9 Tides Outline 1 Chapter 9 Tides 1 Key Questions What causes tides What is the difference between a lunar and solar day What does this mean for tidal periods How do the positions of Sun and Moon affect tidal range How do real life tides differ from idealized predictions 2 Overview of Tides Rhythmic rise and fall of Very long and regular shallow water Caused by gravitational attraction of Sun Moon and Earth 3 Newton s Law of Gravitation Every particle with mass attracts every other particle Gravitational force G m1m2 r2 G Gravitational constant G 6 67 10 11 m3 kg 1 s 2 Gravitational constant 4 Which has the bigger effect on tides Sun or Moon Fig 9 10 Sun has more But Moon is much Sun s force is only 46 of Moon s force creating tides Moon is more important 2x tidal force of Sun 5 Equilibrium Theory of Tides ASSUMPTIONS The ocean has uniform depth on a spherical Earth This ocean responds instantly to the gravitational forces of the sun and moon Obviously these are crude approximations 7 Gravitational forces on water particles Every particle attracts every other particle Gravitational force proportional to product of masses Inversely proportional to square of separation distance 8 Centripetal force Fig 9 3 Fig 9 4 Gravity string holds earth and moon together Orbiting bodies are held together Pulls toward center of orbit parallel to plane of orbit Force is the same at all points on the sphere 9 Centripetal force Fig 9 5 Same magnitude and direction everywhere on earth Tethers Earth and Moon to each other 10 Tide producing forces Fig 9 6 forces differences between centripetal and gravitational forces Tide generating forces are components of resultant forces https goo gl eBCMYZ 10 1 Tidal forces lunar Fig 9 7 Small horizontal forces pull seawater into two bulges on opposite sides of Earth 9 Tides Outline 2 11 Tidal bulges lunar Fig 9 8 Model used in equilibrium tide theory 2 equal bulges Moon side and opposite side of Earth Ocean covers entire earth no continents at uniform depth Assume no friction with the seabed 12 Tidal bulges lunar Moon closer to Earth so lunar tide producing force greater 2x than that of Sun Flood tide seawater moves on shore toward High Tide Ebb tide tide seawater moves offshore toward Low Tide Is there a tide in the atmosphere Lithosphere What if the earth had no moon What would the tides look like 13 Lunar Day Fig 9 9 https goo gl bbYGx0 Moon orbits Earth 24 hours 50 minutes for observer to again see moon directly overhead High tides are 12 hours and 25 minutes apart 14 Tidal bulges solar Similar to lunar bulges but half the Moon closer to Earth New full moon tidal range greatest spring tide Quarter moons tidal range least neap tide Time between spring tides about two Tidal range Spring tide high high tides and low low tides high tidal range Neap tide small high tides and small low tides low tidal range 15 Earth Moon Sun positions and spring and neap tides animation Fig 9 11 https goo gl DmuidP Up to now we have been assuming Moon s orbit is centered on the Orbits are circular Earth s axis is vertical relative to its orbit Now for real life The orbital plane of the moon is not aligned with Earth s equator Orbits are slightly elliptical Earth s axis is tilted 23 5 relative to orbit around sun Moon s orbit around earth is tilted 5 Complicating factors of Earth Moon Sun orientation 16 Complicating factors declination Angular distance Moon or Sun above or below Earth s equator Sun to Earth 23 5o N or S of equator Fig 9 13 5 degree tilt of moon s orbit 23 5 degree tilt of Earth s axis 28 5 degree tilt of 9 Tides Outline 3 Moon to Earth 28 5o N or S of equator Shifts lunar and solar bulges from equator Unequal tides Fig 9 16 17 Declination and tides Unequal tides unequal tidal ranges 19 Idealized tide prediction Two high tides two low tides per lunar day Six lunar hours between high and low tides 20 Real tides Earth not covered completely by Continents and with seafloor modify tidal bulges Tides are shallow water waves with speed determined by depth of water 21 Tidal patterns Fig 9 18 Diurnal tidal pattern one high tide one low tide per lunar day Semidiurnal tidal pattern two high tides two low tides per lunar day Mixed tidal pattern 2 highs 2 lows of different heights http goo gl J2nDva Fig 9 19 Monthly records Tidal patterns remain the same at one location Even through spring neap transitions 22 Tides in coastal waters Amplification of tidal range Example Bay of Fundy maximum tidal range 17 m 56 ft Between Nova Scotia and New Brunswick Canada Fig 9 20 23 Pictures of Bay of Fundy boats harbor 3 slides Fig 9A Fig 9 21 24 Tides in coastal waters A tidal bore moving up a river 25 Tidal bores moving up an estuary river 4 slides 26 Coastal tidal currents Reversing current Flood current sea rises Earth moves into bulge Ebb current sea drops Earth moves out of bulge High speed flow in restricted channels Coastal tidal currents As tide level drops currents Sea level drops water moving off shore Maximum velocity 1 2 way between high and low tide At low tide 9 Tides Outline 4 Velocity 0 low slack water As tide level increases currents Moving toward shore At peak high tide Velocity 0 high slack water 27 Tide generated power resource Does not produce power on demand Possible harmful environmental effects 28 Potential Tidal power sites 29 Fig 9 24 La Rance tidal power plant at Saint Malo France Thanks for picking up your trash as you leave Review Key Questions What causes tides Gravitational attraction between the Earth and moon Earth and sun Tide generating force Depends on mass and distance Sun has more mass but is much farther away from Earth moon is strongest force on tides Tidal bulges formed Earth and Moon orbit around the barycenter center of mass gravitational attraction Centripetal force Two bulges created Moon side Gravitational attraction is greater than centripetal force Opposite side Centripetal force is greater than gravitational force What is the difference between a lunar and solar day Time elapsed from when Moon or Sun is overhead Lunar day 50 minutes longer Moon has moved in orbit around Earth during 24 hours What does this mean for tidal periods Time for one full tidal cycle 24 hrs 50 minutes How do the positions of Sun and Moon affect tidal range Sun moon in line Spring tides big tidal ranges Sun moon 90o to each other Neap tides small tidal ranges 2 weeks between spring tides How do real life tides differ from idealized predictions Tidal bulges are