How do bulges in the earths surface form

Details and complications. The oceans don't cover the entire earth, but "slosh around" daily within the confines of their shores. Timing of the ocean tidal bulges even at mid-ocean can depart considerably from the idealized tides we have described. Reflections from shores can set up interference patterns farther out in the ocean. Coastal tides have considrable local variations due to difference of shoreline slope, and ocean currents.

But the driving force for all of these complications is still those two "daily" lunar tides 12 hours 25 minutes apart , which we have explained above, combined with the two much smaller daily tides 12 hours apart due to the gravitational field of the sun. More misleading textbook illustrations. An oceanography textbook has this diagram that at least shows centrifugal forces of equal size.

One is tempted to think "This book has it right! Then on the very next page we see this diagram in which the author identifies one tide as being from gravitation, the other from inertia.

Comparing the two pictures, one sees that they contradict. The one that shows forces clearly suggests that the moon's gravitational force is responsible for both tides. Unfortunately, like so many other books, this book fails to tell the student the origin of these centrifugal forces, and fails to emphasize that they are not "real" forces, but only a useful device to do problems in rotating coordinate systems. Here the chickens come home to roost. Misunderstanding of centrifugal effects originates in some elementary-level physics textbooks.

Nowhere does this book even suggest that rotating coordinate systems are being assumed. Other lunar misconceptions. We mentioned frictional drag of water on the ocean floor. These forces dissipate rotational energy of the earth.

Similar drag effects act within the solid crust of the earth as well, since it is stressed by tidal forces. This causes the tidal bulges to arrive a little "early" compared to the time of the moon's crossing the observer's meridian.

This diagram illustrates the effect but exaggerates its size. The earth's rotation and the moon's revolution are both counter-clockwise as seen from above the N pole.

The earth rotates faster than the moon revolves around the earth, so the earth drags the high tide bulge "ahead" of the moon. Therefore, as we move with respect to both tidal bulge and moon and faster than both , the moon crosses our meridian nearly 12 minutes before we experience the highest tide. In fact, the angle is only 2.

We doubt that even the most avid surfer would consider this of great significance. Even in mid-ocean, there are variations due to resonance. The moon's gravitational attraction exerts a retarding torque on those tidal bulges.

This is in a direction to reduce the earth's angular momentum and gradually slow the earth's rotation. The bulges also exert an equal size and oppositely directed torque on the moon, gradually increasing its angular momentum.

The angular momentum of the earth-moon system is conserved. Push-Pull language. Often textbooks say something like this: The moon's pull on objects on the near side of the earth is greater than on the center of the earth. Its pull on objects at the far side of the earth is smaller still.

This causes the near ocean to accelerate toward the moon most, the center of the earth less, and the far ocean still less. The result is that the earth elongates slightly along the earth-moon line. This conjures images of motion of parts of the earth moving continually toward the moon. But in the actual situation, this distance doesn't change appreciably during a lunar cycle.

This misleading "explanation" is often found in lower-level physics texts that try to use "colloquial" language to describe things too complex for such imprecise language. Some of these books even say, as if it were a definition: "A force is a push or a pull". To the student mind this implies motion. These textbooks do consider forces acting on non-moving objects, but the harm has already been done by the earlier statement that the student memorizes for exams. This "differential pulling" language exists in textbooks in several forms.

Sometimes the phrase "is pulled more" or even "falls toward the moon faster" is used. All begin with the assumption that earth and moon are in a state of continually falling toward each other, and that's a correct statement, though not likely to be clearly understood by students. But if this "falling" is continual, then the "pulling" refered to in the example above is continual also. Then these texts bring in acceleration, and say that the lunar side of the earth accelerates most, the opposite side least.

So, the student reasonably infers that the acceleration difference is continual. Now if two bodies move in the same direction, the one with greater velocity will move more and more ahead of the other one. It's gain is even greater if the lead one has greater acceleration.

If this "explanatory" language were to be believed as applying to the earth, the earth would continually stretch until it is torn apart.

This explanation goes astray because it doesn't acknowledge 1 the earth's own gravitational field acting to preserve the earth's approximately "round" profile and 2 tensile forces in the body of the earth.

Also, it uses "force" language, without adhering to the fundamental principle of doing force problems: You must account for and include all forces acting on the body in question. And, we suspect, the authors of these explanations may themselves have been misled by a misunderstanding of rotation and centripetal and centrifugal forces. Some dirty little secrets textbooks fail to tell you. The "tidal trivia" summary below puts things into perspective. The so-called equatorial bulge due to the earth's axial rotation lifts the equator about 23 kilometer.

