing trivial demos which can be used to demonstrate what the Coriolis effect is (some of the simplest cases from the turntable / carousel demos) with problems which actually require using Coriolis effects in a rotating frame for their solution. The simple demos are great for an educational purpose, because they can be solved in both the stationary frame and the rotating frame.
• Real non-trivial examples of the Coriolis effect can NOT be solved by simple geometry, nor can they be solved in the stationary frame. It is simply not practical or possible to solve for the motion of the winds in the atmosphere, long distance artillery shells, Foucault pendulum, or various other classic real-world examples, using simple geometry or the stationary frame. These problems can only be handled in the Earth's rotating frame, leading to Coriolis effects. These are the cases that professional physicists would normally refer to as examples of Coriolis effects.
Returning to the original issue at hand here: in order to include anything in Wikipedia, it must be verifiable in reliable sources. There are no reliable sources which state that 3753 Cruithne's motion as observed from earth is an instance of the Coriolis effect (nor the motion of any other astronomical bodies), and so it can not state that in the article. Thanks.

Thank you very much. That makes it a it a lot clearer and understandable, and I am happy to close the discussion.

Cruithne9 (talk) 09:34, 26 August 2015 (UTC)

Seattle Skier, You have explained the physics very well here. Your opinion would be most welcome on the centrifugal force page. The physics there is now correct but there is so much disinformation and confusion about the CF that I think we need to address it in some way.

## Intuitive explanation for Coriolis vertical deflective effect on westward and eastward moving objects (Eötvös effect)

I have created a new section for the example and moved here the image: here is the first draft

An intuitive example to understand the Eötvös effect:

Lets imagine that we have a train that travels through a frictionless railway line along the equator, and that when it is in motion it travels at the necessary speed to complete a trip around the world in one day. We will examine the Coriolis effect in three cases:1. When it travels west, 2. When is at rest and 3. When it is travelling east. We will look at this cases from our rotating frame of reference on Earth first and check it against the fixed inertial frame of a point on outer space above the North pole (see image):

1. The train travels toward the west: In that case it is moving against the direction of rotation so in on Earth's rotating frame the Coriolis term will be pointed inwards towards the axis of rotation (down) this additional force downwards should cause the train and those on board it to be heavier while moving in that direction.
• If we look at this train from our fixed non rotating frame on top of the center of the Earth, we see that it runs at such a speed that it remains stationary as the Earth spins beneath it, so the only force acting on it in this case would be gravity and the reaction from the track. So this force is greater (by 0,34%) than the force that the passengers and the train experience when at rest relative to Earth and therefore rotating along with it. That difference is exactly same and is an intuitive way to understand the Coriolis term on the previous paragraph.
2. The trains comes to a stop: From our point of view on Earth's rotating frame the velocity of the train is 0 so the Coriolis force is also 0 and therefore the train and it´s passengers recuperate their usual weight
• From the fixed inertial frame of reference above Earth, the train is now rotating along with the rest of the Earth. 0,34 percent of the force of gravity provides the centripetal force needed to achieve that circular motion on that frame of reference. The remaining force, as could be measured by a scale, would make the train and its passengers "lighter" than in the previous case.
3. The train changes direction and travels towards the East. In this case as it is moving in the direction of Earth's rotating frame, so the Coriolis term will be directed outward from the axis of rotation (up) this upward force would cause the train to seem lighter still than when at rest.
• From the fixed frame of reference on space the train travelling east will now be rotating at twice the rate as when it was at rest and therefore the amount of centripetal force needed to cause that circular path increases leaving less force from gravity to act on the track. this is what the Coriolis term accounts for on the previous paragraph.
• As a final check we can imagine a frame of reference rotating along with the train. such frame would be rotating at twice the angular velocity as Earth's rotating frame. the resulting centrifugal force component for that imaginary frame would be greater. since the train and it's passengers are at rest within it, that would be the only component in that frame explaining again why the the train and the passengers are lighter as in the previous two frames.

This also explains why high speed projectiles travelling west get deflected up and when they are shot east are deflected down. This vertical component of the Coriolis effect is called the Eötvös effect

Please let me know if you think it is clear and easy to understand intuitively. About the image, I think it is a good idea to slow it down, it will look a bit choppy as I had to make each frame with four layers each so there are only 16 frames, but now is probably to hard to look at without getting a bit dizzy. I will take care of it tomorrow.--Crystallizedcarbon (talk) 20:56, 30 August 2015 (UTC)

Done The animation is now slowed down to 4 frames per second.--Crystallizedcarbon (talk) 09:56, 31 August 2015 (UTC)
The first two cases are are a common undergraduate physics problem and should be easy to find sources for. The third case might be harder.
I would not use the word 'fictitious'. It is not necesary because the Coriolis force 'is' an inertial/fictitious force. Using the word again could suggest that there are two Coriolis forces; one real one and one fictitious one.
It is better to use 'frame of reference' rather than 'point of view'. POV is a not a clearly defined technical term so might be open to incorrect interpretation. Perhaps we could say that it would be natural in many cases for a person on the surface of the Earth to use a frame of reference rotating with the Earth. Martin Hogbin (talk) 08:11, 31 August 2015 (UTC)
I think they are both good points. I have made both of the changes to the text above. --Crystallizedcarbon (talk) 10:08, 31 August 2015 (UTC)
It is important to make clear what frame of reference we are working in and to distingusih between what is experienced by a traveller and the physics. In every case, what is experienced by the traveller is the same in every frame of reference. How this is explained by the physics depends on the frame of reference in which you are working. Martin Hogbin (talk) 10:24, 31 August 2015 (UTC)
Yes, that is what I tried to do by subdividing each of the three cases using bullets. In each case we use first Earths rotating frame. the next bullet is the inertial frame and in the third case we added an extra bullet for a frame rotating along with the train. I have added some extra text to that bullet point to try to clarify that we are using a different frame in that case. Regards.--Crystallizedcarbon (talk) 11:01, 31 August 2015 (UTC)
I have changed the text to try to further clarify the different frames used.--Crystallizedcarbon (talk) 11:19, 31 August 2015 (UTC)
Hello Please feel free to improve it however you see fit it to make sure it is both accurate and intuitive. Regards. --Crystallizedcarbon (talk) 20:24, 31 August 2015 (UTC)
Can I suggest that we start with my wording in the Centrifugal force article. Martin Hogbin (talk) 11:46, 1 September 2015 (UTC)
Sounds good to me, feel free to edit the text above.--Crystallizedcarbon (talk) 13:00, 1 September 2015 (UTC)

I propose using this slower version of the animation. I slowed it down to two frames per second, I think it may be easier to watch and understand. --Crystallizedcarbon (talk) 12:25, 2 September 2015 (UTC)

Hello I have changed the example according to your recommendations. I think I made very clear the frame used for each case. The third point of the third case may or may not be necessary. Any feedback would be apreciated.--Crystallizedcarbon (talk) 16:37, 3 September 2015 (UTC)

