## Tide-Causing Forces

November 11th, 2005

For thousands of years, humans have noted a relationship between the patterns of the tides and the phases of the moon. Sir Issac Newton was the first to formalize this relationship into a mathematical “model” based on his equation for the gravitational attraction of planetary bodies (a function of the products of their mass divided by the square of their distance). Yet teaching of Newton’s equilibrium model of the tides (and perhaps even understanding of it) often gets jumbled, especially where explanations of tidal bulges directed away from the moon (or sun) are concerned. Here’s my attempt to get it right.

First, we know that the gravitational attraction between the sun and the Earth is greater than the gravitational attraction between the moon and the Earth. Earth orbits the sun, not the moon, eh? Yet the moon has twice the effect on tides as the Earth. Why? It turns out that the tide-causing forces come from the gradient of differences in the gravitational forces at various points on the Earth. In other words, the change or difference in the gravitational force of the moon (or sun) from point to point on the Earth is what is responsible for the tides. More formally, it is the deriviative of the gravitational force, dF, across the radius (r) of the Earth, dr, that gives rise to the tides. If we do the calculus and simplify, we find that the tidal forces are roughly proportional to the product of the masses of the attracting bodies divided by the cube of the distance between them. You can easily look up the masses and the distances and do the math to convince yourself that the tidal force of the sun is about half that of the moon (because distance cubed for the sun is such a large number).

The mathematics get a bit complicated but if you calculate the differential tidal forces across the sphere of the Earth, you will find forces directed towards the attracting body and away from the attracting body. One way to think about this is to imagine a hollow rubber ball (or a balloon) sitting on a table that you press down upon. As you press down, the ball elongates in two directions. Of course, the moon (or sun) doesn’t push down on the top of the Earth, but the tidal forces do include vertical components directed inwards. As a result, tidal forces compress and elongate the Earth. The Earth actually experiences daily tides as a result of tidal forces. moving ever so slightly (imperceptibly but measurably). When we add water to the Earth’s surface (assuming no continents), the lack of tensile strength of water (as opposed to Earth) makes the vertical components (the pushing and pulling) very weak. But the horizontal or tangential components of the tidal forces do move water and they move water towards the location beneath the attracting body and away from the attracting body (on the other side of the Earth). To summarize, it is the differential tidal forces-the gradient of variations in the moon’s or sun’s gravity at different points on Earth-that cause horizontal movements of water to locations beneath and away from the attracting body. The water piled up in these two locations is referred to as the tidal bulges (often terribly exagerrated in illustrations).

Note that we have described the causes of the tides with no mention of a moving Earth. That’s because tides would occur even if the Earth, moon and sun were static (admitedly impossible but significant, nonetheless). An explanation of tides does not require the Earth pulling away from the water, it does not require a centrifugal force and it certainly does not require the moon (or sun) to pull water upwards off the surface of the Earth. Tides occur simply because gravitional attraction varies over Earth’s surface.

Generation of the tidal bulges combined with Earth’s rotation give rise to the semidiurnal patterns of tides observed across much of the Earth. Throw in declination, the degree of “elevation” of the moon or sun relative to the equator, and you can derive an explanation for mixed and diurnal tides, too. Of course, the orbit of the moon around the Earth every 27.3 days (29.5 to return to a position in line with the sun, i.e., a tidal month) and the orbit of the Earth around the sun every 365 days generate monthly, annual, decadal and multidecadal patterns to the tides. In fact, a complete orbital cycle of the moon (ending where it started) takes 18.6 years, which is why NOAA bases its National Tidal Datum on 19 years, the National Tidal Datum Epoch.

## The Patterns of the Tides

November 11th, 2005

The daily fluctuations of sea level known as the tides exhibit characteristic patterns. Along the east coast of the United States, the tides rise and fall twice daily with nearly equal height, a daily pattern called semidiurnal tides. The west coast of North America also experiences two tides a day yet the highs and lows vary in height, a daily pattern called mixed semidiurnal tides. In the Gulf of Mexico, one high tide and one low tide mark the day, a daily pattern called diurnal tides. Superimposed upon these daily patterns are the monthly patterns that occur in response to the orbital motion of the moon, generating extreme tidal ranges or spring tides when the moon-earth sun are aligned, and minimal tidal ranges when these three planetary bodies form a 90-degree angle.

The patterns of the tides occupy today’s lecture. Knowledge of these patterns sets the stage for our discussion of the astronomical causes of the tides in our next lecture. Click here for today’s podcast .

## Oceanography in the 21st Century

November 2nd, 2005

In the mid-1970s, oceanography experienced a quiet but radical revolution. The discovery of smaller-than-small phytoplankton, the creation of satellite maps of the ocean’s complex surface tapestry of temperature and chlorophyll, and the encounter with hydrothermal vents and giant worms set the stage for 21st century oceanography. These discoveries dramatically changed the way oceanographers studied the world ocean ocean and the technologies used to study it. The development of robotic vehicles (ROVs and AUVs), the deployment of sensor-laden floats that descend and rise in the water column, the launch of improved, higher resolution satellite sensor systems, the anchoring of moored sensor platforms at key locations, and the design of global ocean observatories are but a few of the technologies now focused on understanding the ocean. In a few short decades, oceanography was transformed from a highly research-based discipline to a research and operational one, much like meteorology.

Despite the dependence on technology, 21st century oceanography continues to embody the spirit of exploration that drove early oceanographers across the deep-blue sea. Scientist/explorers like Craig Ventner, John Delaney and Tommy Dickey are among the many men and women who passionately pursue knowledge about the ocean. To coin a Star Trek phrase, they boldly go where no one has gone before. For many of us, that spark was ignited by The Undersea World of Jacques Cousteau, the the person most responsible for bringing public awareness to the undersea world and its remarkable inhabitants.

To hear more about oceanography in the 21st century, check out my podcast of a seminar presented on November 1, 2005, at the Continuing Learning Experience (CLE) “Oceans Around Us” series at Cal State Fullerton in Fullerton, California.

## The World Ocean Freeway System

October 26th, 2005

Like a freeway system, the world ocean circulation distributes energy, materials and organisms far and wide. Humans have long sought knowledge of the surface circulation for monetary or military gain. Modern efforts to understand the world ocean circulation focus on climate change, weather forecasting and now- and forecasts of ocean conditions.

Today’s lecture focuses on the processes that generate the surface circulation of the world ocean. Click here for today’s podcast .

## Global Warming and Humans

October 21st, 2005

Here I begin a discussion of the greenhouse effect and evidence for global warming, including melting of the Arctic ice cap. This lecture was followed by two lectures devoted to the NOVA/Frontline video “What’s Up With the Weather” produced in 2000.

## Why the Ocean is Blue

October 21st, 2005

Here I discuss my favorite topic: light and its propagation through the upper ocean. Light is fundamentally important to many processes, including heating, climate change, habitat definition and photosynthesis.

## The Concept of Density

October 21st, 2005

Here I discuss density and the factors that affect it in the world ocean.

## Salts: Sources and Sinks

October 20th, 2005

Here I discuss why the ocean is salty.

## Explore the Seafloor

September 23rd, 2005

Take a journey to the bottom of the sea.