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. Can this explain tides? Is this what we observe? Earth! Moon s Gravity! Moon!
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
What we actually observe: Two tidal bulges (two daily high tides in some places) One near moon Other opposite moon Earth! Moon! What force is Force of Moon s Gravity! this?!
Consider the Center of Mass Center of Mass (C m ) Equal mass in all directions Example: Teeter-totter C m
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.
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.
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.
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
Amphidromic point 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.
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
Relatively inexpensive Work with tides of lower power Proposed tidal power plants in Australia Tidal Turbines
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?