The tide-generating force is produced by the combination of (1) the gravitational attraction between Earth and the moon and sun, and (2) the rotation of the Earth-moon and Earth-sun systems. Forces combine to deform Earth’s ocean surface into a roughly egg-shape with two bulges. One ocean bulge faces towards the moon and the other is on the opposing side of the planet, facing away from the moon (figure below). A similar interaction between Earth and sun produces two other ocean bulges that line up towards and away from the sun.
According to Isaac Newton (1642 - 1727), the gravitational attraction between two bodies is directly proportional to the product of the masses of the two bodies and inversely proportional to the square of the distance between them. Simply put, the greater the mass, the greater is the force of attraction whereas the greater the distance, the smaller the force of attraction. Although the sun is 27,000,000 times more massive than the moon, the moon is much closer to Earth and for that reason has a greater gravitational pull on Earth. In fact, the tide-generating force of the moon on the Earth is more than twice that of the sun on the Earth. For now, we will ignore the influence of the sun and focus on the moon.
The gravitational pull of the moon on Earth is primarily responsible for the bulge in the ocean surface that is directly under the moon. On the opposing side of the planet, the gravitational pull is weaker and the rotation of the Earth-moon system is primarily responsible for the tidal bulge. Earth and moon revolve around a common center of mass. Because Earth is much more massive than the moon, the center of mass of the system is within 4700 kin (2900 mi) of Earth's center, that is, 1700 km (1060 mi) below the Earth's surface. This has been likened to a see- saw with an adult seated at one end and a child at the other end. The pivot point (center of mass of the adult-child system) must be moved toward the adult for the two individuals to balance the seesaw.
Newton's first law of motion predicts that a net force must operate in any rotating system and this net force in the rotating Earth-moon system gives rise to the tidal bulge on the side of the planet opposite the moon. Recall from Chapter 4 that according to Newton's first law of motion, an object in constant straight-line motion remains that way unless acted upon by an unbalanced (net) force. Ina rotating system, the net force confines an object to a curved (rather than straight) path. Consider an analogy. Suppose that you are a passenger in an auto that rounds a curve at high rate of speed. You feel a force that pushes you outward from the turning auto. Actually, you experience the tendency for your body to continue moving in a straight path while the auto follows a curved path. In the same way, the rotation of the Earth-moon system causes the ocean to bulge outward on the side of the planet opposite the moon.
So far in our discussion of tide-generating forces, we have used the equilibrium model of tides, which assumes a frictionless Earth entirely covered by water. With this model, ocean bulges would always align with the celestial body that caused them. Furthermore, any location on the planet that is moved by Earth's rotation through the bulges would experience rising and falling sea level (i.e., tides). If only one celestial body (moon or sun) were present, each day a low-latitude locality would experience two high tides (when bulges pass) and two low tides (when halfway between the bulges). If the positions of the Earth and the other celestial body remained the same in space the period of these waves would be the time it takes for one half a rotation of Earth, about 12 hrs.
While Earth is rotating, however, the moon is revolving around Earth. The moon revolves around Earth once each lunar month (averaging 29.5 days, between new moons) and in the same direction as Earth's daily rotation. Hence, Earth must make more than a full rotation in order for a specific location on the planet to line up again with the advancing moon. Catching up with the advancing moon requires 24 hrs plus 1/29.5 of a day, which is approximately 24 hrs and 50 min. This moon-based day (24 hours, 50 minutes) is also called the tidal day. Because the tidal day is longer than the solar day, the times of high and low tide change by about 50 minutes from one solar day to the next.
The ocean's tidal bulges produced by the moon remain in the same alignment relative to the moon, but change their latitudinal (north-south) positions on Earth from day to day as they follow the moon during its monthly revolution about Earth. The plane of the moon's orbit is inclined by 5 degrees to Earth's equatorial plane so that during one lunar month, the moon's latitudinal position moves from directly over the equator northward to 28.5 degrees N (5 degrees beyond the Tropic of Cancer), back to the equator, on southward to 28.5 degrees S (5 degrees beyond the Tropic of Capricorn), and then back to the equator where another cycle begins.
When the moon is at its maximum latitudinal position, the center of one tidal bulge is just north of the Tropic of Cancer and the center of the other tidal bulge is on the other side of the planet just south of the Tropic of Capricorn. Consequently, a location along or near the Tropic of Cancer or the Tropic of Capricorn experiences only one significant tidal bulge in 24 hrs.
Sun-related ocean tidal bulges are produced in the same way as those caused by Earth-moon interactions. That is, the gravitational attraction between Earth and sun plus Earth's annual revolution around the mutual center of mass of sun and Earth generate a second set of similar but smaller tidal bulges that are aligned with the sun. As noted earlier, because of the sun's much greater distance from Earth, the sun's tidal pull on the ocean is less than half (about 46%) of the moon's tidal pull. These tidal bulges follow the sun (just as moon-related bulges track the moon), their latitudinal positions changing as Earth follows its yearly orbit about the sun.
The tide-generating force diminishes rapidly with increasing distance so that celestial bodies at greater distances from Earth than the sun are too far away to exert a significant tidal pull on Earth's ocean. The tide-generating force (arising from a combination of gravitational and rotational forces) is inversely proportional to the cube of the distance between Earth and any other celestial body. Hence, doubling the distance between two bodies reduces the tide-generating force by a factor of 2 or 8 times.
Adapted from DataStreme Ocean and