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The tides at a given place in the Earths 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 Newtons 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 Earths 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
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