The moon's gravity gradient lifts water mid-ocean where the ocean is deep no more than 1 meter, that's only 1. Why do we fuss about this? Because over an ocean of large area, that represents a very large volume of water. Also, it's the driving mechanism that controls the periods of the much larger tides at shorelines. This effect is simply too small to account for the tidal bulges in ocean water.

The tangential components tangent to earth's surface exert tractive forces on large bodies of water directed toward the tidal bulges. These are also proportional to the inverse cube of distance from the moon. This is the dominant reason for tides in large bodies of water.

The reason water can rise as much as 1 meter in mid-ocean is primarily because the ocean is so large that water can relax into the tidal bulge. The tidal rise in Lake Michigan is smaller because the lake's volume and surface area are much smaller. The tide in Lake Michigan would be about 5 cm [Sawicki].

Smaller still is the tide in your backyard swimming pool. It's unmeasurably small. Don't even bother with the tide in your bathtub or your morning cup of coffee. There's tides in all of these, but the land, table and cup all rise, and the coffee rises with it, all by nearly the same amount, perhaps a fraction of a meter when the moon is high in the sky.

But you don't notice anything unusual. Since the earth's axial rotation affects only the "baseline" level of land and water, against which tidal variations are referenced, a discussion of tides does not need to mention centrifugal forces. That only invites confusion and misconceptions. Centrifugal forces are not tidal tide-raising forces. In a rotating coordinate system the centrifugal forces of moon on earth are of constant in size and direction over the volume of the earth at any time, therefore they can not raise tides.

The folks who do tidal measurements don't get into the physics theory much. Tide tables are constructed from past measurements and computer modeling that does not usually take underlying theory into account.

It is much like the pretty weather maps you see on TV, computer generated without any detailed use of all the physical details. The task is just too complicated for even our largest computers, and the data fed into them is far from the quality and completeness we'd need. You might think that with global positioning satellites we'd know the measurements of water and land tides accurate to a fraction of a smidgen.

You'd be wrong. If you check the research papers of the folks who do this, you see that they are still dissatisfied with the reliability of such data even over small geographic regions. We can map the surface of land to less than a meter this way, and get relative height measurements equally well, but absolute height measurements relative to the center of the earth are much poorer.

Many of the numbers you see tossed about in elementary level books are copied from other elementary level books, without independent checking and without inquiring whether they were guestimates from theory or from actual measurement. You may also think that modern computers have made tide prediction more accurate. In fact, the analog mechanical computers devised for this purpose in the 19th century did nearly as good a job, even if they have ended up in science museums.

Tidal trivia. Amplitude of gravitational tides in deep mid-ocean: about 1 meter. Shoreline tides can be more than 10 times as large as in mid-ocean. Amplitude of tides in the earth's solid crust: about 20 cm. The gravitational force of sun on earth is times as large as the force of moon on earth. Tidal stretch of human body standing changes its height by the fraction 10 , an amount times smaller than the diameter of an atom.

By comparison, the stress produced by the body's own weight causes a fractional change in body height of 10 Angular velocity of moon's revolution around earth: 2. Earth's mean radius 6, km. Earth polar diameter, 12, km. Earth's equatorial diameter: 12, km. Difference between earth's polar and equatorial diameters: 46 km. Difference between earth's polar and equatorial radii: 23 km, or 0.

Thickness of earth's atmosphere, about km. Final Exam. These pictures are from various internet sources. Find the misleading features of each.

If the Earth were not rotating, and the Moon stopped revolving around it, and they were "falling" toward each other, would the Earth have tidal bulges? If not, why? If so, would they be significantly different from those we have now? In what way? Here's an example of how untrustworthy textbooks are. This is from a college level introductory college physics text. From this explanation previously given it would seem that the tides should be highest at a given location when the moon is directly overhead or somewhat more than 12 hours later.

In fact, high tide always occurs when the moon is near the horizon. The reason is that the friction of the rotating earth tends to hold the tides back so that they always occur several hours later than we should expect.

Find the serious error s in this short paragraph. If not, why not? If so, how would they compare with the tides we now have? If the tides may be thought of as a "stretching" of the earth along the axis joining the earth and moon, then why are all materials not stretched equally, resulting in no ocean tides?

If elastic strain is the reason for tides, then since the elastic modulus of water is so much smaller than rock, wouldn't you expect that rock would "stretch" more than water, causing water levels to drop when the moon is overhead? When we say that the tide in deep mid-ocean is about half a meter, what is this measured with respect to? If the earth were in a rotating, uniform parallel field lines, constant strength external gravitational field don't ask how we might achieve this , would we have tides at the period of earth's rotation?

