PHY 121 Arizona State University

Spring 2000

(The above images are courtesy of the Earth and Moon Viewer and Microsoft Clipart)


What Makes Tides

    Tides are the daily rise and fall of the sea's edge and are caused by the gravitational forces between the Earth, Moon, and Sun.  The Moon exerts a force on the Earth just as the Earth exerts a force on the Moon: F = (G*M*m)/r^2 = 1.98 x 10^20 Newtons.  The Moon attracts water on the near side of the Earth more strongly than on the far side when rotating, which means that the Moon attracts the near side water more than the center of mass of the Earth.  This leads to a bulge in the water distribution toward the Moon.  The Moon also attracts the water on the far side of the Earth less than it attracts the center of mass, leaving behind a second bulge on the far side.  These two bulges result in two high tides per day.  Furthermore, between each of these high tides there also exists a low tide. There are usually two high and two low tides occurring each 24 hours and 50 minutes.  Specifically, the Moon moves about 1/28'th of the way around the Earth daily.  This is 12.86 degrees or 51 minutes, which is in addition to the 24 hours needed for the Earth to make one rotation.  The Sun also contributes to tide formation, but its effect is less than the Moon's.  The gravitational force of the Sun is larger than the Moon's, about 175 times larger (3.465 x 10^22 Newtons).  The difference in the Sun's gravitational force from one side of the Earth to the other is smaller due to the fact that the Earth's radius is much smaller than the Earth-Sun distance.  This simply means that the actual value of the force of gravity does not matter, but the derivative with respect to the radius does (d/dr(F_g) = (-2*G*M*m)/r^3).  These results show the effect of the Moon is a little more than twice as big as the effect of the Sun: Ratio = Moon-Earth system / Sun-Earth system = -1.032 x 10^12 Newtons / -4.736 x 10^11 Newtons = 2.18.  Moreover, tides also occur in large lakes, the atmosphere, and within the solid crust of the Earth, acted upon by these same gravitational forces of the Moon and Sun (Physics for Scientists and Engineers 332-335).

The History of Tidal Analysis and Prediction

    The study of tidal phenomena was undertaken by notable individuals from the past.  Most importantly, Sir William Thomson (Lord Kelvin) devised the method of reduction of tides by harmonic analysis in 1867.  His system was based on the fact that any periodic motion or oscillation can always be resolved into the sum of a series of simple harmonic motions.  This theory was build upon several other important developments beforehand.  For example, Eudoxas (356 B.C.) explained the irregular motions of the planets by combinations of uniform circular motions.  Also, in the early nineteenth century, Laplace recognized the "existence of partial tides that might be expressed by the cosine of an angle increasing uniformly with the time, and also applied the essential principles of the harmonic analysis to the reduction of high and low waters."  However, Sir William Thomson is the one associated with taking this information and moving it into a practical realm.  Thus, as an expert, he prepared the British Association for the Advancement of Science on extension, improvement, and harmonic analysis of tidal observations.

    The methods for the prediction of the tides are defined as either harmonic or non-harmonic. By the harmonic method "the elementary constituent tides, represented by harmonic constants, are combined in to a composite tide. By the non-harmonic method the predictions are made by applying to the times of the moon's transits and to the mean height of the tide systems of differences to take account of average conditions and various inequalities due to changes in the phase of the moon and in the declination and parallax of the moon and sun."

    Until 1984, all predictions were made by curves constructed from the results of tide observations at the different ports.  From 1885 to 1911, the predictions were generally made by the Ferrel Tide-Predicting machine and from 1912 to 1965 by the Coast and Geodetic Survey Tide-Predicting Machine No. 2.  In 1966, the introduction of digital electronic computers changed this.  Initially these computers were large main-frame computers, but these were replaced quickly.  In the 1980s, they were replaced by the booming industry of desktop computing. These are now used exclusively by the National Ocean Service in making predictions for the standard ports and at other locations were observational data exists (National Oceanic & Atmospheric Administration).

Spring and Neap Tides

    During a new moon there is more gravitational pull than usual because the gravitational pull of the moon and the sun are combined, causing especially high tides and low tides.  These are referred to as spring tides.  The same thing occurs during a full moon, when the sun and moon line up on opposite sides of the Earth.  Spring tides have ranges of about 2.5 meters and are about 20% higher or lower than average (Fitzgerald Marine Reserve).

    When the moon and sun are at a ninety degree angle to each other, or when the moon is in the quarter phase, the gravitational pulls cancel out, producing a smaller difference between high and low tide.  This is known as a neap tide.  Neap tides have ranges of about 1.7 meters and are about 20% higher or lower than average.  The below diagram shows how spring and neap tides develop.

(The above picture is from 'The Physical Environment')

To see an animation of spring and neap tides click here.

Tides Around the World

Tidal changes differ across the world.  Near the equator, there is very little change between high and low tide because a large volume of water is spread out over a wide range.  

The highest tides in the world are at the Bay of Fundy in Nova Scotia.  The bay is very narrow, so water rushing in from the ocean can rise and fall up to 20 meters a day.  The picture below is from this particular location.


This picture comes from the Minas Basin, the eastern extremity of the Bay of Fundy, where the average tide range is 12 meters and can reach 16 meters. (Courtesy of

Best Places to See High Tides:

(This picture is courtesy of



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