# Gravitation Causes Tides on Earth

by Ron Kurtus (7 September 2010)

Tides are periodic rise and fall of sea levels, as seen in a specific location on the shore. They are caused by the gravitational forces from the Moon and Sun that attract the ocean water toward them and away from other areas in the ocean.

The rotation of the Earth and the position of the Moon cause the level of the tide to change in a given location. There are two high and low tides each day.

Although you would think the rise in water would only occur on the side toward the Moon and Sun, high tides actually occur on opposite sides of the Earth, caused by a gravitational differential.

The orientation of the Moon and Sun with respect to the Earth determine when the highest and lowest tides occur, as well as when the moderate tides occur. At the times of the month when the Moon and Sun are aligned, their combined gravitational pull cause the highest tides. The lowest tides are seen at locations on Earth at right angles to the alignment of the Moon and Sun.

Questions you may have include:

• What causes tides?
• Why are there high tides on both sides of the Earth?
• What role does the alignment of the Moon and Sun have on the tides?

This lesson will answer those questions. Useful tool: Units Conversion

## Gravitation and tides

If you live near the ocean, you have probably seen the rise and fall of the sea level that happens twice a day. When the sea level is above normal, it is called the high tide. Similarly, low tide is when the sea level on the shore is below normal.

### Gravitation from Moon

The gravitational pull on the water from the Moon is the primary cause of the rising tide. Gravitation from the Sun also can contribute to the height of the tide. Centrifugal force on the water from the Earth's rotation also provides a small contribution to the tides.

The gravitational attraction between the Earth and the Moon is F = 1.99*1020 N (See Gravitational Force Between Two Objects for the calculations). That force is sufficient to slightly distort the solid surface of both objects toward each other.

### Water level rises

Since shape of a body of water can easily be changed, the force from the Moon pulls the ocean toward it a maximum of about one meter. In some areas where the shore inclination is shallow, a one meter change in sea level can result in even a 10 meter or 40 foot rise in the tide along the shoreline.

1 meter rise results in several meter rise in tide

### High tide every 12 hours 25 minutes

Since the Earth rotates on its axis, the Moon appears to orbit the Earth and is over head every 24 hours and 50 minutes. The extra 50 minutes is a result of the Moon's 27 day actual orbit around the Earth.

Force from Moon pulls ocean toward it

Although the Moon is overhead every 24 hours and 50 minutes, the high tide comes every 12 hours and 25 minutes. One high tide corresponds to when the Moon is overhead and the other high tide is when the Moon is on the opposite side of the Earth.

## Cause of tides on both sides

Since the tides are primarily caused by the gravitation of the Moon acting on the oceans and pulling the surface of the water toward the Moon, you would think the shape of the oceans would be pulled toward the Moon, as opposed to having a high tide on both sides of the Earth. In fact, the configuration seems counter-intuitive.

### Simple explanation

A simple explanation for the double tides is that normally a fluid or liquid in space will take on a spherical shape. When you pull or apply a force on one side, the sphere elongates into an oval shape.

Thus, when the Moon pulls the water toward it, the action causes a high tide or bulge on the side of the Earth facing the Moon. But also, the Moon is pulling on the Earth and causes it to move slightly toward it and away from the ocean on the opposite side. This results in the high tide on the side away from the Moon.

Although this explanation is somewhat correct, it really isn't very satisfying.

### Theory of the tidal configuration

A more sophisticated explanation is the theory of the tidal configuration which states that the various parts of the Earth's ocean are attracted toward the Moon, according to their separation from the Moon, as well as the angle to the Moon's center. This is also called a gravitational differential.

The force of attraction of the water on the side of the Earth that is closer to the Moon is greater than that on the far side of the Earth. This is represented in the illustration below by the force-line arrows or vectors.

Moon attracts ocean and Earth toward it

But also, the Moon is attracting the mass of the Earth toward it. This can be approximated by considering the mass of the Earth concentrated at its center of mass (CM). This approximation is explained in the Universal Gravitation Equation lesson. The heavy vector represents the attraction of the Earth's mass toward the Moon.

If you subtract the force of attraction on the Earth's center of mass from each of the vectors or force lines to the Moon, the resulting forces on the ocean water are toward and away from the Moon on the ends and moving inward on the sides.

Subtraction of vectors results in double bulge

## Tides and orientation of Moon and Sun

Although the gravitational pull from the Moon is the major factor in the creation of the tides, gravitation from the Sun also affects the height of the tide.

When the Sun and the Moon are aligned on the same side of the Earth, it is called a New Moon. With this configuration, the gravitational forces combine and cause a very high tide known as a spring tide. The name has nothing to do with the season and actually occurs slightly after the Moon is overhead, due to the inertia of the ocean and the rotation of the Earth.

When the Sun and Moon are on opposite sides of the Earth, each contributes a pull on the water, resulting in another spring tide. The two spring tides occur two weeks apart.

Alignment of Sun and Moon for spring tides

When the Moon is located at a right angle to the Sun with respect to the Earth, it is called the first quarter or third quarter Moon. In such a case, the difference between the high tide and low tide is much smaller, since the gravitational forces cancel each other. These low tides are called neap tides.

Since the orbit of the Moon around the Earth is elliptical, once every 1.5 years the Moon is closest to the Earth. This situation results in an unusually high tide called the proxigean spring tide.

## Summary

Tides are periodic rise and fall of sea levels that are caused by the gravitational forces of the Moon and Sun on the oceans. There are two high and low tides each day.

High tides occur on opposite sides of the Earth, as do low tides, according to the theory of the tidal configuration. The orientation of the Moon and Sun with respect to the Earth determine when the highest and lowest tides occur, as well as when the moderate tides occur.

You have potential

## Resources and references

Ron Kurtus' Credentials

### Websites

Saltwater Tides - Predictions of tides in various U.S. states

Moon Tides - How the Moon affects ocean tides

Tides - Wikipedia

Ocean Tides - NASA - Ocean Motion

Gravitational Tides - Astronomy 221 - Case Western Reserve University

Gravitation Resources

### Books

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