Would we have tides at the half-period of earth's rotation? If a huge steel tank were filled with water, and a sensitive pressure gauge were put inside, would the pressure gauge register tidal fluctuations with a period of about Your tax dollars at work to propagate misconceptions.

Gravity and inertia are opposing forces acting on the earth's oceans, creating tidal bulges on opposite sides of the planet. On the "near" side of the earth the side facing the moon , the gravitational force of the moon pulls the ocean's waters toward it, creating one bulge. On the far side of the earth, inertial forces dominate, creating a second bulge. Identify the specific misconceptions in the picture and the text.

This picture, commonly seen in elementary textbooks, shows the lunar gravitational force large on the side of earth nearest the moon, smaller at the earth center, and even smaller on the side opposite the moon. What's misleading about this? A textbook says "Tides are caused by the moon pulling on the ocean waters more strongly on the side nearest to the moon. Why doesn't this happen? Tidal Catastrophe. If the moon were covered with an ocean, would it have tidal bulges?

Exam answers. The first picture shows the actual tides being the sum of two tidal bulges, implying that those bulges have independent origins. We have shown this is not so. The second picture speaks of "rotational force", which may mean centrifugal force, but we can't be sure. We also have no clue whether "gravity" means the moon's gravitational attraction, the earth's gravity, or both together. The tidal bulges in this situation would be essentially the same size as those we have now in mid-ocean.

Of course, they wouldn't move across the earth's surface, so the complications due to oceans sloshing around within their shorelines would be absent. However, coastal and resonance effects modify this greatly, and there are places where the tides are highest when the moon is at the horizon, but this is not typical.

Blackwood uses the word "always", which is clearly inappropriate. It is not one point. Each point on earth revolves around its own center of revolution.

Only the center of the earth revolves around the barycenter. And if you made a map of the centripetal forces everywhere on earth, they would all be parallel to the earth-moon line. Arons' answer: "The tide-generating effects now have the same magnitude and the same symmetry as in the existing situation. It's useful to think of this using the superposition principle. A moon of half size produces half as much tidal force.

Where the present tides on opposite sides of the earth are slightly unequal, the tides due to two opposing half-size moons would be of equal size on opposite sides of the earth. Water has a high elastic modulus. It flows easily, but rock does not.

Water levels are affected by tractive forces the tangential component of the tidal force , which directed toward the tidal bulges. Textbooks don't tell you this, do they? The high tide level in shoreline water is usually measured from low tide or from the mean water level there.

Coastal tide levels are measured with respect to solid land not shifting sand on the shore. There would be no tides in a uniform field. A field gradient is required for a tide.

The elastic modulus of steel and water are different, so this would alter the water pressure as water and steel respond differently to tidal forces. Follow-up question: Would the water pressure inside be higher at high tide, or lower? The picture suggests that the near bulge is only due to gravitation, the other one only due to "inertial forces". The text speaks of "inertial forces", without saying that such a term has no meaning except in a non-inertial coordinate system.

The phrase "pulls the ocean waters toward it" implies "motion toward it". The moon exerts gravitational forces on the far side bulge not much smaller than on the near side, and if these forces are "pulling" toward the moon on the near side, they are also pulling toward the moon on the far side. No mention is made of that. The three arrows show gravitational forces due to the moon. No other forces are shown. This leaves the impression that these are the only forces responsible for the tides.

But, as we have shown, earth tides are due to the combination of gravitational force due to the moon, gravitational force due to the earth, and tensile forces in the material body of the earth. Does the picture represent how things are in an inertial frame? If so, then in view of the above observation, these can't be the only forces acting on the earth. So where are the other forces in the diagram, and what is their source? If so, then the centrifugal and Coriolis forces should be explicitly shown, for they must be included when doing problems in such a frame of reference.

Gravitational forces due to the moon, gravitational forces due to the earth, and tensile forces of materials are the only real forces acting on the material of the earth. These alone account for the tidal bulges. Rotation plays no role. The answer is simple: the net force due to the moon on the body of the earth is solely responsible for that.

We are here ignoring the sun. It must be so, for aside from the sun the moon's gravitational force is the only external force acting on the earth. Therefore they need not be included in the equation of motion of the body itself. I think what irks me about textbook treatments of tides is that they undo the good work we try to accomplish in introductory physics courses.

We emphasize correct applications of Newton's laws of motions. First we tell the students to identify the body in question, the body to which we will apply Newton's law. We stress that they must identify the forces on the body in question and only the real forces, due to bodies external to the body in question. We ask students to draw a "free-body" vector diagram showing all these forces that act on the body in question. One must not include forces acting on other bodies. If the net force on the body is non-zero, then it must accelerate.