•  Comment: Another very interesting point from this example is that if the westward train moves any faster, the downward Coriolis component (Eötvös effect) starts diminishing. When the train doubles its speed it completely disappears (as the train would be rotating in the inertial frame at the same speed as Earth but in the opposite direction) so it would need the same amount of centripetal force as when at rest. Any further increase of speed would make it seem lighter. Do you think it is worth mentioning that Eötvös effect only "works" up to a certain westward speed. Can it be sourced? --Crystallizedcarbon (talk) 16:37, 3 September 2015 (UTC)
I don't think it needs a source, other than WP:CALC. But this effect is more than just increased weight-- it's decreased weight also. Obviously the increased weight from the Eötvös effect reaches a max when the train reaches the speed of the rotating Earth as seen in the inertial frame: at that point, Eötvös effect has simply undone any existing centrifugal "lightening," and now that full gravity acts, that's all the increased "heaviness" you can get. However, going in either direction from that speed, makes it lighter symmetrically whichever way it goes, and this effect continues until it is in orbit and is weightless, and if you go faster in either direction, even has to be held down by the rails, increasing its outward acceleration without limit as you keep increasing velocity. SBHarris 05:41, 4 September 2015 (UTC)
Graph of the force experienced by a 10 grams object as a function of it's speed moving along Earth's equator (as measured within the rotating frame). (Positive force in the graph is directed upward. Positive speed is directed eastward and negative speed is directed westward).
Right, I agree with you. I created this graph to explain the force experienced by a 10g object due to its speed along the equator. The parabola is explained by the centripetal force needed to keep its circular motion on the inertial frame, and the reason that is not centered in the axis accounts for the fact that we measure the speed and its effects within Earth's rotating frame. I think the graph will also be a good complement to the example, and I will add it to the Eötvös effect article as well.--Crystallizedcarbon (talk) 09:09, 4 September 2015 (UTC)

If the current version is OK with everybody I will add it to the article tomorrow and we can continue to make improvements there. --Crystallizedcarbon (talk) 08:36, 5 September 2015 (UTC)

Hello I have added the example to the article, feel free to insert additional references to it if you want. This afternoon I will probably insert a couple more. --Crystallizedcarbon (talk) 09:41, 6 September 2015 (UTC)

## Apparent deflection

The Foucault's Pendulum shows it is an apparent deflection towards the left in the northern hemisphere and towards the right in the southern hemisphere. Movement of pendulum is set in a straight direction (let's say, from south to north) which is kept, by inertia, in the same direction as long as the pendulum moves. However, pendulum will push down a small ball from the circle every half an hour if we previously set 24 little balls on the outside circle separated, therefore, by 15 sexagesimal degrees of angular separation. Every hour, the moving pendulum will push down two little balls (one going north to south and the other coming the other way around) and, therefore, the pendulum will throw down the 24 balls in half a day, that is, in 12 hours. And the reason for this is not a deflection of the pendulum (since it keeps its original direction as far as it moves) but a consequence of the rotation movement of the Earth. The center of the circle where balls are set gives a complete turn every 24 hours (since it moves along the parallel of latitud of this exact point), but every point (and ball) on the outside circle gives two complete turns every 24 hours (one around the parallel of latitude of each ball and another around the center of the circle). This is the reason why all the 24 little balls are thrown down in 12 hours: pendulum moves, apparently, 15º per hour to the left going north to south and another 15º coming the other way around, also to the left. The only exception to this rule is when the center of the pendulum's circle is at one of the Earth's poles because, in this case, all the little balls are located at the same latitude because it's a parallel of latitud around the pole (remember that a parallel of latitude is a minor circle around the pole).

In sum, deflection of the pendulum to the left on the northern hemisphere (and to the right in the southern one) is apparent because it is caused, not by a deviation of the pendulum's direction itself, but by the rotation movement of the Earth. I think these ideas should be revised and included in this page. --Fev 22:43, 20 September 2015 (UTC) — Preceding unsigned comment added by Fev (talkcontribs)

## Coriolis effect and Geography

This article is maybe OK from the standpoint of Physics (many phormulae and other atracting considerations), but it is awful from the point of view of Geography. Two examples:

1. The article says: As a result, in tornadoes the Coriolis force is negligible. On the contrary, it is very strong and, besides, it is not a force, but an effect of the Earth's rotation movement. In Geography, moving of objects such as air masses must take into account its length, width, AND HEIGHT, being this last dimension the real reason why wind speed in a tornado is so high. So, it is impossible to reduce the Coriolis effect to a plane of rotation.
1. The article also says: Contrary to popular misconception, water rotation in home bathrooms under normal circumstances is not related to the Coriolis effect or to the rotation of the earth. This statement is not referenced because it is FALSE. As well as tornadoes, bathroom toilets use Coriolis effect to accelerating flushing down of water: it is like a water tornado and moves the same way as toilets do (counterclockwise in the Northern Hemisphere). Deflection of air and water masses is toward the left on the Northern Hemisphere and to the right on the southern one, regardless of the object's size, let's say, a bathroom toilet OR the Mediterranean sea, where all the ports are closed to the left (seeing from the coast) and open to the right, to avoid coastal current that is counterclockwise (like the Baltic sea and others). Some examples on the western Mediterranean as they are seen in Google maps:
• Barcelona: [1]
• Ametlla de Mar: [2]
• Tarragona: [3]
• Hospitalet del Infante (Tarragona): [4]
• Vinaroz: [5]
• El Grao de Castellón: [6]
• Valencia: [7]

And the geometry of these examples has nothing to do with prevailing winds (westerlies at this latitude) — Preceding unsigned comment added by Fev (talkcontribs) 11:22, 25 September 2015 (UTC)

The Coriolis force that is due to the rotation of the Earth is negligible within a tornado itself but the direction of rotation of a tornado is determined by the rotation in the larger air masses from which it forms and this rotation is due by the Coriolis force (or the rotation of the Earth, if you prefer).
There is a force deflecting the water draining from a basin, just as you say, but it is negilgible compared with the effect of other factors such as any residual rotation from the filling, or the plumbing. Martin Hogbin (talk) 10:37, 26 September 2015 (UTC)

## A commentary on this 2 statements

The two statemens are not referenced and are wrong. Nothing is negligible regarding effects of the rotation movement of the Earth. But I don't like to go on with this discussion and, therefore, I quit. Sincerely --Fev 00:53, 27 September 2015 (UTC) — Preceding unsigned comment added by Fev (talkcontribs)

## Expect that this point is made above but I am too lazy to read all the way through it.

So I am making the point briefly in its own section. I am not at all happy to accept that either the Coriolis force or the centrifugal force is a non-force. I write as an engineer who must consider real forces, such as those which might result in the bursting of a rotating machine, or which might stress the casing of a centrifugal pump, but who may happily and safely ignore anything which does not exist, or which may exist in only a metaphysical sense. If a force is of significance in a practical case, then it must be defined in such a way that its reality is properly acknowledged. It makes no sense to me to define a force, and then say it is a non-force, or, as in the preceding section, to speak of a force when the observed motion depends precisely on the absence of any such force, and is properly described strictly in accordance with Newton's first law (unaccelerated motion in a straight line relative to an inertial frame).

Here is a better approach to the C force which acknowledges it in cases where it exists, and excludes it where it does not: The Coriolis force is the force required to constrain a moving mass to move in a straight line relative to a rotating frame of reference. For example, if a body is constrained to move radially on a rotating turntable, a lateral (tangential) force must be applied. Convention might require that we say that the C force is actually the reaction to the force so defined - others others can argue about that. If a moving body is not so constrained (as in the case of clouds moving in a cyclone), it is obvious and pleonastic to say that no lateral force exists (the motion is unconstrained). The observed lateral acceleration must then be explained without recourse to a force which simultaneously exists and does not exist. Such an explanation can be given by deducing that the observed motion (i.e. acceleration without a force) is observed with respect to a rotating frame, and then applying Newton's first law.

