The Effects of Tidal Friction

If the movement of water on the surface of the Earth encountered no friction, the tidal bulges would remain along the Earth-Moon line as the Earth rotated beneath it. But there is friction, especially in shallow sea basins. This causes the tidal bulge of the Earth to be carried forward of the sublunar point by 2-3°, as Figure 4.12 illustrates (that is, the bulge precedes the Moon).

The Moon's gravitational attraction on the near-side tidal bulge of the Earth slightly exceeds that on the far side of the Earth. The result is that the Earth is very slightly braked in its rotation. At the same time, the nearer tidal bulge on the Earth accelerates the Moon forward in its orbit to a greater extent than the bulge on the far side retards it. This accel-

25 As any navigator knows, the height and effects of "high water" and "low water," which occur roughly twice each as the Earth rotates under the Moon, are complicated by local currents, monsoon, or other seasonal occurrences, by the presence of local land masses, and by the shal-lowness of the water. For current purposes, however, this level of discussion will suffice.

Figure 4.12. The tidal bulge is carried forward of the sublunar point by about 2° due to tidal friction. The direction of the Earth's rotation is shown as viewed from the north celestial pole. Drawing by E.F. Milone.

eration has the effect of increasing the Moon's distance (by an amount between 3 and 6cm/year). As the Moon recedes, its mean angular motion decreases with time, and this slowing down causes departures from positions predicted from lunar and planetary theory. Thus the slowing of the Earth's rotation is accompanied by a slowing of the Moon's orbital motion. This affects the timing of events involving the Moon, and departures from predicted times of those events are observed (see §5 for descriptions of those events). From them, the rotation deceleration can be computed. The basis for the computation is the conservation of angular momentum. The angular momentum gained by the Moon is roughly lost by the Earth; however, the expressions are complicated by the friction involving the tidal effects of the Sun.

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