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An applet for tidal force calculation

Illustration of sun and moons gravitational effect on the earth

"Tide goes in, tide goes out. Never a miscommunication... You can't explain that!" (Bill O'Reilly)

Not just can we explain it, but we can also calculate the tidal effects. Tides are the rising of Earth's ocean surface caused by the tidal forces of the Moon and the Sun acting on the oceans. Tides cause changes in the depth of the marine and estuarine water bodies and produce oscillating currents known as tidal streams, making prediction of tides important for coastal navigation. The strip of seashore that is submerged at high tide and exposed at low tide, the intertidal zone, is an important ecological product of ocean tides.

The changing tide produced at a given location is the result of the changing positions of the Moon and Sun relative to the Earth coupled with the effects of Earth rotation and the bathymetry of oceans, seas and estuaries. Sea level measured by coastal tide gauges may also be strongly affected by wind. More generally, tidal phenomena can occur in other systems besides the ocean, whenever a gravitational field that varies in time and space is present.

(description taken from Wikipedia)

Implementation details


This applet illustrates the tidal forces that are caused by sun and moon. Most people know that tides are caused by the gravitional pull of the moon. So the naive explanation would be assuming that all the water gets pulled to the side of earth closer to the moon. The problem is: It is'nt. If this were true there would be only a single bulge of water on the side of earth that is facing the moon whilst in reality there is a second bulge of water on the side of earth facing away from the moon. If you ever went to an ocean you will see the time between low tide and high tide is just 6 hours and not 12. This may appear strange at the first glance but it's actually quite easy to explain.

First of all: For our model forget about earths rotation! We don't need it for explaining the underlying principle of tidal forces so will ignore it. We are merely looking into a "revolution without rotation". It's common knowledge is that moon is orbiting the earth. A fact often ignored is that although moons mass is low compared to earths mass it is by no means negligable. Moon is pulling earth too so in reality both moon and earth are orbiting around the common center of mass which is different from the earths center. Different by not much, but still different. So what implication does this have? It brings another kind of force into the equation: The centrifugal force! You can easily calculate the common center of mass. The angular velocity of the moon is known so you know how fast the system earth-moon is spinning around it's center. You also know the diameter of the earth and consequently for every point on the earths surface there is a distinct centrifugal force pointing away from the common centre of mass. This may be the time for thanking Isaac Newton for inventing finding the law of gravity since without it you would be shot right into the sky. So taking the law of gravity you can compute the gravitaional pull of moon for every point of the earths surface and of course you can calculate the much larger gravitational pull of earth itself. By adding all three forces you will get a resulting force vector. This is the vector illustrated in this applet. This is the force driving the water from one side of the earth to the other The next logical extension is adding the sun to the system. Since the sun is much heavier than the earth you can neglect the gravitational pull of earth on it. This reduces the problem to just adding the gravitational force of the sun to our forces and we are done.

Thats what this simulation does but i'd like to point out that for a more precise calculation of tidal effects you need to include the following:

But thats beyond the scope of this article...

java plugin is missing

Download and Useage


Download icon  Download jar file
Download icon  Download source code (requires Netbeans)

In order to use the applet add the following lines to your html code:

  <object classid="java:tides.class" type="application/x-java-applet" width="600" height="600">
    <param name="archive" value="JTides.jar"/>
    <param name="code" value="tides.class"/>
    <param name="sleep" value="30"/>
    <param name="preview" value="false"/>
  </object>
    

The following table lists the applet parameters and their meaning.

Parameter Meaning
sleep time to wait after each frame is drawn (in milli seconds)
preview If this value is true the applet looks like an image only moving when the mouse is over the applet.