Similarly we can define a real centripetal force as a force required to constrain a mass to move in a circular path, and the centrifugal force is then the reaction to the centripetal force. Such a reaction is experienced by our bodies while in a cornering car. 1 Oct 2015

I have returned to this after having read some more of the contributions above, but still find I have not sufficient energy to give the entire discussion proper critical consideration. I will add two further points however. (1) Many internet sources discuss the "Coriolis Effect" (this is also the title of the present article), which avoids the problem of a force which does not exist, and merely seeks to explain the movement of, for example weather features, in terms of the rotation of the earth. This is commendable, and raises no objections. (2) The question of whether the Coriolis "force" exists is entirely a matter of giving precedence to either a rotating frame, or an inertial frame. In the first case it is a real force (from that point of view), in the 2nd case it does not exist (from that point of view). Thus it appears that those who write of it as a non-force are making an implicit and unstated assumption about their preferred frame of reference. However, the choice of the point of view that gives the C force reality must be seen as unsatisfactory, since there is no way of measuring such a force, and its existence must remain mystifying and metaphysical. Better to say plainly that it does not exist (and therefore need not be discussed) unless, that is, it is defined in the way I have suggested above (constrained radial motion on a rotating system). g4oep

You are probably wrong but I am too lazy to read all that you have written. Martin Hogbin (talk)
@77.96.58.212: Regardless of your personal anecdotes and opinions, the current article sticks pretty close to reliable sources. Either indicate where you feel reliable sources are being represented improperly or poorly, or provide other reliable source not currently represented in the article. Otherwise, whether correctly or incorrectly, you're likely to be ignored for pushing fringe viewpoints. --FyzixFighter (talk) 06:52, 3 November 2015 (UTC)

lol.. i would expect that the view that something that does not exist need not be discussed would warrant a more serious comment. Would you like to take it as a challenge  ? where is my 'anecdote'. Have you a comment on my suggestion that the C force should be more satisfactorily defined as a real force which can be measured using conventional force-measuring equipment, and that a non-force definition or usage of it is objectionable as mystification ? g4oep — Preceding unsigned comment added by 77.96.58.212 (talk) 09:10, 3 November 2015 (UTC)

The article already says, 'The Coriolis effect exists only when one uses a rotating reference frame. In the rotating frame it behaves exactly like a real force (that is to say, it causes acceleration and has real effects). However, the Coriolis force is a consequence of inertia,[12] and is not attributable to an identifiable originating body, as is the case for electromagnetic or nuclear forces, for example'. If you do not understand what this means you can ask on my talk page. Martin Hogbin (talk) 17:38, 3 November 2015 (UTC)

Ok- I can see that the alternative definition I am referring to is unfamiliar to some. I have added a short paragraph which supports the definition with a diagram. The text I have added is almost verbatim from the sources I refer to. Someone deleted this without giving a reason, but it seems to me that the references are impeccable, and that what I have written is an established alternative definition of the C force & acceleration. Please do not delete it again without good reason. g4oep — Preceding unsigned comment added by Andrewg4oep (talkcontribs) 14:14, 8 November 2015 (UTC)

Actually, IMO, your alternative definition is the same mentioned in the article. I don't have access at the moment to the first source, but I do for the second source. I have a few concerns from what I have been able to access. First, at least with respect to the second source, I think you are misreading the source. I think that might also be true for the first source. Could provide the verbatim text that you are trying to paraphrase so other editors can also assess. Second, I doubt that statements like "Note that the accelerations are relative to a fixed, non-rotating reference frame" or "The Coriolis force, thus defined, has an origin (the rotating arm) and is in no sense a pseudo-force" are actually supported by the cited references (again, I didn't see it in the one I was able to access), and therefore represent WP:OR. Third, I would argue that the source I can see is poorly worded in parts and perpetuates a common misconception with respect to the centrifugal force (a misconception identified by a few other sources and seen when compared to the larger body of reliable sources).
More particularly, because you are describing the motion along the rotating arm, you are necessarily in a rotating system. Leibniz made the same implicit assumption when he first described the centrifugal force (for example, see Aiton, The celestial mechanics of Leibniz in the light of Newtonian criticism, who noted "Leibniz's study of the motion along the radius vector was essentially a study of motion relative to a rotating frame of reference.") Section 1.3.3 in your second source is unfortunately vague on whether it is in a rotating frame or not, but IMO it appears to be Leibniz-like and therefore not a stationary frame. On the other hand, section 1.3.4 in the same source is explicit in showing that the Coriolis force arises only when we are relating the acceleration in a non-moving coordinate system to acceleration and motion in the moving coordinate system.
You were bold, but others have reverted you. Now, per the suggestions of WP:BRD, we should discuss before reinserting. Again, providing the verbatim text you are paraphrasing would be helpful to the discussion. As an aside, I you can sign your posts on the talk page using ~~~~, and your attempt at getting the header for the subsection still wasn't correct - see MOS:HEADINGS for the correct method --FyzixFighter (talk) 15:09, 8 November 2015 (UTC)

Yes - I have gone beyond my sources with some very minor comments and added emphases. But I feel that the extent to which I have done so does not exceed other extrapolations in the article. To me it seems very clear that this is truly an alternative definition which is commonly used among engineers, and which therefore deserves inclusion. The C force is here defined as the force which is required to constrain a moving body in a straight-line path relative to a rotating frame; the force is not a pseudo force. It does not conform to this definition: "The force F does not arise from any physical interaction between two objects, but rather from the acceleration a of the non-inertial reference frame itself. " (taken from the wikki entry on pseudo-force). The force I am talking about is applied to the radially moving element by the rotating arm. As I have written, this force could cause the rotating arm to fail mechanically, and it is for this reason that engineers take an interest in it. The situation is quite distinct from that which occurs when a weather formation is seen to be moving in a curved path when viewed from the surface of the earth. In this latter case the curved path appears to need a force for its explanation, but no such force exists; the curved path would appear straight when viewed from an inertial frame. According to the engineers, if the clouds were constrained to move in a straight path relative to the surface of the earth, THEN a coriolis force would be required, but in fact no such force acts on the clouds; they are unconstrained and move strictly according to Newton's first law. They are NOT seen to move in a straight line relative to the surface of the earth. The two situations under consideration are quite distinct. One requires a real force which can be measured and which might cause a mechanism to fail when set in motion, the other requires no force at all, or at best a pseudo-force or notional force which exists only in the imagination and which is therefore of no interest to an engineer. Andrewg4oep (talk) —Preceding undated comment added 16:01, 8 November 2015 (UTC)

Andrewg4oep, I agree with FyzixFighter. You seem to be trying to add your own interpretation of Coriolis force and pseudo-force (in my opinion better called an inertial force because it can be very real) to this article based on an combination of two sources. Please do as FyzixFighter suggests and give us the verbatim text from both the sources that you think support your assertions so that we can discuss this further. Martin Hogbin (talk) 16:46, 8 November 2015 (UTC)
@Andrewg4oep - I think we need to be careful to distinguish between accelerations and forces. Only in simple cases is there a one-to-one correspondence between the individual forces and the terms within the expression for acceleration for a given coordinate system. For example, the second source, Smith's "Mechanical Engineer's Reference Book, only talks about accelerations on page 1/7. In the example on that page, the four parts of the total acceleration are the terms when writing out the acceleration in polar coordinates (${\displaystyle {\ddot {\vec {r}}}=({\ddot {r}}-r{\dot {\theta }}^{2}){\hat {r}}+(2{\dot {r}}{\dot {\theta }}+r{\ddot {\theta }}){\hat {\theta }}}$). And here is where we get into an apparent confusion in the literature. Smith calls the ${\displaystyle 2{\dot {r}}{\dot {\theta }}}$ term of the acceleration the "Coriolis acceleration", and I have seen others use similar terminology - I've also seen people call it a "Coriolis term", which is my preference. The term "Coriolis acceleration" is also used in sources to refer to the apparently anomalous acceleration perpendicular to an object's velocity when describing motion in a rotating frame, which we attribute to the Coriolis inertial force. The confusion arises because the "direction" of this Coriolis term is actually opposite that of the Coriolis force (the inertial force) acting on the block in the frame tied to the rotating link. While there appears to be disagreement in the literature what "Coriolis acceleration" should refer to, I have yet to see a reliable source that talks about a Coriolis force/effect outside of a rotating frame.
Back to the block on link example, if we assume this is a simple example, then the only forces on the block are a contact force from the link in the theta-hat direction and any frictional force between the block and link in the r-hat direction. However, I would still not call the theta-hat contact force a Coriolis force since, in Newton's 2nd law, it is the force paired with both the Coriolis term and the angular acceleration term - also note that Smith does not call anything a Coriolis force. More generally, there is no requirement that the force that generates the "Coriolis term" acceleration be a single force, it could be very easily a sum of forces, hence why I don't think it is wise to call anything a Coriolis force in this context. --FyzixFighter (talk) 20:05, 8 November 2015 (UTC)

