Unformatted text preview: Notice that we never assumed that M1=M2 was either 1 or 1, so our
formulas apply both for the Sun and for the Moon. It is a numerical coincidence that the tides they raise are of the same order (though some have
speculated that the resulting more-variable tides produced could have been
somehow necessary to mix the oceans in a way that furthered the evolution
of life | or its emergence from the sea). 4.3.2 Tidal drag and the lengthening of the day
Real tides are not exactly the size we have calculated, primarily because the
Earth is rotating. Thus the continents are \dragged through" the oceanic
tidal bulges, causing water to pile up on the continental shelves, ow into
and out of bays, etc. There can also be resonance eects in some cases like
the famous Bay of Fundy.
This kind of \friction" between the rotating Earth and the tidal bulges
produces two eects.
1. The tidal bulge is, on average, dragged ahead of where it would be if
it \pointed at" the Moon. 13 /day ϕ
36 0 /d ay 2. The drag slows down the rotation of the Earth.
Since angular momentum must be conserved, as the Earth loses angular momentum, it must be gained by the Moon's orbital motion! How does this
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- Fall '09