7.6 The Tides
Earth is unique among the planets in that it has large quantities of liquid water on its surface. Approximately three-quarters of Earths surface is covered by water, to an average depth of about 3.6 km. Only 2 percent of the water is contained within lakes, rivers, clouds, and glaciers. The remaining 98 percent is in the oceans.
A familiar hydrospheric phenomenon is the daily fluctuation in ocean level known as the tides. At most coastal locations on Earth, there are two low tides and two high tides each day. The "height" of the tidesthe magnitude of the variation in sea levelcan range from a few centimeters to many meters, depending on the location on Earth and time of year. The height of a typical tide on the open ocean is about a meter, but if this tide is funneled into a narrow opening such as the mouth of a river, it can become much higher. For example, at the Bay of Fundy, on the U.S.Canada border between Maine and New Branswick, the high tide can reach nearly 20 m (approximately 60 feet, or the height of a six-story building) above the low-tide level. An enormous amount of energy is contained in the daily motion of the oceans. This energy is constantly eroding and reshaping our planets coastlines. In some locations, it has been harnessed as a source of electrical power for human activities.
What causes the tides? A clue comes from the observation that they exhibit daily, monthly, and yearly cycles. In fact, the tides are a direct result of the gravitational influence of the Moon and the Sun on Earth. We have already seen how gravity keeps Earth and Moon in orbit about each other, and both in orbit around the Sun. (Sec. 2.7) For simplicity, let us first consider just the interaction between Earth and the Moon.
Earths oceans undergo the greatest deformation because liquid can most easily move around on our planets surface. (A bulge is actually raised in the solid material of Earth, but it is about a hundred times smaller than the oceanic bulge.) Thus, the ocean becomes a little deeper in some places (along the line joining Earth to the Moon) and shallower in others (perpendicular to this line). The daily tides we experience result as Earth rotates beneath this deformation.
The variation of the Moons gravity across Earth is an example of a differential force, or tidal force. The average gravitational interaction between two bodies determines their orbit around each other. However, the tidal force, superimposed on that average, tends to deform the bodies themselves. As discussed in more detail in More Precisely 7-3, the tidal influence of one body on another diminishes very rapidly with increasing distancein fact, as the inverse cube of the separation. For example, if the distance from Earth to the Moon were to double, the tides resulting from the Moons gravity would decrease by a factor of eight. We will see many situations in this book where tidal forces are critically important in understanding astronomical phenomena. Notice that we still use the word tidal in these other contexts, even though we are not discussing oceanic tides and possibly not even planets at all.
Both the Moon and the Sun exert tidal forces on our planet. Thus, instead of one tidal bulge, there are actually twoone pointing toward the Moon, the other toward the Sunand the interaction between them accounts for the changes in the height of the tides over the course of a month or a year. When Earth, the Moon, and the Sun are roughly lined up (Figure 7.23a), the gravitational effects reinforce one another, and so the highest tides are generally found at times of new and full moons. These tides are known as spring tides. When the EarthMoon line is perpendicular to the EarthSun line (at the first and third quarters; Figure 7.2b), the daily tides are smallest. These are termed neap tides.
EFFECT OF TIDES ON EARTH'S ROTATION
Earth rotates once on its axis (relative to the stars) in 23h 56mone sidereal day. However, we know from fossil measurements that Earths rotation is gradually slowing down, causing the length of the day to increase by about 1.5 milliseconds (ms) every centurynot much on the scale of a human lifetime, but over millions of years, this steady slowing of Earths spin adds up. At this rate, half a billion years ago, the day was just over 22 hours long and the year contained 397 days.
A number of natural biological clocks lead us to the conclusion that Earths spin rate is decreasing. For example, each day a growth mark is deposited on a certain type of coral in the reefs off the Bahamas. These growth marks are similar to the annual rings found in tree trunks, except that in the case of coral, the marks are made daily, in response to the daynight cycle of solar illumination. However, they also show yearly variations as the corals growth responds to Earths seasonal changes, allowing us to perceive annual cycles. Coral growing today shows 365 marks per year, but ancient coral shows many more growth deposits per year. Fossilized reefs that are five hundred million years old contain coral with nearly 400 deposits per year of growth.
This process will continue until Earth rotates on its axis at exactly the same rate as the Moon orbits Earth. At that time the Moon will always be above the same point on Earth and will no longer lag behind the bulge it raises. Earths rotation period will be 47 of our present days, and the distance to the Moon will be 550,000 km (about 43 percent greater than at present). However, this will take a very long timemany billions of yearsto occur.
In what ways do tidal forces differ from the familiar inverse-square force of gravity?