## Atmospheric slippage?

As a disclaimer, I am not an expert on this nor anything close to it. However, when considering the example of the coriolis affect causing drift of a bullet fired over a large distance, it seems intuitive that the only reason this drift occurs is because the bullet is no longer "fixed" to the earth and does not gain the angular momentum of the lower latitude when it travels there. For example, assume that you shoot the bullet at a latitude with a rotation of 1000 mph and it impacts at a latitude of 1001 mph. Theoretically, if there was no atmospheric slippage (in a fluid dynamics sense of the word slippage) then the atmosphere would simply "push" the bullet sideways at the same speed it is rotating and therefore the bullet would gain the additional 1 mph in angular momentum and would not seem to drift. So, in a sense, the coriolis effect in the sense of the atmosphere seems to be due to this atmospheric slippage, at least from the way I am understanding it, which could very well be flawed. Can someone who understands this better clarify this point in the article? If I don't get any responses I'll try to do some research on this when I have some "free time" but that might not be for a few weeks/months. Thanks! (PS - I was thinking about this after considering how oars suffer slippage through water in a rowboat or racing shell.) Ahp378 (talk) 03:33, 27 December 2015 (UTC)

Hello @Ahp378: There is a Coriolis effect on a moving bullet. Think of a projectile fired north from the equator with the speed and firing angle necessary to reach, for example, the Tropic of Cancer. the difference in latitude 23.437° in the example implies a cos(23.437)=8.3% smaller radius, so at impact, (disregarding friction up to that point) and due to Newton's first law, the bullet is moving 8.3% faster towards the right than Both the ground and the atmosphere. So the atmosphere may indeed reduce slightly the Coriolis effect, how much would depend on the aerodynamics of the projectile, my intuitive feeling is that in a projectile capable of reaching such a long distance the effect of that side air drag would be almost negligible with respect to Coriolis (and orders of magnitude less than the front air drag). The reduction should probably be similar to the drag that the projectile would experience if you could throw it sideways (and it stayed that way) towards the East at a speed equal to the difference of the surface speeds at the equator and the tropic as measured from an inertial frame of reference, approximately 465*(1-cos(23.437)) = 38.36 m/s (138 km/h)
Another way of understanding this with a practical example that you can actually try, is to see what happens when you are swinging a whistle in circles on a cord and you let it wrap around your finger. You will see how the angular velocity of the whistle increases as the radius of rotation gets smaller. Even if you blow against the whistle as it rotates to account for the atmospheric slippage of our example you would notice very little difference, the angular velocity of rotation would still increase. In our previous example the projectile would be the whistle and gravity the cord that shortens the radius of rotation when moving north from the equator. I hope that helps explain your question. Regards.--Crystallizedcarbon (talk) 10:06, 28 December 2015 (UTC)
Hi , thanks for your write-up. I think I understand what you're saying, that one would essentially consider friction negligible, and so the "base state" of the coriolis force is frictionless and you then add in any applicable friction, as opposed to the other way around, starting out at a base state of perfect friction and then considering the amount subtracted to be the coriolis force. I guess another way to phrase my line of thinking is this: in the example of the sphere rolling in a straight line along a rotating circle, what would happen if you replaced the sphere with a cylinder? Or as another example, if instead of a bullet flying through the air, you simply drive your car south on a road - you wouldn't drift sideways. I'm just trying to think if there's some way to clarify in this article that the coriolis force is essentially created by a lack of friction, since that was not quite clear to me when I was reading it. Thanks! Ahp378 (talk) 01:01, 5 January 2016 (UTC)

## Misconception by omission

I have read the article and the discussion of the article on this Talk Page. From all of this, it is clear that the article does not do justice to what has been discussed at length on this Talk Page.

In the Introduction to the article, “the Coriolis effect is [defined as] the apparent deflection of moving objects when the motion is described relative to a rotating reference frame”. This statement is not qualified by exceptions or limitations. This is correct. It applies to ALL motion observed from a rotating frame of reference, which includes all the examples given in the article (of missiles launched across rotating turntables or spinning bowls of water, and of trains speeding east- or westwards along, especially, the equator). But it also includes EVERYTHING ELSE observed from our rotating and orbiting earth. While several types of motion seen on earth (such as the winds, the circulation of the oceans, the trajectory of missiles fired from cannons resting on the earth, and the apparent difference in weight of aircraft flying eastward or westward along a lines of latitude, especially the equator) are universally accepted as genuine instances the Coriolis Effect, the definition of the Coriolis Effect is not limited to these examples. Yet the article is written as if these are indeed the only examples of the Coriolis Effect. This is misleading and confusing, in addition to being dishonest.

The definition of the Coriolis Effect makes no distinction between these examples and, for instance, the apparent movement of the “fixed” stars, the planets, various asteroids and meteorites and even the artificial satellites (including the geostationary satellites) as seen from our rotating and orbiting earth. The only difference between these last named movements, and the ones mentioned in the article, is that in the former, invoking Coriolis Forces to calculate their motion as seen from our rotating frame of reference is unnecessarily clumsy. It is far simpler to understand these motions as if observed from an inertial frame of reference, away from the earth, and then applying the Newtonian Laws of Motion to them. This does not invalidate the fact that the complex movement of the planets in the sky, as observed from our orbiting earth, are instances of the Coriolis Effect. The same applies to the apparent spinning of the “fixed” stars round an axis that passes through the Earth’s north and south poles. It is simply not convenient, or helpful, to calculate the apparent Coriolis Forces that would account for these puzzling movements. And therefore these movements are never referred to as instances of Coriolis Effects in any physics or astronomy textbooks. A student is considered better off thoroughly understanding Newton’s Laws of mechanics than getting embroiled in Coriolis Forces, which are, in any case, “fictitious” forces, which do not further the student’s understanding of the universe. The important point remains, nevertheless, that the motion of the planets during the course of the year, and those of the fixed stars during the course of the night ARE instances of the Coriolis Effect. There is no reason why this cannot be explained in the article. I do not believe that students, or Wikipedia’s wider readership, need to have this information withheld from them. In fact doing so simply adds confusion, and puzzlement.

From a historical point of view, it was these very Coriolis Effects that confused the pre-Copernicus astronomers. These effects are very real, but mathematically enormously confusing, until Copernicus, Galileo and Newton (among others) suggested metaphorically stepping off our rotating frame of reference, and calculating these movements from an inertial frame of reference. This last sentence would adequately and simply put the Coriolis Effect, as it applies to astronomy, in the correct perspective (as agreed to by most if not all the contributors to this Talk Page).

