Oceanography

Tide producing forces

All objects in space exert a gravitational attraction on the oceans, but only the Sun(because of its great mass) and the Moon (because of its promixity / exert sufficient attraction to produce a noticeable bulge of water. Despite its great mass (332,960 x the mass of the Earth), the distance between the Earth and Sun (149,700,000km) reduces the solar tidal attraction to only 46% of the attraction by the Moon. The Moon is much smaller than the Sun [even smaller than the Earth ], but it is closer to the earth and thus exerts a gravitational attraction disproportionately strong for its size.

Centrifugal force is the force directed away from the center of rotation. As the Earth revolves on its axis, centrifugal force attempts to throw objects from the Earth’s surface into space. If earth’s gravity was sufficiently weak or its speed of rotation sufficiently great, objects would be hurled into space. 

As the earth travels in its orbit about the Sun, centrifugal force act on the side of the earth away from the Sun and attempts to fling the Ocean into space. Gravitational attraction between the earth and ocean is greater than centrifugal force and the ocean remains on the earth, but a tidal bulge is produced.

In contrast to common belief, the moon does not revolve about the earth, but rather the earth and moon rotate about a point 4700km toward the moon from the center of the earth. As the earth and Moon revolve around this point, centrifugal force produces a tidal bulge on the side of the earth facing away from the moon. Thus, the Sun and Moon each produce two tidal bulges in the ocean. One pair of bulges is produced by gravitational attraction and the other pair by centrifugal force.

 To understand the tide-producing forces, let us first consider the influence of the moon alone. The earth and the moon form a single system mutually revolving around a common centre of mass. The period of this revolution is 27.3 days. Even though the orbits are slightly elliptical, for simplification they can be treated as circular. So, all points upon the earth follow circular paths, which have same radius and each point will also have the same angular velocity of 2 /27.3 days. Since all the points travel with the same angular velocity and the radio of their circular paths are the same, all points on the earth experience an equal centrifugal force. The total of all centrifugal forces resulting from the motion of the earth-moon system around its common centre of gravity completely balances the forces of gravitational attraction between the two bodies and hence the system as a whole is in complete equilibrium. The centrifugal forces are directed parallel to a line joining the centers of the earth and the moon.

However, the magnitude of the gravitational force exerted by the moon on the earth is not the same at all points on earth, because all these points are not at the same distance from the moon. The gravitational force of the moon is largest at the point E, which is closed to the moon, the weakest at the point A on the earth’s surface, which is farthest from the moon. The gravitational force is dominant on the half of the earth facing away from the moon. In addition, the direction of the moon’s gravitational force at all points will be directed towards the centre of the moon, and therefore will not be strictly parallel to the line joining the centers of the earth and the moon except for those points which on the line joining the centers of the earth and the moon. The combined effect of the centrifugal force and gravitational force is the tide-producing force. Only at the centre of the earth ‘X’ these two forces cancel each other. At all other points on the earth, there will be tide-producing forces.

            Similarly, the sun is also the source of a tide-producing force. Because of the greater distance of the earth from the moon,, the tide-producing force due to sun is smaller than that of the moon. At the tide-producing forces are given by the difference between the gravitational forces and the centrifugal forces, and as these forces depend on the distance of the earth from the sun and the moon, the tide-producing forces will vary according to the changing distances of the sun and the moon from the earth.