ppt9 part1 - Tides Chapter 9 Prof Weatherly Today...

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Tides Chapter 9 Prof. Weatherly Today: Equilibrium theory of tides (Completely ocean covered earth) Explains ●2-tidal bulges ●spring/neap tides ●diurnal tides/semidiurnal/mixed tides
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Tides result from astronomical effects: gravitational attraction of moon & sun AND centripetal acceleration of earth-moon & earth-sun rotating about their centers of mass.
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First consider earth-moon. Earth and moon rotate about their center of mass – the barycenter. The earth spins about the barycenter and the oceans experience a centripetal acceleration.
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What keeps the ball going around is the string. What keep the earth spinning around the barycenter is the gravitational attraction of the moon.
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The centripetal force (the red arrows) is every where the same. The red arrows are all the same length and point in in the same direction.
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At earth’s center centripetal force = G M moon /r 2 (G=gravitational constant, M moon = mass of moon, r = distance from earth center to moon center) = the gravitational force of the moon.
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On the other hand, the gravitational force of the moon (the black arrows) varies in strength and direction.
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The gravitational force is largest on the side closer to the moon and least on the side furtherer from the moon. The force is always directed toward the center of the moon.
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The tidal generating force (blue) is the difference of the moon’s gravitational force (black) and the centripetal force (red).
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The tide generating forces are shown again here, but now they are black.
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