I think that not acknowledging the spinning of the fixed stars round Polaris (in the northern hemisphere) as an instance of the Coriolis Effect, is equivalent to describing Evolution by Natural Selection, but pointedly ignoring Human origins by these means. It is not necessary to actively deny the Human relatedness to the apes, to instill, propagate or support a misconception about Human origins. The same applies to the discussion of the Coriolis Effect.

I hope this helps. Cruithne9 (talk) 11:37, 14 January 2016 (UTC)

I agree with what you say although I did not think that the article was quite as bad as you seem to be suggesting. Do you have any specific suggestions for improvements? Martin Hogbin (talk) 12:30, 14 January 2016 (UTC)
(edit conflict)
Yes, our article says:
The vector formula for the magnitude and direction of the Coriolis acceleration is
${\displaystyle {\boldsymbol {a}}_{C}=-2\,{\boldsymbol {\Omega \times v}}}$
where (here and below) ${\displaystyle {\boldsymbol {a}}_{C}}$ is the acceleration of the particle in the rotating system, ${\displaystyle {\boldsymbol {v}}\,}$ is the velocity of the particle with respect to the rotating system, and Ω is the angular velocity vector which has magnitude equal to the rotation rate ω and is directed along the axis of rotation of the rotating reference frame, and the × symbol represents the cross product operator.
So looking at the relevant vectors, indeed a star's apparent tangential ${\displaystyle {\boldsymbol {v}}\,}$ (caused by the rotation), trivially produces a constant magnitude Corriolis acceleration toward the poles, resulting in pure circular motion. I don't see any objection saying something about this in the article. - DVdm (talk) 12:49, 14 January 2016 (UTC)

From our point of view here on Earth, fixed stars rotate on the night sky
To an observer on the rotating Earth, both satellites appear stationary in the sky at their respective locations.

A thought I have had on this subject, although I am not convinced it is necessarily the best suggestion possible, is the creation of a new heading: Other instances of the Coriolis Effect. Here the various illustrations that appear on this page, like the stars circling Polaris, and the diagram of geostationary satellite, could be used together with a few words of explanation, along the lines indicated above, noting that these are other instances of the Coriolis Effect, but that, while it is possible to calculate the Coriolis Forces that would apply to these cases, the math is clumsy and not useful. It is better to follow Copernicus, Galileo and Newton's suggestion to metaphorically step off our rotating frame of reference, and calculate these movements from an inertial frame of reference.

Cruithne and Earth seem to follow each other because of a 1:1 orbital resonance.
Cruithne appears to make a bean-shaped orbit from the perspective of Earth.

I also like the curious orbit of 3753 Cruithne as seen from our orbiting frame of reference round the sun, as a particularly spectacular instance of the Coriolis Effect. But because astronomers have little use for Coriolis "forces" in their calculations of the orbits of objects in our solar system, most of them seem to be unaware of the term "Coriolis Effect", even though the diagram on the right shows that they are acutely aware of the phenomenon (despite not having a name for it). Cruithne9 (talk) 13:39, 14 January 2016 (UTC)

I added three simple examples to the Centrifugal force article. One of them Centrifugal_force#An_equatorial_railway might be useful here. Martin Hogbin (talk) 13:55, 14 January 2016 (UTC)
Two quick thoughts. First, the geostationary satellites are not a good example for the Coriolis effect/force. If they are stationary, ie their velocity is zero, in the earth's rotating frame, then the Coriolis force is also zero. Second, the example of the 3753 Cruithne looks to me like an example, albeit slightly extreme example, of the stability of the L4/5 Lagrangian point. I would rather include mentioning the stability L4 and L5 points in the context of the Coriolis effect/force, with the appropriate references of course, than focus on a single asteroid. A quick google search of "Lagrangian point" and "Coriolis" would probably show more results then "Cruithne" and "Coriolis". --FyzixFighter (talk) 00:50, 15 January 2016 (UTC)
Also, how does the proposed Other instances of the Coriolis Effect section differ from the existing Coriolis effects in other areas section? Perhaps the heading could be reworded and the section moved within the article, but IMO the existing section is where such examples of the Coriolis effect in astronomy would fit so there is no need to add a new heading. --FyzixFighter (talk) 07:40, 17 January 2016 (UTC)

Sorry, I had not noticed that heading - only its contents. You are quite right that the astronomical examples of the Coriolis effect should be slotted into there.

I will not be able to write this subsection, because I do not have suitable references to hand; but also because I am sure I will get into trouble! For instance, in the Introduction the Coriolis Effect is defined as the apparent deflection of moving objects when the motion is described relative to a rotating reference frame. Then there is the Coriolis Force which is the fictitious force an observer on a rotating frame of reference needs to postulate to account for the curved trajectories of objects moving across his/her field of view. Obviously, when an object co-rotates with the rotating frame of reference, the observer records a zero Coriolis Force; but to my mind that does not mean that there is no Coriolis Effect. Consider the following example: An object moves in a straight line at uniform speed across a rotating turntable, from one rim to the other. It does not cross the center point of the turntable. The velocity of the object is adjusted so that it crosses the rim (onto the turntable) at the same point as where it leaves the turntable a short while later. The track of the object on the turntable forms a loop. At the point on the loop nearest the center of the turntable, the object is, for an instant, stationary with respect to the turntable – its velocity is exactly the same as the angular velocity at that point on the turntable. Thus, for that instant in time, v is zero, and the Coriolis Force is zero. So, for a moment the Coriolis Effect is suspended, which sound very much like the contention that when a missile is shot vertically upwards and its velocity slows to zero at the apex of its flight, the force of gravity acting on it is zero.

A similar argument can be mounted against the geostationary satellite not being an example of the the Coriolis Effect, because its motion relative to the rotating earth is zero, so there must be a zero Coriolis Force at play here. But change its orbital path slightly, and immediately the Coriolis Forces come into play again, either as the "Eötvös effect", if it continues orbiting in the plane of the equator, or as a curved trajectory if it starts crossing lines of latitude.

Someone who can authoritatively deal with these contradictions will have to write the proposed subsection on the "Astronomical examples of the Coriolis Effect", or whatever heading is deemed appropriate. Cruithne9 (talk) 09:06, 17 January 2016 (UTC)

What is the objection to Centrifugal_force#An_equatorial_railway? It is a well know undergraduate problem showing how the same situation can be analysed in two different frames; on rotating and one not. Martin Hogbin (talk) 12:51, 17 January 2016 (UTC)
@Martin: Don't we already have the equatorial railway example in the Coriolis effect#Eötvös effect section? What would you add to it or how would the example you propose be different? --FyzixFighter (talk) 17:20, 17 January 2016 (UTC)
Yes we do. I forgot that. Martin Hogbin (talk) 17:57, 17 January 2016 (UTC)
@Cruithne9: Let me counter by going to the other extreme - do we talk about a Coriolis effect when talking about a person sitting still on the surface of the earth? It's technically geosynchronous motion. Maybe it does make sense for geosynchronous satellites, but I would feel more comfortable if we had a source that connected the two ideas together. On a related note, I might try rearranging the sections a bit and adding something on Lagrangian points and the Coriolis force/effect (I know I have sources for a section on that). --FyzixFighter (talk) 17:20, 17 January 2016 (UTC)

I did think about the person sitting on the surface of the surface of the earth as posing the same coriolis problem as the geostationary satellite. Anything observed from a rotating frame of reference will appear to be moving or not moving differently if viewed from an inertial frame of reference. This could be pointed out in the new section. I'll give another example: User:DVdm, above has pointed out that the stars circling Polaris have Coriolis Forces acting on them, and are therefore a good example of the Coriolis Effect. But that raises the question about Polaris itself. Why should it be the single exception simply because its velocity is zero when viewed from our rotating frame of reference? The new section would be incomplete if these seemingly contradictory instances were not explained or discussed.

