Factors Affecting Tides

The rise and fall of the tides has a profound effect on life on planet Earth. As long as there have been coastal communities that depend on the sea for sustenance, people have timed their food-gathering activities to be in harmony with the tides. For their part, marine plants and animals have adapted to the cyclical ebb and flow in numerous ingenious ways.

Gravitation causes the tides, but the tidal cycle isn't synchronized to the movement of any single heavenly body. It's easy to imagine that the moon's what affects the ocean's tides on Earth, but it's more complicated than that. The sun also affects the tides.

Even other planets, such as Venus and Jupiter, exert gravitational influences that have a minuscule effect. Put all these influences together, though, and even they can't explain the fact that any given point on Earth experiences two high tides a day. That explanation requires an appreciation of how the Earth and moon orbit around each other.

It's an idealization to consider the tides as the result solely of gravitational forces. The weather patterns on Earth, along with the structure of the planet's surface, also influence the movement of water in its ocean basins. Meteorologists must take all these factors into account when predicting the tides for a particular locality.

When you think of Sir Isaac Newton, you may picture the familiar image of the English physicist/mathematician being struck on the head by a falling apple. The image reminds you that Newton, drawing from the work of Johannes Kepler, formulated the Law of Universal Gravitation, which was a major breakthrough in our understanding of the universe. He used that law to explain the tides and refute Galileo Galilei, who believed tides were the solely the result of the motion of the Earth around the sun.

Newton derived the law of gravitation from Kepler's third law, which states that the square of a planet's period of rotation is proportional to the cube of its distance from the sun. Newton generalized this for all bodies in the universe, not just the planets. The law states that, for any two bodies of mass _m₁ and m₂, separated by a distance r, the gravitational force F_ between them is given by:

_F = Gm₁m₂/r²_

where G is the gravitational constant.

This immediately tells you why the moon, which is so much smaller than the sun, has more effect on Earth's tides. The reason is that it's closer. The gravitational force varies directly with the first power of mass but inversely with the second power of distance, so the separation between two bodies is more important than their masses. As it turns out, the sun's influence on the tides is about half that of the moon.

Other planets, being both smaller than the sun and more distant than the moon, have negligible effects on tides. The effect of Venus, which is the closest planet to Earth, is 10,000 times less than that of the sun and moon together. Jupiter has even less influence – about one-tenth that of Venus.

The Earth is so much larger than the moon that it appears that the moon orbits around it, but the truth is that they orbit around a common center, known as the barycenter. It's about 1,068 miles below the Earth's surface on a line that extends from the center of the Earth to the center of the moon. The Earth's rotation around this point creates a centrifugal force on the surface of the planet that is the same at every point on its surface.

A centrifugal force is one that pushes a body away from the center of rotation. much as water is flung away from a rotating sprinkler head. On a random point – point A – on the side of the Earth facing the moon, the moon's gravity is felt the strongest, and gravity combines with the centrifugal force to create a high tide.

However, 12 hours later, the Earth has turned, and point A is at its farthest distance from the moon. Because of the increase in distance, which is equal to the Earth's diameter (almost 8,000 miles or 12,874 km), point A experiences the weakest lunar gravitational attraction, but the centrifugal force is unchanged, and the result is a second high tide.

Scientists depict this graphically as a an elongated bubble of water surrounding the Earth. It's an idealization, because it assumes the Earth is uniformly covered in water, but it provides a workable model of the tidal range due to the moon's gravitation.

At the points separated from the Earth-moon axis by 90 degrees, the normal component of the moon's gravitation is sufficient to overcome the centrifugal force, and the bulge flattens. This flattening corresponds to low tides.

The imaginary bulge surrounding the Earth is approximately an ellipse with semi-major axis along the line that connects the center of the Earth to the center of the moon. If the moon were stationary in its orbit, each point on Earth would experience high tides and low tides at the same time each day, but the moon isn't stationary. It moves 13.2 degrees each day relative to the stars, so the orientation of the major axis of the bulge also changes.

