# Calculation of the Magnitude of Lunar and Solar Tidal Forces on the Earth

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This page first made public: Jul 25, 2006

#### Summary

Extra-credit project in which students calculate the magnitude of lunar and solar tidal forces on the earth. Students find physical and orbital parameters about the earth, moon, and sun. They use these parameters in four applications of Newton's law of universal gravitation to calculate the difference in lunar gravitational attraction across the earth and the difference in solar gravitational attraction across the earth. Students use these differences to demonstrate that the solar tidal effect is about 46% that of the lunar tidal effect on the earth. They calculate the relative magnitude of the solar tidal effect to the combined solar/lunar tidal effect for spring-tide conditions. Students draw five process diagrams prior to any calculations.

## Learning Goals

2. Students learn how to find information on the internet about solar system orbital parameters and physical data.

3. Students diagram the forces acting on the earth before calculating the magnitude of these forces.

4. Students learn how to calculate the tidal influence of the sun and moon on the earth.

5. Students enhance their analytical, synthetic, and critical thinking skills.

## Context for Use

2. As an extra-credit project, class size is not so important. However, freshman students will require considerable guidance, so the professor should expect to offer a problem-solving session or dedicate several office hours for this purpose.

3. Students need to know how use the scientific-notation function on their scientific calculator.

## Description and Teaching Materials

Newton's law of universal gravitation

Value of the gravitational constant, G

Orbital radius of the earth (semi-major axis)

Mass of the earth

Radius or diameter of the earth

Mass of the moon

Orbital radius of the moon (semi-major axis)

Mass of the sun.

II. Course textbook: fundamental explanation of the tidal effect.

Frank Stacey's "Physics of the Earth" offers a first-order analysis of the tidal force exerted by the sun and moon on the earth and shows how this force can act to deform the earth into the approximate shape of a prolate ellipsoid.

Google and wikipedia are online resources that point to qualitative and simple quantitative explanations of the various approaches to understanding the forces which cause the tidal effect.

III. Newton's approach is used to calculate the tidal effect. This approach assumes that the gravitational force provides a sufficient explanation for the tidal effect. Tidal Forces (Rich Text File 17kB Jun28 06)

## Teaching Notes and Tips

2. Roman numeral II on the assignment sheet should be completed and reviewed by the instructor prior to student progressing to Roman numeral III.

3. Students should have one week to complete the project.

## Assessment

2. Right or wrong answers.

3. Students must show their detailed calculations.

## References and Resources

2. http://tidesandcurrents.noaa.gov/restles3.html provides detailed diagrams about the forces which induce the tidal effect.

3. Earth Science: Understanding Environmental Systems, 2003, McGraw-Hill, by Edgar W. Spencer, pp. 212-215. Student's textbook. Briefly explains the problem to be solved.

4. Physics of the Earth, 1992, 3rd ed., Brookfield Press, by Frank D. Stacey, pp. 83-90, 115-118. Provides detailed background information about the problem to be solved. Mathematically advanced.

5. Google provides links to qualitative and simple quantitative explanations of the tidal effect.