the earth's center-of-mass around the center-of-mass of the earth-sun system, in an exactly analogous manner to the earth-moon relationship. The position of this force envelope shifts with the relative orbital position of the earth in respect to the sun. Because of the great differences between the average distances of the moon (238,855 miles) and sun (92,900,000 miles) from the earth, the tide producing force of the moon is approximately 2.5 times that of the sun.
Second, there exists a wide range of astronomical variables in the production of the tides caused by the changing distances of the moon from the earth, the earth from the sun, the angle which the moon in its orbit makes with the earth's equator, the superposition of the sun's tidal envelope of forces upon that caused by the moon, the variable phase relationships of the moon, etc. Some of the principle types of tides resulting from these purely astronomical influences are describe below.
Chapter 4
Variations in the Range of the Tides: Tidal Inequalities
As will be shown in Fig. 6, the difference in the height, in feet, between consecutive height and low tides occurring at a given place is known as the range. The range of the tides at any location is subject to many variable factors. Those influences of astronomical origin will first be described.
1. Lunar Phase Effect: Spring and Neap Tides. It has been noted above that the gravitational forces of both the moon and sun act upon the waters of the earth. It is obvious that, because of the moon's changing position with respect to the earth and sun (Fig. 3) during the monthly cycle of phases (29.53 days) the gravitational attraction of moon and sun may variously act along a common line or at changing angles relative to each other.
When the moon is at new phase and full phase (both positions being called syzygy) the gravitational attractions of the moon and sun act to reinforce each other. Since the resultant or combined tidal force is also increased, the observed high tides are higher and low tides are lower than average. This means that the tidal range is greater at all locations which display a consecutive high and low water. Such greater-than-average tides resulting at the syzygy positions of the moon are know as spring tides - a term which merely implies a "welling up" of the water and bears no relationship to the season of the year.
At first- and third-quarter phases (quadrature) of the moon, the gravitational attractions of the moon and sun upon the waters of the earth are exerted at right angles to each other. Each force tends in part to counteract the other. In the tidal force envelope representing these combined forces, both maximum and minimum forces are reduced. High tides are lower and low tides are higher than average. Such tides of diminished range are called neap tides, from a Greek word meaning "scanty".
2. Parallax Effects (Moon and Sun). Since the moon follows an elliptical path (Fig. 4), the distance between the earth and moon will vary throughout the month by about 31,000 miles. The moon's tide-producing force acting on the earth's waters will change in inverse proportion to the third power of the distance between the earth and moon, in accordance with the previously mentioned variation of Newton's Law of Gravitation. Once each month, when the moon is closest to the earth (perigee), the tide-generating forces will be higher than usual, thus producing above-average ranges in the tides. Approximately two weeks later, when the moon (at apogee) is farthest from the earth, the lunar tide-raising force will be smaller, and the tidal ranges will be less than average. Similarly, in the earth-sun system, when the earth is closest to the sun (perihelion), about January 2 of each year, the tidal ranges will be enhanced, and when the earth is farthest from the sun (aphelion), around July 2, the tidal ranges will be reduced.
When perigee, perihelion, and either the new or full moon occur at approximately the same time, considerably increased tidal ranges result. When apogee, aphelion, and the first- or third-quarter moon coincide at approximately the same time, considerably reduced tidal ranges will normally occur.
3. Lunar Declination Effects: The Diurnal Inequality. The plane of the moon's orbit is inclined only about 5o to the plane of the earth's orbit (the ecliptic) and thus the moon monthly revolution around the earth remains very close to the ecliptic. The ecliptic is inclined 23.5o to the earth's equator, north and south of which the sun moves once each half year to produce the seasons. In similar fashion, the moon, in making a revolution around the earth once each month, passes from a position of maximum angular distance north of the equator to a position of maximum angular distance south of the equator during each half month. (Angular distance perpendicularly north and south of the celestial equator is termed declination.) twice each month, the moon crosses the equator. In Fig. 5, this condition is shown by the dashed position of the moon. The corresponding tidal force envelope due to the moon is depicted, in profile, by the dashed ellipse. |
