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Unformatted text preview: UCSD: Physics 8; 2008 Tides
Moon, Sun, Earth, Water 1 UCSD: Physics 8; 2008 Tides are caused by difference in gravity Gravitational Force looks like: F = GMm/r
2 m r M Since F = ma, a = F/m, so mass m accelerates with a = GM/r2 Not all points on earth are equidistant to the moon closest side accelerates faster toward moon than does center farthest side accelerates slower toward moon than does center 2 UCSD: Physics 8; 2008 Differential acceleration As earth free-falls toward moon... ...and why shouldn't it: the moon pulls on the earth, and nothing holds the earth from accelerating due to this force! The near side tries to accelerate faster gets ahead of the rest of the earth The far side doesn't accelerate as fast lags the rest of the earth Result is a bulge in front (eager), and a bulge behind (sluggish) 3 UCSD: Physics 8; 2008 In picture form (exaggerated) Near side experiences greater acceleration toward moon Center acceleration is "just right" (just is what it is) Far side experiences lesser acceleration toward moon r R M
difference in acceleration is: a = GM/(r- 2 - GM(r+R)2 R) 4GMR/r3 So tidal influence on planet scales like M/r3, where M is the mass of the tidal perturber
4 UCSD: Physics 8; 2008 Tides are caused by the Difference in Gravity
Tides are caused by the difference in the pull of gravity across a body. The difference decreases as 1/r3. Tides are largest for close (small r) objects. Tides are important for Mercury's orbit, Moon's spin, Earth's spin, they heat Jupiter's moon Io.... 5 UCSD: Physics 8; 2008 High Tide Twice Per Day As Earth rotates underneath the bulge (which stays pointing roughly toward the moon), a fixed point on earth experiences two high tides and two low tides per day Not only are oceans affected: the "solid" earth (not completely rigid) moves up and down about 0.4 meter peak-to-peak twice a day!
6 UCSD: Physics 8; 2008 Tidal friction makes the moon's orbit grow http://spiff.rit.edu/classes/phys235/no_moon/no_moon.html The bulge is carried forward by rotation (via friction), producing a gravitational "carrot" after which the moon races, gaining orbital energy. Moon moved 3.8 cm per year farther from Earth Earth's day is getting longer 7 UCSD: Physics 8; 2008 Huge Ancient Tides 4.6Gyr ago, 100 Myr after moon formed, it was 10 times nearer than today Tidal force 103 = 1000 times larger 3m tides become 3km high, moving hundreds of miles inland Day only 6 hours long, and 2 tides per day Dissolved minerals into oceans 100 Mph winds daily from rapid rotation By 3.2Byr ago, moon still much nearer than it is today 1 month = 20 (24hour) days (27.5 24h days today) Seen in rock layers 8 UCSD: Physics 8; 2008 The Sun is a Player Too The M/r3 ratio for the sun is 45% that of the moon Sun's effect is about 1/3 of the total tide When earth, moon, and sun are aligned (new moon, full moon), the tides add called spring tides When 90 out of phase (first quarter, last quarter), they partly cancel called neap tides moon dominates, so high tide still along earth-moon direction
inaccurate view: should be polar view of earth 9 UCSD: Physics 8; 2008 The Sun is a Player Too The M/r3 ratio for the sun is 45% that of the moon When earth, moon, and sun are aligned (new moon, full moon), the tides add called spring tides When 90 out of phase (first quarter, last quarter), they partly cancel called neap tides moon dominates, so high tide still along earth-moon direction inaccurate view: should be polar view of earth 10 UCSD: Physics 8; 2008 San Diego full moon last qtr new moon 1st qtr Hawaii 11 UCSD: Physics 8; 2008 Tidal Resonance In Hawaii, the tides are less than a meter peak-to-peak representing the natural size of the bulge On a continental shelf, can get greater amplitude due to "sloshing" behavior 8 ft (2.5 m) peak-to-peak in San Diego Some inlets (Puget Sound, Washigton, Bay of Fundy, Nova Scotia) experience resonance if natural "slosh" time has a 12-hour period, can get substantial amplification greater than 10 m peak-to-peak in some special locations 12 Power Generation from Tides UCSD: Physics 8; 2008 Energy = water mass x g x Height Power=E/time = 2135 MW max for 6h/day, advancing 52min/day
San Onofre gives 2100 MW 24h/day Damages shore line, fish breeding, expensive maintenance etc. 13 ...
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