Modeling the Tides

Have you ever wondered how the tides work?  This project involves using information available on the Internet to investigate this question.

A good place to start is the National Oceanic & Atmospheric Administration's Tides Online site:
or their National Ocean Service site:
where you can search for "tides."  This will bring up a number of resources including a glossary of terms under "t"

This will lead to the excellent article:


This assignment supplements reading this article with answering various questions.

1. What is the definition of tide as relates to both ocean?  How is it different from tidal flow?

Tide is the relatively short-period, astronomically induced vertical change in the height of the sea surface (exclusive of wind-actuated waves and swell); the expression tidal current relates to accompanying periodic horizontal movement of the ocean water, both near the coast and offshore (but as distinct from the continuous, stream-flow type of ocean current).

2.  What are the sublunar and subsolar points?  What path(s) do these points take over the course of a day?

Ans:  The subsolar and sublunar points are the points on the surface of Earth that is closest to Sun and Moon, respectively.  Over the course of a day, the subsolar point will traverse the solar ecuator, while the sublunar point will traverse an analogous great circle that may as well be dubbed the lunar ecuator.

3.  Approximate the magnitudes of the three largest (instantaneous) astronomical forces acting on you at this moment, in Newtons.  In what directions do these forces act? Under what circumstance would all three forces point in the same direction?  Note: many relavant facts are at  You fill also need the formula for gravitational force field of a mass M whose center is a distance r:

In order of decreasing magnitude the forces acting on you at any particular time are the force of the Earth's gravity, which is

Our sun exerts the next strongest gravitational force on you, roughly

While the force of the moon is

4.  Why is it that the earth's gravitational attraction at the earth's surface is a thousand times greater than that of the moon, and yet it is the existence of the moon that has the greater influence on the tides?  Similarly, why is it that the sun's gravitation at the earth's surface is 100 times greater than that of the moon, and yet the moon has a greater influence on the tides?
Hint:  the information you need to answer the second question is in chapter three of the Our Restless Tides article.

5.  Read the 1969 Encyclopedia Britannica article on the history of tides here. Who established the principle of forced oscillations, which forms the foundation of the harmonic methods?  In general terms, how do these methods work?

6. Read the 1969 Encyclopedia Britannica article on tide-generating forces here.  What is the equilibrium form of the tide, and why is it useful in modeling tides?  What simplifying assumption(s) are involved?

7.  What is the diurnal inequality?

8.  What is the anomalistic month?

9. What are the three major species of tidal constituencies?

10.  Experiment with different values from the table of tidal constituencies in various harmonic combinations of the form .

Extra credit: check out these web sites: