 | The Earth orbits the Sun and the Moon the Earth because ofthe mutual gravitational attractions between the bodies. Oceantides are caused by thedifferences in the gravitationalpulls of the Moon and Sun across the body of the Earth (gravity dropping off with theinverse square of distance). To the left, we look only at theeffect of theMoon. The depth of theocean and relative sizes of Earth and Moon are greatly exaggerated(the Moon actually a quarter the size of Earth and 30 Earthdiameters away). At the top (a), the arrows symbolically show thegravitational force between the Moon and Earth at differentdistances from the Moon. At center (b), the central force issubtracted from all the arrows. What remains is the differentialforce, which causes the ocean waters to flow toward the linebetween the Earth and Moon. As the Earth rotates, we thereforepass under high water, then low, then high again, making the watersrise and fall at the coasts. As a result of the Earth's rotationand the time it takes the water to flow, the tidal bulge leads theMoon (c). Because the Moon is moving counterclockwise around theEarth with a period relative to the Sun of 29.5 days (the phaseperiod), high tides are separated not by 12 hours, but by anaverage of 12 hours 24 minutes. Though theSun is much farther away, it is also muchmore massive, so it produces a tide as well, of about 45 percentthe strength of the lunar tide. The Sun thus contributes about athird toward the total of the two when they line up to produce thehighestspring tides atnewand full Moons. At the lunar quarters, when the Moon and Sunare at right angles to each other, the solar tide fills in thelunar, resulting in much smallerneap tides. The height ofthe tide is also influenced by the distances of the Earth from theMoon and Sun, which change because of the eccentricity of the lunarand terrestrial orbits. The strongest tide will generally occurwhen new or full Moon coincides with lunar perigee, where the Moonis typically 5.5 percent closer to the Earth than average. TheMoon and Sun pull back on the tidal bulge to slow the Earth'srotation and increase the length of the day by about 0.0014 secondsper century. The effect must be taken into account in timekeeping. In reality, the situation is much more complex, involving shorelines, the position of the Moon relative to the celestial equator,the time of year, the latitude of the observer, and various otherfactors. (Image and some text fromThe Ever-Changing Sky, J. B. Kaler,Cambridge University Press, 1996, 2002.) |
