sol12 - HW Solutions 12 8.01 MIT Prof Kowalski Universal...

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Unformatted text preview: HW Solutions # 12- 8.01 MIT - Prof. Kowalski Universal Gravity and Harmonic Oscillators . 1 ) Whither the Moon? a ) TIDES : The water (and to some extent the liquid core) of the earth bulge out toward and away from the moon to the fact that its gravitational attraction is stronger on the side of the earth toward the moon than on the center of the mass of the earth itself, so the water is pulled up relative the earth. On the far side of the earth (away from the moon) the moon’s gravitational force is weaker and this water is left behind this accelerating earth, producing another tidal bulge. Therefore there are two high tides per day (in most places on the earth). The height of the tide is scaled by ∼ a tidal g . a tidal = ∆ g moon = GM m ( 1 ( D em + R e ) 2 − 1 D 2 em ) ≈ = − 2 GM m R e D 3 em ≈ 10 − 7 g Where D em = 3 . 84 × 10 8 m. This produces tides about 1 m high (Since R e = 6 . 378 × 10 6 m) in mid-ocean but it can be magnified by over an order of magnitude by resonances with bays like the Irish Sea and the Bay of Fundy.by resonances with bays like the Irish Sea and the Bay of Fundy....
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sol12 - HW Solutions 12 8.01 MIT Prof Kowalski Universal...

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