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Tides

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Ocean tides are caused by tidal forces. First we’ll look at the ocean tides, and then consider what forces in nature could cause this.

Beach in the UK

Beach in the UK

High and low tide in Robinhood Bay, North Yorkshire, United Kingdom

Bay of Fundy

Low tide at Winthrop, MA, revealing the local ocean floor as a walkway from the beach to the breakers.

Five Sisters Winthrop Tides

1st section adapted from “Gravitation Causes Tides on Earth”, Ron Kurtus, September 2010
http://www.school-for-champions.com/science/gravitation_tides.htm

• What causes tides?

• Why are there always high tides on both sides of the Earth?

• What role does the alignment of the Moon and Sun have on the tides?

When the sea level is above normal, it is called high tide. The opposite is low tide.

The moon’s gravity is the primary cause of the rising tide.

The Sun’s gravity also matters – but less than that of the moon

The force from the Moon pulls the ocean toward it, a maximum of about 1 m (one meter) – but it also causes water to pile up on the opposite side of the Earth?! We’ll have to figure out why that happens!

Small changes in sea-level can make big changes in shoreline rise

Where the shore is shallow, a 1 m change in sea level can result in even a 10 m or more rise along the shoreline.

Cause of tides on both sides

Since the tides are caused by the Moon’s gravity pulling on Earth’s oceans, you might think the shape of the oceans would only be pulled toward the Moon.

Wiley.com Textbook animations for tides

Tides on opposite sides of the Earth?

The oceans are stretched so that there are high tides on both sides of the Earth. How does that happen ?!

What causes this to happen?

All parts of the Earth’s ocean are attracted toward the Moon – but the amount of pull isn’t the same everywhere.
The water closest to the moon is pulled more.
The water further away from the moon is pulled less.
So there is a difference in the amount of pull between one side of the earth and the other:
This is a gravitational differential.

The pull of gravity is represented here:

The Moon is also attracting the mass of the entire Earth toward it (not just the oceans)

So consider the mass of the Earth as being concentrated at its center of mass (CM).

The heavy vector (arrow) in the center shows the attraction of the Earth towards the Moon.
What’s the net result? Instead of subtracting numbers,
we’ll subtract arrows.

Subtract [the force of attraction on the Earth’s center of mass] from [the force pulling water to the Moon]

The resulting forces on the ocean water look like this:

So the difference in gravity creates two tidal bulges.
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Spring and Neap Tides

http://www.astronomyknowhow.com/moon-tides.htm

“Spring” tides – When the sun, moon and earth all line up at new (as in the picture) or full moon then we get the highest (and indeed lowest) tides

…In fact it takes a bit of time for the enormous mass of water to move –

so the spring tide will occur a couple of days after the new (or full) moon….

“Neap” Tides – When the moon is at first or third quarter then the moon and sun are exerting forces from two different directions.

So the overall effect on the water is less, so the high tides are lower than average and the low tides are higher than the average.

Spring and Neap Tides Animation
http://oceanservice.noaa.gov/education/kits/tides/media/supp_tide06a.html

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Consider an object near the surface of the Earth. We assume Earth’s gravity acts equally on all parts of the object – the object’s top and bottom. For all practical purposes, this is true enough.

But it is not precisely true. The Earth’s gravity really acts on the bottom part of a falling object more than the top part. The bottom part is slightly closer to the center of the Earth.

Why don’t we notice this? Why don’t we feel the Earth tug on our feet more than on our head? The difference in height between the center of the Earth and the top of the object, and the bottom of the object, is slight. It is so tiny that it makes no measurable difference

But now consider a large object, like an asteroid or small moon. These can be tens, or hundreds, of miles in diameter. In this case, the difference in height between the center of the Earth and the top of the object, and the bottom of the object, is not so slight. It is large enough that it does make a measurable difference!

Now consider an object the size of the Earth being pulled by the moon’s gravity.

The diameter of the earth at the equator is 7,920 miles (12,760 kilometers)

Here, the difference in height between the center of the Moon and the near part of Earth, and the center of the Moon and the far part of Earth, is large. Since the Earth has water over most of its surface, we can easily see the result of this difference in gravitational force. A difference in gravitational force is called a “tidal force”.

Applets on Tides from the PBS NOVA website

What causes the tides?