When a point on the major axis of the bulge completes a rotation, the major axis has moved. It takes the Earth about 4 minutes to rotate through a single degree, and the major axis has moved by 13 degrees, so the Earth has to rotate for an extra 53 minutes before the point will be back on the major axis of the bulge. If the moon's orbital movements were the only factor influencing the tides (spoiler alert: it isn't), the high tide would occur 53 minutes later each day for a point on the equator.

In terms of the the moon's effect on tides, two other factors affect the timing of the tides as well as the height of the water.

• The inclination of the moon's orbit: The moon's orbit is inclined about 5 degrees relative to the Earth's orbit around the sun. This means that its effects are sometimes felt more strongly in the Southern Hemisphere and at other times more strongly in the Northern Hemisphere. 

• The elliptical nature of the moon's orbit: The moon doesn't orbit in a circular path, but an elliptical one. The difference between its closest approach (perigee) and its farthest distance (apogee) is about 50,000 km (31,000 miles). The first high tide tends to be higher than normal when the moon is at perigee, but the one 12 hours later tends to be lower. 

The sun's gravitation creates a second bulge in the imaginary bubble surrounding Earth, and its axis is along the line that connects the Earth to the sun. The axis advances about 1 degree per day as it follows the sun's apparent position in the sky and is about half as elongated as the bubble created by the moon's gravitation.

In the Equilibrium Theory of Tides, which gives rise to the tidal bubble model, superimposing the bubble created by the moon's gravitation and that created by the sun's gravitation should provide a way a predict the daily tides in any locality.

Things aren't that simple, however, because the Earth isn't covered by a giant ocean. It has land masses that create three ocean basins connected by fairly narrow passageways. However, the sun's gravitation does combine with that of the moon to create bi-monthly peaks in the heights of the tides around the world.

Spring tides and neap tides: Spring tides have nothing to do with the season of spring. They occur at new moon and full moon, when the sun and moon are aligned with the Earth. The gravitational influences of these two heavenly bodies combine to produce unusually high tidal waters.

Spring tides occur, on average, every two weeks. Approximately one week after each spring tide, the Earth-moon axis is perpendicular to the Earth-sun axis. The gravitational effects of the sun and moon cancel each other, and the tides are lower than usual. These are known as neap tides.

Besides the three main ocean basins – the Pacific, Atlantic and Indian oceans – there are several smaller basins, such as the Mediterranean Sea, the Red Sea and Persian Gulf. Each basin is like a container, and as you can see when you tilt a glass of water back and forth, water tends to slosh between the walls of a container. The water in each of the world's basins has a natural period of oscillation, and this can modify the gravitational tidal force of the sun and moon.

The period of the Pacific Ocean, for example, is 25 hours, which helps explain why there is only one high tide per day in many parts of the Pacific. The period of the Atlantic Ocean, on the other hand, is 12.5 hours, so there are generally two high tides per day in the Atlantic. Interestingly, in the middle of large water basins, there are often no tides, because the natural oscillation of water tends to have a zero point at the center of the basin.

Tides tend to be higher in shallow water or in water that enters a confined space, such as a bay. The Bay of Fundy in the Canadian Maritimes experiences the highest tides in the world. The shape of the bay creates a natural oscillation of water that forms a resonance with the oscillation of the Atlantic ocean to produce a height difference of almost 40 feet between high and low tide.

Before adopting the name tsunami, which means "big wave" in Japanese, oceanographers used to refer to the large movements of water that follow earthquakes and hurricanes as tidal waves. These are basically shock waves that travel through the water to create devastatingly high water at the shore.

Sustained high winds can help drive water toward the shore and create high tides known as surges. For coastal communities, these surges are often the most effects of tropical storms and hurricanes.

This can work the other way as well. Strong offshore winds can push water out to sea and create unusually low tides. Large storms tend occur in areas of low air pressure, called depressions. Gusts of air rush in from high-pressure air masses into these depressions, and the gusts drive the water.