Lunar
Tides
The tides at a given place in the Earth's oceans occur about an hour later
each day. Since the Moon passes overhead about an hour later each day, it was
long suspected that the Moon was associated with tides. Newton's Law of Gravitation provided a quantitative understanding of that association.
Differential Forces
Consider a water
molecule in the ocean. It is attracted gravitationally by the Earth, but it
also experiences a much smaller gravitational attraction from the Moon (much
smaller because the Moon is much further away and much less massive than the
Earth). But this gravitational attraction of the Moon is not limited to the
water molecules; in fact, the Moon exerts a gravitational force on every object
on and in the Earth. Tides occur because the Earth is a body of finite extent
and these forces are not uniform: some parts of the Earth are closer to the
Moon than other parts, and since the gravitational force drops off as the inverse
square distance, those parts experience a larger gravitational tug from the
Moon than parts that are further away.
In this situation, which is illustrated
schematically in the adjacent figure, we say that differential forces
act on the body (the Earth in this example). The effect of differential forces
on a body is to distort the body. The body of the Earth is rather rigid, so
such distortion effects are small (but finite). However, the fluid in the
Earth's oceans is much more easily deformed and this leads to significant tidal
effects.
A Simple Tidal Model
We may illustrate the
basic idea with a simple model of a planet completely covered by an ocean of
uniform depth, with negligible friction between the ocean and the underlying
planet, as illustrated in the adjacent figure. The gravitational attraction of
the Moon produces two tidal bulges on opposite sides of the Earth.
Without getting too much into the technical
details, there are two bulges because of the differential gravitational forces.
The liquid at point A is closer to the Moon and experiences a larger
gravitational force than the Earth at point B or the ocean at point C. Because
it experiences a larger attraction, it is pulled away from the Earth, toward
the Moon, thus producing the bulge on the right side. Loosely, we may think of
the bulge on the left side as arising because the Earth is pulled away from the
water on that side because the gravitational force exerted by the Moon at point
B is larger than that exerted at point C. Then, as our idealized Earth rotates
under these bulges, a given point on the surface will experience two high and
two low tides for each rotation of the planet.
More Realistic Tidal Models
The realistic situation
is considerably more complicated:
1.
The
Earth and Moon are not static, as depicted in the preceding diagram, but
instead are in orbit around the common center of mass for the system.
2.
The
Earth is not covered with oceans, the oceans have varying depths, and there is
substantial friction between the oceans and the Earth.
These make a more
realistic description much more complicated, but the essential ideas remains as
illustrated in the preceding diagram. Here are realtime links to the present
tidal conditions in San Francisco Bay and Houston-Galveston and here is a link to a set of graphs for the tidal levels over current 24-hour periods for various tidal stations. Notice
in comparing these graphs the differences in the detailed tidal fluctuations
for different locations (for example, compare the graph for Tacoma, Washington, with that for South Pass, Louisiana). These differences are produced by the
complicating factors mentioned above.
Spring Tides and Neap Tides
Another complication of
a realistic model is that not only the Moon, but other objects in the Solar
System, influence the Earth's tides. For most their tidal forces are negligible
on Earth, but the differential gravitational force of the Sun does influence
our tides to some degree (the effect of the Sun on Earth tides is less than
half that of the Moon).
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Competition between the Sun and Moon in producing tides. |
For example,
particularly large tides are experienced in the Earth's oceans when the Sun and
the Moon are lined up with the Earth at new and full phases of the Moon. These
are called spring tides (the name is not associated with the season of
Spring). The amount of enhancement in Earth's tides is about the same whether
the Sun and Moon are lined up on opposite sides of the Earth (full Lunar phase)
or on the same side (new Lunar phase). Conversely, when the Moon is at first
quarter or last quarter phase (meaning that it is located at right angles to
the Earth-Sun line), the Sun and Moon interfere with each other in producing
tidal bulges and tides are generally weaker; these are called neap tides.
The figure shown above illustrates spring and neap tides.
http://csep10.phys.utk.edu/astr161/lect/time/tides.html (Astronomy 161)