This analysis, done in an inertial system, is adequate to understand the tidal forces, in fact that's the way Newton did it when he discussed tides. This is, of course, a joke.

However, as with so many absurd notions, this isn't easy to explain. Yes, there would be tides on a lunar ocean. In fact, there are land tide bulges on the moon. As you notice, these questions were designed deliberately to expose misconceptions arising from misleading textbook and website treatments. Abell, George O. Exploration of the Universe. Sixth Edition, Saunders, This textbook has a short non-calculus treatment that is better than those found in some other elementary Astronomy texts.

Clearly the authors thought this through themselves; they didn't simply copy material found elsewhere. Arons, Arnold B. Proposal for a noncalculus treatment of ocean tides without reference to fictitious forces and without recourse to a potential.

Common misconceptions are noted. Barger, Vernon D. Classical Mechanics, A Modern Perspective. McGraw-Hill, This is an advanced undergraduate level textbook, with clear discussion and illustration of tidal tide-generating forces.

This treatment does not use non-inertial coordinates. Second edition. Norton, Later editions appear often, but I don't keep up with them. This treatment has some original ways to explain the deformation of the earth and oceans without explicitly using calculus. At least it never mentions centrifugal force. Bolemon, Jay. Physics, an Introduction. Prentice-Hall, An original, thorough, and correct, treatment at a non-mathematical level. Butikov, Eugene I.

A dynamical picture of the oceanic tides. French, A. Newtonian Mechanics. An extensive discussion at an advanced undergraduate level. Morrison, David and Tobias Owen. The Planetary System. Addison-Wesley, A brief and correct description in less than a page, which tells no lies.

Sawicki, Mikolaj. The Physics Teacher, 37 , October , pp. A pdf revised version is available online. This article discusses a wide range of misconceptions about the tides. Swartz, Clifford E. Teaching Introductory Physics, a Sourcebook. American Institute of Physics, A brief discussion on pages Quincey, Paul. Addresses misleading press and media misrepresentations of tides. Tsantes, Emanuel.

A mathematical treatment that does not use rotating non-inertial coordinates and does not mention centrifugal force. Explicitly discusses role of elasticity of materials. The best books wisely omit even mentioning "centrifugal force" or tides. This is a huge book of over one thousand pages that weighs over seven pounds. In a brief paragraph "The Fictitious Centrifugal Force" and a footnote, he defines the two meanings of centrifugal force: 1 The real inward axial force that counters the centripetal force, and 2 a fictitious outward force in a rotating reference frame.

Then he cautions, "Because of this ambiguity in meaning the beginninng student is advised not to use the term. Web sites with reliable information. Listing a link here does not imply total endoresement of everything found there, nor of anything by the same author on other subjects.

But that should go without saying. Butikov, Eugene. We have treated only the case of tides on a spherically symmetric earth, either an earth with no continents covered with water , or a solid earth with no oceans. Once you include oceans and continents, resonance effects occur in ocean basins. This can be complex. Butikov's paper is an excellent treatment. A set of Java-applets that are beautiful dynamical illustrations of the tide-generating forces and for the wave with two bulges that these forces produce in the ocean.

See Sirtoli's paper for equivalent animations. Oceanic Tides: a Physical Explanation and Modeling. Computer tools in education, No. A somewhat simpler treatment of the subject of the previous paper. The Physics of the Oceanic Tides. A further development of the approach of Butikov's paper. Denker, John. A treatment of tides with a personal style and viewpoint, not just an echo of standard treatments.

Hicks, Steacy Dopp. Understanding Tides. A comprehensive and readable treatise on tides. Johnson, C. Mathematical Explanation of Tides. This treatment is more complete than mine. I would choose to express some things differently, but it makes the same important points as my document: 1 you don't need to talk about centrifugal force or use a rotating coordinate system to understand the tides, and 2 many textbook treatments are misleading or wrong.

Many textbooks mention that some places on earth experience only one tide per day, but few take the trouble to explain why. This website does. A comprehensive and readable treatise on tides, especially the worldwide coastal tidal effects. McDonald, Richard. Tidal Forces and their Effects in the Solar System. Over the rest of the globe gravity and inertia are in relative balance. Because water is fluid, the two bulges stay aligned with the moon as the Earth rotates Ross, D.

The sun also plays a major role, affecting the size and position of the two tidal bulges. The interaction of the forces generated by the moon and the sun can be quite complex.

As this is an introduction to the subject of tides and water levels we will focus most of our attention on the effects of the stronger celestial influence, the moon.

Tides and Water Levels Gravity, Inertia, and the Two Bulges The gravitational attraction between the Earth and the moon is strongest on the side of the Earth that happens to be facing the moon, simply because it is closer.

Welcome What are Tides?