5. The Moon: stepping stone to the planets

Tides and the once and future Moon

The pattern of the tides

Fig. .. 

Walking along the ocean beach some morning, we might notice that the waves seem to be reaching farther and farther up the sand. The tide is flooding the beach. A few hours later, it hesitates and then begins to ebb, retreating onto the flats where the clams may often be found. The high tides occur simultaneously and symmetrically on opposite sides of the Earth; they return every 12 hours 25 minutes in each location, although not precisely to the same height. The time between consecutive high tides is slightly more than half a day because the Moon's revolution around Earth is in the same direction as the Earth's rotation on its axis, so Earth needs an extra 25 minutes of rotation to out-race the Moon and get into position. On a slowly rotating planet without continents, the tide would be highest along the line joining the centers of the Earth and Moon, that is, when the Moon is overhead. This is not the case for the Earth. The friction of the continents and the rapid rotation of the Earth carry the ocean's tidal bulge forward so it precedes the Earth-Moon line by about 3 degrees. This means that in the open ocean the high tide actually occurs about 12 minutes after the Moon is overhead.

The Moon creates two high tides because the gravitational force of the Moon draws the ocean out into an ellipsoid, or the shape of an egg. We can understand this by remembering that the gravitational force decreases with distance, so the Moon pulls hardest on the ocean facing it, and least on the opposite ocean; the Earth between is pulled with an intermediate force. As a result, the water directly beneath the Moon is pulled up away from the Earth's center, and the Earth's center is pulled away from the water on the opposite side, causing another high tide. Thus the differences of the gravitational attraction of the Moon on opposite sides of the Earth produce two tidal bulges - one facing the Moon and one facing away.

On a slowly rotating planet without continents, the tide would be highest along the line joining the centers of the Earth and Moon, that is, when the Moon is overhead. This is not the case for the Earth. The friction of the continents and the rapid rotation of the Earth carry the ocean's tidal bulge forward so it precedes the Earth-Moon line by about 3 degrees. This means that in the open ocean the high tide actually occurs about 12 minutes after the Moon is overhead.

Fig. .. 

The Sun and the Moon both contribute to the formation of the tides, but the major portion of this rhythmic ebb and flood is driven by the Moon, whose tide is 2.2 times as high as the Sun's. In the course of a month, the changing alignment of the Sun and Moon causes the tides produced by these two bodies to alternately reinforce and interfere, leading to the cycle of spring tides and neap tides. The spring tide occurs near new and full moon, when the Sun and Moon reinforce each other's tides, and the neap tide occurs near first and third quarter, when they interfere with each other. The spring tides can be 2 or 3 times as high as the neap tides. The Sun's tides also vary by a small amount over the year as the Earth travels around its eccentric orbit and the Sun-Earth distance changes, with the greatest solar tides when the Earth is nearest the Sun.

The days are getting longer

As the Earth rotates, the bulge raised on its surface by the Moon's gravity is always a little ahead of the Moon rather than directly under it. The Moon pulls back on the bulge, and in the process it slows the whole planet down. In other words, our planet meets resistance in its daily rotation caused by the tidal interaction of the Moon with the Earth.

As the tides flood and ebb, they create eddies in the water, producing friction and dissipating energy at the expense of the Earth's rotation. The ocean water is heated ever so slightly by the motion of the tides and the Earth's rotation is slowed. The tides therefore act as brakes on the spinning Earth, slowing it by friction in much the way that the brakes of a car slow its wheels and become warm. The friction of tides dissipates energy at the rate of 5 billion horse-power (4 x 1012 watt). Tidal friction is slowing the rotation of the Earth, and the day is becoming longer at a rate of 2 milliseconds, or 0.002 seconds, per century. In other words, the days are getting longer at the rate of one second every 50,000 years, and tomorrow will by 60 billionths of a second longer than today.

Earth's tidal influence on the Moon

The Moon pulls the Earth's oceans, and the oceans pull back, in accord with Newton's third law that every action has an equal and opposite reaction. The net effect is to swing the Moon outward into a more distant orbit. This is because the tidal bulge on the side facing the Moon is displaced ahead of the Moon, and this bulge pulls the Moon forward.

As the Earth slows down, the angular momentum it loses is transferred to the Moon, which speeds up in its orbit around us. It is not hard to see that this will swing the Moon away from the Earth if we look at the key equations. When we do the arithmetic, we find that the change of 0.002 seconds per century in the length of the day implies an outward motion of the Moon amounting to about 0.04 meters per year. Small as it is, this value is just measurable with the laser reflectors planted on the Moon by the Apollo astronauts. The lunar laser ranging data indicate that the Moon is moving away from the Earth at a rate of 0.0382 0.0007 meters per year.

Stabilizing the Earth

The orientation of the Earth's rotation axis causes the annual seasonal variations of our climate, and small variations in its orientation contribute to the advance and retreat of the ice ages. The obliquity of the Earth, the angle that its spin axis makes with the perpendicular to its orbital plane, is now a modest 23.5 degrees, but this is sufficient to bring summer and winter as the northern or southern hemisphere is tilted toward or away from the Sun. Variation in the Earth's obliquity as small as 1.3 degrees, around a mean value of 23.3 degrees, may contribute to, or trigger, the ice ages.

Fig. .. 

The climate forecast for a Moon-less Earth would be a lot bleaker. The gravitational pull of our large Moon acts as an anchor, limiting excursions in the Earth's rotation axis and keeping the climate relatively stable. Without the Moon, the tilt of Earth's spin axis would vary chaotically between 0 and 85 degrees. Such large variations in the planet's obliquity would result in dramatic changes in climate. With an obliquity of 0 degrees, there would be no seasonal variation in the distribution of sunlight on Earth. At 85 degrees, the Earth's axis would be tipped completely over. The equatorial tropics could then be permanently in cold winter snows, and the poles would be alternately pointed almost directly at or away from the Sun over the course of a single year. Such wide climate changes might be hostile to many forms of life on Earth.

(page 8 of 9)

Copyright 2010, Professor Kenneth R. Lang, Tufts University