Maybe all that is necessary, if no sources can be found for these conundrums, to mention that the "Coriolis Effect" is riddled with conventions. Then at least the reader is informed about the Coriolis Effect's real scope.

I like your idea about including a discussion about the Lagrangian points. They definitely deserve a mention in the new section. The article would be incomplete if they were not described. Cruithne9 (talk) 04:52, 18 January 2016 (UTC)

You seem to be straying off the main subject, which is the Coriolis force. The thrust of your original post was that the article was not clear enough about what the Coriolis force is. The fact that the same thing may have a different motion when viewed from a different frame of reference is, of course, true but not the main point of this article which about one particular aspect of rotating frames.
By the way, there are no real conundrums and or conventions necessary for special cases. The Coriolis force is clearly defined as the force acting on an object when considered in a rotating frame. The physics is quite clear and there are no exceptions that need special conventions. Martin Hogbin (talk) 11:23, 18 January 2016 (UTC)

Thanks @Martin Hogbin. Actually my original plea was to separate the Coriolis Force from the Coriolis Effect (the discrepancy between what is seen from a rotating frame of reference and that seen from an inertial reference frame). But I realize that the convention states that there is only an Effect if the Force is not zero. The article should state that unambiguously with a reason. (The reason is probably that most people accept that a tree remains where it is because there are no forces, Coriolis or otherwise, acting on it - wind and storms excepted). That then suggests that trees which co-rotate with the earth, are unaffected by the Coriolis Effect. But this then leads to a variety of conundrums which include making Polaris an exception to all the other stars, as seen from our rotating frame of reference, as well as making the geostationary satellites exceptions to all the other satellites that orbit the earth. It also then means that a ball moving in a straight line at uniform speed across a rotating turntable, crossing the rim on to the turntable at the same point from which it leaves it, without going through the turntable's center, suddenly, for an instant, not subject to the Coriolis Effect, even though it is one smooth continuous movement. I have absolutely no objection to this, but the convention and its curious consequences must be acknowledged. Science, and physics in particular, 'abhor' such arbitrary exceptions. (In the physics of gravitation, even a mote of dust exerts a gravitational force, even though it is negligible in almost every practical application, and can consequently be ignored.) The only place in the article where zero velocity on the earth's surface is treated as a point in a continuum of values is when the "Eötvös effect" is described.

Of course the tree is subject to a Coriolis Force, but because it is anchored to the rotating frame of reference, it does not move; whereas the air around it is affected by Coriolis Forces, and moves accordingly. If we replace the tree with a Foucault pendulum it immediately becomes apparent that there is a Coriolis Force acting on that anchored spot. Cruithne9 (talk) 16:33, 18 January 2016 (UTC)

Polaris and Geostationary satellites are exceptions in the rotating refernce frame of the Earth because both happen to be stationary in that frame. There are no exceptions in the physics. In a frame rotating about a different axis there could be a Coriolis force on both. I think it is important, as you said, to make clear that the Coriolis force on an object depends entirely on what reference frame you use. Because the Earth's rotating frame is particularly convenient for some purposes, like meteoroloigy, it is often incorrectly thought that the Coriolis force has something to do with the physical rotation of the Earth. Martin Hogbin (talk) 14:58, 19 January 2016 (UTC)

Hi . I think this would be a brilliant idea. In the article under the new name, it could be explained that in addition to objects that do not move relative to the rotating frame of reference having no Coriolis Force acting on them, objects whose trajectories are along great circles on the rotating earth also have no Coriolis Force acting on them, because they would be moving in straight lines as seen from our (earth-bound) rotating frame of reference. In effect this means that stars on the celestial equator, and satellites orbiting the earth in the plane of the equator, though moving, have no Coriolis Force acting on them. It could be mentioned that as one considers stars closer and closer to Polaris the Coriolis Force acting on them approaches zero, becoming zero at the celestial pole. Similarly stars close to the celestial equator also have Coriolis Forces acting on them that approach zero the closer they are to the celestial equator. I think an explanation of this sort would remove the temptation to think of these instances as "exceptions", but rather as points in a continuum of values, which, in this case does not have negative values (or are they theoretically possible, for certain types of motion seen from earth?) Cruithne9 (talk) 05:22, 21 January 2016 (UTC)

This will not be easy, I think the subject has been discussed before.
The reason I would like to make the move is that the Coriolis force is a very well defined concept of general applicability. The effect is rather less well defined.
For example, this article starts with a sentence saying, 'In physics, the Coriolis effect is the apparent deflection of moving objects when the motion is described relative to a rotating reference frame'. Problems that I see with this are:
It is inherrently vage because it suggests no way of putting numbers to the 'effect'.
There may not actually be a deflection, if the object is constrained, for example.
If there is a deflection, it is real deflection, not an apparent one when measured in the moving frame
As soon as the article starts to make any serious inroads into the subject it moves on to talk about the Coriolis force. Martin Hogbin (talk) 10:32, 21 January 2016 (UTC)

## Proposed move to 'Coriolis Force'.

I propose moving this article to 'Coriolis force'. Martin Hogbin (talk) 17:15, 21 January 2016 (UTC)

• Support per Google Scholar "coriolis force" (53,700) vs Google Scholar "coriolis effect" (15,000) and Google Books "coriolis force" (91.700) vs Google Books "coriolis effect" (35.400). - DVdm (talk) 19:06, 21 January 2016 (UTC)
• Support (as proposer above). The term 'Coriolis force' is much more clearly defined than 'Coriolis effect'. 'Coriolis effect' seems to refer only to effects caused by the Earth's rotation. These are definitions from the first few Google links: 'The Coriolis effect causes a deflection in global wind patterns', 'Offers a fairly simple explanation of why objects curve on the Earth when they should move straight', 'Learn about the Coriolis effect, which appears to deflect items moving on or above the earth's surface based on the rotation of the earth. Martin Hogbin (talk) 16:07, 22 January 2016 (UTC)
• Support - while the term "Coriolis effect" is more probably more common in meteorological literature, where as pointed out above it is almost exclusive in the context of earth's rotation. However in the more general physics literature, "Coriolis force" is more common. I favor going with the broader and more general article title. --FyzixFighter (talk) 15:08, 23 January 2016 (UTC)
• Support I strongly support this proposal as it will eliminate a considerable amount of confusion on this topic. But may I put in a request that the new article is not confined to a discussion of objects moving across the surface of the earth, or turn tables in a laboratory, but that due consideration is also given to the apparent motion of the "fixed stars", and orbiting earth satellites (which in the present article are only discussed in terms of the curvature of great circles on Mercator Projection maps - nothing to do with Coriolis forces or even "effects"). The earth's orbit around the sun is also a rotating frame of reference and therefore a source of Coriolis Forces. Cruithne9 (talk) 07:12, 24 January 2016 (UTC)
No problem, provided anything you like to add is properly sourced. Only if the established literature refers to Coriolis force in a particular context, we can mention that context here. Otherwise we cannot have it, even if it stares us in the face, so to speak. In other words, be well aware of wp:original research, and specially WP:SYNTHESIS. DVdm (talk) 09:55, 24 January 2016 (UTC)
In that case, it might be worth mentioning that effect X which appears to be a genuine instance of a Coriolis Force acting on an object Y, is nowhere, in the astronomical or physical science literature, referred to as such. This information about the Coriolis Force is worth knowing and being informed about. Cruithne9 (talk) 10:16, 24 January 2016 (UTC)
Perhaps, but, again for the same reason we can only mention that "something is not mentioned in the literature", provided that this is mentioned in the literature itself. - DVdm (talk) 10:23, 24 January 2016 (UTC)
I was going to add that the problem could be stated in the positive: that Coriolis Forces are calculated and used almost exclusively in the following contexts..... In all other cases it is generally considered simpler and more convenient to use an inertial frame of reference, even though the observations are being made from a rotational frame of reference. But I suppose this too would have had to have been said before in an authoritative text book or review article. Pity, but understandable. Cruithne9 (talk) 10:36, 24 January 2016 (UTC)