Tidal curiosities – Questions & Answers

The cause of the tides

By William Newtspeare http://squishtheory.wordpress.com/the-tides/

Take a large spherical, rubber ball. This represents the Earth – and it’s oceans.

Attach strings to several parts of it.

If you pull each string, in the same direction, then the ball moves without distorting.

But if you pull harder on one string than on another, and pull each in a slightly different direction, then the ball distorts

The moon’s gravity pulls with different strengths, and at different angles, on the particles that make up the earth.

Therefore the Earth stretches in this same way.

* The solid part of the Earth stretches very little – these are called Earth tides.

* The liquid (ocean) parts stretch more – these are ocean tides.

* The atmosphere is also pulled – atmosphere tides.

Let’s draw the Earth as a red circle with 5 independent particles.

Allow each of these five parts to “fall” a small distance towards the moon (due to its gravity)

It falls, or stretches, into the blue ellipse: Each side is a tidal bulge!

There is one tidal bulge on each side of the Earth.
If we subtract the motion of the earth towards the moon, and just consider how this affects the shape of the earth, then we get the above image.
The arrows indicate the strength of the force.

The Bay of Fundy

The Bay of Fundy is a bay on the Atlantic coast, on the northeast end of the Gulf of Maine, between the Canadian provinces of New Brunswick and Nova Scotia. It has highest tidal range in the world.

http://en.wikipedia.org/wiki/Bay_of_Fundy

http://www.bayoffundy.com/about/highest-tides/

http://bayoffundytourism.com/ecozones/worlds-highest-tides/

More than 2 tides a day?

http://www.astronomyknowhow.com/moon-tides.htm

Although the sun, the moon and the rotation of the earth are the major forces involved in creating the tides the local conditions such as the shoreline and the contour of the ocean floor also have an effect.

Because of this not everywhere has 2 tides a day – there are some places that experience what is known as a double-high water (e.g. Southampton) or double-low water (e.g. Portland).

The highest tides of all (17m) occur in Canada and after a long running dispute between the famous tides of the Bay of Fundy and those of Ungava Bay on the northern coast of Quebec, the Canadian Hydrographic Service has declared a draw.

Further reading

Why Is There a Tidal Bulge Opposite the Moon? Stephen J Edberg, Jet Propulsion Laboratory, California Institute of Technology

https://pumas.gsfc.nasa.gov/files/01_25_11_1.pdf

Tidal Misconceptions, by Donald E. Simanek

http://www.lhup.edu/~dsimanek/scenario/tides.htm

AP Physics resources on tidal forces

An overview of oceanic tides (AP Physics only)

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

8.MS-ESS1-2. Explain the role of gravity in ocean tides, the orbital motions of planets, their moons, and asteroids in the solar system.

HS-ESS1-4. Use Kepler’s laws to predict the motion of orbiting objects in the solar system.
Describe how orbits may change due to the gravitational effects from, or collisions
with, other objects in the solar system.

HS-PS2-4. Use mathematical representations of Newton’s law of gravitation and Coulomb’s law to both qualitatively and quantitatively describe and pre

HS-PS2-10(MA). Use free-body force diagrams, algebraic expressions, and Newton’s laws of motion to predict changes to velocity and acceleration for an object moving in one
dimension in various situations.

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)

PS2.B: TYPES OF INTERACTIONS

Gravitational, electric, and magnetic forces between a pair of objects do not require that they be in contact. These forces are explained by force fields that contain energy and can transfer energy through space. These fields can be mapped by their effect on a test object (mass, charge, or magnet, respectively). Objects with mass are sources of gravitational fields and are affected by the gravitational fields of all other objects with mass. Gravitational forces are always attractive. For two human-scale objects, these forces are too small to observe without sensitive instrumentation. Gravitational interactions are non-negligible, however, when very massive objects are involved. Thus the gravitational force due to Earth, acting on an object near Earth’s surface, pulls that object toward the planet’s center. Newton’s law of universal gravitation provides the mathematical model to describe and predict the effects of gravitational forces between distant objects. These long-range gravitational interactions govern the evolution and maintenance of large-scale structures in the universe (e.g., the solar system, galaxies) and the patterns of motion within them… Newton’s law of universal gravitation and Coulomb’s law provide the mathematical models to describe and predict the effects of gravitational and electrostatic forces between distant objects.

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