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The Tides: Consider Moon’s Gravity •  Pulls all points on Earth toward

Moon’s center of mass. •  ‘near’ side of Earth is attracted

more than ‘far’ side because force of gravity decreases with increasing distance.

•  This creates a ‘bulge’ in oceans toward moon.

•  Earth rotates through this bulge = high tide.

Earth!

Moon!

Moon’s Gravity!

Can this explain tides? Is this what we observe?

So, what complications can you find that argue against this explanation for tides?

Which of the following are correct?

A.  Coastlines experience two high tides each day. B.  High tide occurs once each lunar month. C.  High tide occurs simultaneously along all

coastlines of an ocean. D.  All of the above E.  None of the above

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What we ‘actually’ observe: •  Two tidal bulges (two daily high tides in

some places) –  One ‘near’ moon –  Other ‘opposite’ moon

Earth!

Moon!

Force of Moon’s Gravity!What

force is this?!

Consider the Center of Mass •  Center of Mass (Cm)

–  Equal mass in all directions

•  Example: Teeter-totter

Cm

Consider Earth - Moon system •  Lunar mass = 1.2% of Earth mass!

–  ~239000 miles from Earth

•  The center of mass of Earth-Moon system is within the Earth!

•  So, BOTH Earth and Moon rotate about this point

•  This rotation results in inertia –  Directed away from the center of mass –  Example: spinning figure skating couple.

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Combine Gravity & Inertia:

•  Near side –  moon’s gravity overcomes inertia –  Produce near bulge (crest of tide

wave) •  Far side

–  Moon’s gravity is less than inertia –  Produce far-side bulge

What we just described are called Lunar Tides:

•  Earth rotates through the gravity and inertial bulges of Earth-Moon system

•  Prediction –  We should have two high

tides –  12 hours apart (twice

daily)

Complexities: Are there two tides 12 hours apart?

•  Moon completes orbit in 29.5 days, in other words it orbits Earth 12.2º per day •  So, Earth must rotate an additional 12.2º to complete tidal day (372.2º or 24

hours + 50 minutes (24.81hrs)). •  So, no. Tides are not 12 hours apart, rather they are 12 hours 25 minutes apart.

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What about Sun’s effect •  Gravity & inertia in this system too - so,

there must be solar tides too •  Combined with phases of the moon….

–  Full & New Moon = Spring tide –  First and last 1/4 Moon = Neap tide

Note: these occur twice each lunar cycle, not annually

So, result of Earth - Moon -Sun System…

•  Maximum tide level changes during the month! •  And varies with latitude (Earth-Moon ‘tilted’)…

Moon is not above equator:

•  Gravity and inertial bulges & the axis of Earth’s rotation are not ‘perpendicular’. So, tides vary with latitude… –  Diurnal tides (one daily high) –  Semidiurnal (twice daily)

•  So, we don’t always have two high tides per day. That depends on latitude.

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More complexity…

•  Recall Sun’s angle in sky changes during year? –  23.5ºN (Tropic of Cancer) to 23.5ºS

(Tropic of Capricorn) –  This is because Earth’s axis of rotation is

tilted relative to Earth’s orbital plane. •  Moon’s angle also varies (28.5ºN to

28.5ºS) over 19 years •  Result:

–  some places change from diurnal to semidiurnal

–  Level of tides changes too

What is true about the tides on all coastlines?

A.  There will be two high tides in a 24 hour period. B.  High tides will be separated by 12 hours and 25 minutes. C.  The level of high tide will be the same each day. D.  The number of high tides in a day will be constant E.  Tidal patterns and periodicity depend on latitude,

coastline geography, phases of the moon, season, and orbital variations between the Moon-Earth and Sun.

Dynamic Theory of Tides: •  Tidal wavelength = 1/2

circumference of Earth! –  Shallow water waves and their

speed is proportional to water depth

–  Slowed most where seafloor is shallow

•  Thus, tidal bulges are refracted in the ocean basins, and they ‘splash’ against continents.

•  So, the idealized bulges we just described are not adequate to explain tides.

•  Further, the bulges cannot keep pace with the speed of rotation, so they are disrupted by the Coriolis Effect into tidal cells that rotate around a single point called an amphidromic point

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Thus, tides ‘rock’ around basins like water in pan

• Within a given rotating tidal cell, low tide falls ~6 hours after high tide. • There are > 150 factors influencing tides on a given coast

•  Factors result from variations in elliptical orbit of Moon and Earth and variations in the distance between Moon, Earth and Sun •  Seven factors describe >80% of variability in tides.

Amphidromic point

Tidal Power Systems •  Currently in use in Nova

Scotia, and Brittany, France, Russia, China

•  Problem: Expensive. Require powerful tides to justify cost

•  New technologies make this more economical…

Tidal Turbines •  Relatively inexpensive •  Work with tides of lower

power •  Proposed tidal power

plants in Australia

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Tidal Bore •  Occur on Shallow coast lines •  Tide ‘rushes’ up into river •  Result: fast shallow-water wave •  Qiantang River, China - 8 m bore

Review Questions

•  Why can’t gravity alone explain lunar tides? •  Why aren’t lunar tides exactly 12 hours apart? •  How do Neap and Spring tides prove that solar tides

influence the Earth? •  Why do we need a Dynamic Theory of Tides?