### Consensus to move

Anyone know how to do this? I tried but could not because of the existing (redirected to here) article at Coriolis force. Martin Hogbin (talk) 17:33, 24 January 2016 (UTC)

The redirected page must be deleted first. See WP:RM#TR. I made the request. When the redirected page is gone, the move can be done. - DVdm (talk) 18:15, 24 January 2016 (UTC)

Done Thirteen subpages, mostly archived talk pages, have also been moved. --Malcolmxl5 (talk) 19:03, 24 January 2016 (UTC)

I see that you also created Coriolis effect and redirect to here. Thanks! - DVdm (talk) 20:21, 24 January 2016 (UTC)
Thanks Malcolmxl5 and DVdm. I have changed the first sentence of the lead to match the new title. Martin Hogbin (talk) 21:23, 24 January 2016 (UTC)
I have changed the article now to reflect the new title so generally now we use 'force' rather than 'effect' although 'effect' is stll appropriate in some cases. Martin Hogbin (talk) 21:38, 24 January 2016 (UTC)

## What now?

The move to Coriolis force is now complete. What changes, if any, do we now want to make? Martin Hogbin (talk) 11:50, 25 January 2016 (UTC)

Whatever that was discussed above, but properly backed by sources, without wp:ORing or wp:SYNTHing . - DVdm (talk) 13:13, 25 January 2016 (UTC)
Cruithne9, I am finding it hard to understand the point that you are making above. Could you give an example of the text that you would like to add to the article. Martin Hogbin (talk) 17:08, 25 January 2016 (UTC)

Thank you for inviting me to comment. I stated my original problem with the article at the beginning of the Misconception by omission section. I am concerned that the text deals with events only on the surface of the earth, and with high school laboratory examples of rotating turn tables and spinning bowls of water. There is no mention of motion beyond the earth’s surface observed from our rotating frame of reference either in the form of the rotating earth or the orbiting earth. In the course of the ensuing discussion Martin Hogbin stated: “The fact that the same thing may have a different motion when viewed from a different frame of reference is, of course, true but not the main point of this article which about one particular aspect of rotating frames.” My point is that a general article entitled “Coriolis Force” cannot confine itself to “one particular aspect of rotating frames”. This is equivalent to an article entitled "Gravity", only describing the physics of gravity on earth. The apparent spinning of the stars round Polaris when seen from our rotating frame of reference on earth is not mentioned in the article even though DVdm states this to be a simple application of Coriolis Forces. The apparently curved trajectories of the artificial satellites across the earth’s surface is described inaccurately and totally inappropriately as being examples of great circles drawn on Mercator projections of the earth. (In fact they do not trace great circles across the earth’s surface, but tracks that are influenced by the earth’s rotation, i.e. Coriolis Forces. The Mercator projection is a red herring in this context.)

Cruithne and Earth seem to follow each other because of a 1:1 orbital resonance.
Cruithne appears to make a bean-shaped orbit from the perspective of Earth.

Obviously the Coriolis Forces acting on objects that are co-rotating with the earth, or are opposite the poles, are zero. This is not the same as saying that saying there are "no Coriolis Forces acting on these objects", which leads one to suspect that Polaris and the geostationary satellites are exceptions to the rules of the Coriolis Effect. But Martin Hogbin makes it quite clear (and I agree) that “The Coriolis force is clearly defined as the force acting on an object when considered in a rotating frame. The physics is quite clear and there are no exceptions (my italics) that need special conventions.” In other words, zero force is just part of a continuum of values (from positive through to negative) that can be obtained for Coriolis Forces acting on different objects – or, state differently: the closer a fixed star is to Polaris the smaller the Coriolis force acting on it (as seen from earth), until the value becomes zero at the celestial poles. Similarly, the closer a star is to the celestial equator the more the Coriolis Force acting on it approaches zero (stars and artificial satellites in the plane of the equator seem to travel in straight lines along a great circle). As one crosses the equator the sign of the Force changes and stars start rotating clockwise, whereas, in the northern hemisphere, they turn counter-clockwise. It is this sort of explanation that turns the article from an exercise in pure math, into an informative encyclopedic entry.

The earth orbiting the sun is another rotating frame of reference from which the objects moving in the solar system can be viewed, and this too causes Coriolis forces. But as DVdm points out this “is not a problem, provided anything you like to add is properly sourced…. Otherwise we cannot have it, even if it stares us in the face, so to speak. In other words, be well aware of wp:original research, and specially WP:SYNTHESIS.” But it is clear from the diagram on the right, taken from the 3753 Cruithne article, that the authors of that article and the diagram are very obviously thinking in Coriolis terms, though without using the word “Coriolis”. The whole point about the discussion of Cruithne’s bean-shaped orbit and it being dubbed (incorrectly) earth’s “second moon” is that it is an exercise in pure, unashamed Coriolis physics. That is reason and justification enough to include it into the Coriolis article. It is a very simple, uncomplicated application of the general principle, which has no exceptions referred to by Martin Hogbin. It is not original research, or an original idea, and therefore not subject to a very narrow interpretation of wp:original research, and WP:SYNTHESIS. Cruithne9 (talk) 06:58, 27 January 2016 (UTC)

Re "But it is clear from the diagram... ...though without using the word “Coriolis”": well, that is precisely what wp:OR and wp:SYNTH are about. We really cannot take that. - DVdm (talk) 12:29, 27 January 2016 (UTC)
I agree with DVdm on this - you have to understand that there have been a number of proponents of fringe science on this and related pages, and a close reading of WP:OR and WP:SYNTH is the quickest way to keep those editors in check without the talk page discussions devolving into long-winded physics lessons. Some of your comments above actually, imo, show why this is necessary. Stars that lie on the celestial equator do experience a non-zero Coriolis force. They have a non-zero velocity in the earth's frame and that velocity is not parallel to the axis of rotation of the frame, therefore the Coriolis force is non-zero. And there ends the physics lesson - maybe I'm wrong though and maybe I'm missing something in the math or mechanics, but the best way to rebut that reason for excluding that type of example is to provide a reliable source. The example of 3753 Cruithne is different matter, complicated by the fact that the kidney bean shaped orbit also drifts around the earth's orbit - it's not just stuck at the L4/5 points. I think that the better example, which is relevant to this page, addresses your concern, and can be properly sourced, is the stability of Lagrangian points. Perhaps take a broader view than just that particular asteroid and look at the more general case and see what you can write up. --FyzixFighter (talk) 13:09, 27 January 2016 (UTC)
Yes, for example from this[1]

