## Introduction

Tides, by definition, is the vertical motion of a mass of water caused by differential forces which includes centrifugal force, gravitational force etc.  In this project, we are going to explore the how the tides is formed, how its formation relate to one of the significant laws in the world -- Newton's Law, different types of tides, and some important effects caused by the tides.

### Earth-Moon System and Earth-Sun System

Before looking into the tides, we should have some basic idea of the rotation and orbit for the Earth and the Moon and the relationship between them.

By observation, people always have a wrong idea that the Moon rotates around the Earth.  However, both planets actually revolve together around a common point -- the center of mass for the Earth-Moon System.  Both the Earth and the Moon are attracted to each other by the gravitational forces which avoid escaping from its orbits.  Simultaneously, the existence of centrifugal forces -- created by the individual rotation of the planet around the center of mass of the system -- separate these two bodies with a constant distance.  Likewise, the gravity and the centrifugal forces exists in the Earth-Sun system produced by the revolution of the center of mass of the Earth around the center of mass of the system.

### A Simple Physical Model for Tides

Let us have a look to the most significant matter that results the tides -- the Moon.

Figure 1. The Moon's Gravitational Force applied to the Earth

The above illustration shows that the Moon exerts the gravitational force to the Earth and results the tides.  The strength of the gravity from the Moon to the Earth varies with different points on the Earth.  The Moon's gravity pulls on the near side of the Earth more strongly than the Earth's center. These forces cause the Earth to be distorted.  Compare to the ocean, the body of the Earth is much more rigid, so the distortion on the Earth's body is not that much.  Then the ocean is deformed into a tidal bulge on the side near the Moon.

Realistically, the tides is formed by a different kind of forces acting on the fluid mass (ocean) of the Earth, but not only the Moon's gravitational forces.