References

1. ^ Guéry-Odelin, David; Lahaye, Thierry (2010). Classical Mechanics Illustrated by Modern Physics: 42 Problems with Solutions (illustrated ed.). World Scientific. p. 223. ISBN 978-1-84816-480-2., Extract of page 223
More to pick from Google Books. - DVdm (talk) 13:36, 27 January 2016 (UTC)
Cruithne9, I cannot understand what it is that you wnat to change in this article. Could you propose a change of wording for discusion.
I think we all agree that in a reference frame rotating with the Earth round the sun, Cruinthe, along with all other objects will, in general, be subject to the centrifugal and Coriolis forces. The orbit of Cruinth could be analysed in such a frame, as could the orbits of all the planets but I do not know of any advantage, except as an academic exercise, in doing so. I do not think that your two animations are particularly instructive regarding the Coriolis force.
I, for one, do not understand what your point is. By all means make a change to the article to show what you want. It is likely that it will quickly be reverted but then at least we would know what your point is. Martin Hogbin (talk) 15:34, 27 January 2016 (UTC)

I was too hasty with my example of the stars on the celestial equator - I realized my mistake after I had recorded it on this page. I withdraw from this discussion and any attempt to edit the article. I do not have the resources at my disposal to contribute anything meaningful to either. I thank you all for your patience in trying to discuss this fascinating topic with me. Cruithne9 (talk) 18:51, 27 January 2016 (UTC)

## British English

The English used in this article was mixed Brit US. I have changed it all to British as that is how it started out. SeeWP:Engvar. Martin Hogbin (talk) 20:25, 29 January 2016 (UTC)

## Lowercase Phi

Hi readers. Can someone explain why phi appears in two different cases in this section? As a non-scientist, I had to look up the Greek alphabet to refresh myself on the difference between upper- and lowercase phi. As a shameless editorializer, I think this section intentionally alienates non-specialized readers and attempts to subjugate the non-elite to a technocentric, fascistic point of view of the role science plays in everyday life. It reaffirms that, if you can't understand a difficult concept in the terms prescribed by post-secondary education at elite universities, you don't deserve to learn about it. I think the people who contributed to this portion of the article are capital-B bad humans for that reason. Just my two cents. But someone change the case of the Greek letters though seriously. — Preceding unsigned comment added by 2602:306:CCA6:67E0:993D:7412:9FA8:E4CF (talk) 03:48, 6 March 2016 (UTC)

Please put new talk page messages at the bottom of talk pages and sign your messages with four tildes (~~~~). Thanks.
I don't see any uppercase ${\displaystyle \Phi }$ or Φ in the article, only ${\displaystyle \varphi }$ in the equations and the corresponding φ in the text. - DVdm (talk) 09:46, 6 March 2016 (UTC)

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## Trimming the examples

Currently, we have a number of examples in this article. In fact, some IMO would cross the line into textbook-like example problems (the editor who added these in often was criticized by others, myself included, for crossing the textbook line). The example sections we have are:

• Cannon on turntable
• Tossed ball on a rotating carousel
• Bounced ball

I'd like to trim it down to a single simple case, but would like to hear others' thoughts. If we were to trim it to one example, which should it be? --FyzixFighter (talk) 22:20, 9 September 2016 (UTC)

Comment - I don´t have a set stance in this matter, I see the problem as a trade-off, in my personal opinion, I think that having three examples is not too much of a problem in this case. The subject of the article is not an easy concept to grasp for most readers, so having more than one example (like the second and third) might help readers not familiar with Coriolis in gaining an intuitive understanding. --Crystallizedcarbon (talk) 16:55, 10 September 2016 (UTC)

## Clarifications regarding Coriolis force

First of all, at least in Newtonian physics, all forces arise from corrections to velocity; a force serves one function only, that is, to describe any discrepancy or 'acceleration' that deviates from linear motion. It doesn't matter whether a force is labeled 'real', 'fictitious', 'geometric', or 'physical', as long as the accelerations are consistent from description to description. There are ways to not 'feel' a physical force, such as when falling in orbit (although the experience may feel unnatural because we're so used to having the Earth 'below' us preventing any acceleration). One may argue that 'fictitious' forces arise to compensate for non-inertial/non-linear motion of an observer's frame; but there is no special accelerating or non-accelerating frame, just as there is no special moving or at-rest frame. An observer in a rotating frame may well argue that a 'non-rotating' frame is a special case in which the centrifugal force becomes zero due to the relative rotation, from his or her perspective, of the 'non-rotating' frame.

Second, it is clear from the math that the Coriolis term is distinct from the centripetal/centrifugal term. Therefore, Coriolis force describes a very specific type of acceleration, namely, one that arises when a target is in motion even when observed in a frame that is rotating at an angular velocity Ω. This is why the circumpolar motion of the stars, as viewed from a fixed location and orientation on the surface of the Earth, is typically not explained using Coriolis acceleration, because it is typically already taken into account by the centripetal/centrifugal acceleration. There is typically zero velocity in the rotating frame of the stars that is set up, so the math would reflect that the Coriolis term is zero, unlike the centripetal/centrifugal term. Viewed from a fixed orientation and location on Earth, the stars are moving under centripetal acceleration with no velocity in the rotating frame. Viewed from a frame co-rotating with the stars, however, the 'stationary' stars will have a velocity as seen from Earth and thus generate a Coriolis term that is twice as large as an opposing centripetal/centrifugal acceleartion. After summing, everything comes out the same in terms of acceleration, even though the attribution may go to different 'forces'. From our point of view, the motion of 3753 Cruithne seems to require non-inertial explanations, but whether they invovle Coriolis acceleration specifically, although likely, should be calculated, specifying the frames being used, and not just assumed.

Third, there may be a point of confusion when applying any velocity that moves tangentially or circumferentially in the plane of rotation, as opposed to radially. Sometimes Ω is pegged to another value (eg the rotation of the Earth), and any discrepancy between it and any circumferential velocity is factored into the v in the 2Ω(cross)v Coriolis term (v=0 in the typical treatment of circumpolar stars). Sometimes Ω is derived from the tangential velocity directly, and any change to it updates the Ω in the Ω(cross)Ω(cross)r centripetal/centrifugal term as well as the Ω in the 2Ω(cross)v Coriolis term, but you'd also have to transform v into its value as observed under the updated Ω, not the original Ω. Otherwise, things won't be applied correctly per equation and cancel out to give the same result regardless of your approach. This is also why the Eötvös effect is sometimes considered Coriolis but other times centripetal/centrifugal. For those of you more familiar with the coordinate transformation derivation from, say, x and y into r and θ, that would match the second approach above, which may be easier to remember, since any circumferential velocity goes into the centripetal/centrifugal term, whereas only radial velocity contributes to the Coriolis term. I think FyzixFighter gave the nice formula ${\displaystyle {\ddot {\vec {r}}}=({\ddot {r}}-r{\dot {\theta }}^{2}){\hat {r}}+(2{\dot {r}}{\dot {\theta }}+r{\ddot {\theta }}){\hat {\theta }}}$ previously.

Hopefully, this clarifies things a little bit for anyone who's become more confused after reading the earlier Talk page discussions or is interested in improving the article further.

204.89.11.242 (talk) 02:02, 13 October 2016 (UTC)

## Simple Coriolis force

There's a very simple and very observable display. We have all seen it, whether we have paid attention to it or not. Watch the water in the bathtub while it drains. In the Northern hemisphere, it will "whirlpool" (spin) counter-clockwise. In the Southern Hemisphere, this will be clockwise. — Preceding unsigned comment added by 50.141.41.219 (talk) 03:50, 1 April 2017 (UTC)

You can read the article to find out how and why it doesn't. - DVdm (talk) 09:39, 1 April 2017 (UTC)