For many years, people have been puzzled by the idea of gravity. Even today the ultimate nature of gravity remains a mystery. However, the basic properties and effects of gravity are easy to describe and have many useful applications.

One typical physics experiment is to measure the acceleration of gravity near the surface of the earth. Although gravitational acceleration varies slightly from place to place, it is referred to simply as "g". The value of "g" depends, first of all, on the latitude where the observation is made. Secondly, it depends on the elevation above sea level. A third factor is the type of material present under the ground. These variations in the acceleration of gravity have important practical applications, most notably, in oil and mineral exploration.

In this lesson, students will learn how gravity values differ throughout the United States by accessing information about gravity measurements on the Internet.

This activity is designed for a high school physics course but could also be used in an earth science or physical science course. It could also be adapted for use in a mathematics or statistics course.

Students are expected to be able to use a search engine on the Internet. They should have studied uniform acceleration and the acceleration of gravity "g". They should be able to complete metric conversions and evaluate formulas with trigonometric functions on their calculator. They should know how to find the latitude and longitude of a location on a map.

Gravity Activity Worksheet, Internet access, scientific calculator.

To define the terms "Gal", "milliGal" and "gravity anomaly" by searching the Internet.

To use dimensional analysis to convert measurements.

To calculate the observed gravity value using latitude, elevation above sea level, and a gravity anomaly value.

Students will first use the Internet to obtain information about gravity anomalies. They will then compute the values of "g" for a number of locations around the United States and mark them on a U.S. map.

Completion of the Gravity Activity Worksheet and the gravity map.

Students may want to explore more gravity-based activities at the following sites:

http://www.gcn.ou.edu/~jahen/enviro/lab/grav_free-air.html

http://feature.geography.wisc.edu/sco/maps/maps.html#Earth-RelatedMaps

!!!! Warning !!!! The Web sites given in this lesson may have changed! Before using this lesson with your students, be sure to check if the sites are still working or if you must find another site. Sometimes the sites still have the relevant data but you may need to change the directions to access the data.

Other information about gals, milligals, anomalies and methods of measuring g may be obtained at the following sites:

http://www.mines.edu/fs_home/tboyd/GP311/MODULES/GRAV/NOTES/gravforce.html

http://www.es.lancs.ac.uk

http://www.ngdc.noaa.gov

http://edcwww.cr.usgs.gov

TI-83 instructions:

http://www.ti.com/calc/docs/act/koehler001.htm

http://www.wku.edu/~neal/manual/ti83.html

In order to print out just a copy of the student worksheet, highlight this section, then copy and paste it into your word processor. You may then revise the worksheet if you wish. 

Activity Sheets.  

1. Choose a search engine and type in "gravity values" and milligals. Browse some websites to answer the following questions.

a. Define a Gal.

b. Define a milliGal.

c. Using dimensional analysis, convert 3321.78 milliGals to m/s².

d. What is a gravity anomaly?

e. Why are gravity anomaly maps useful?

If you are having trouble finding sites to answer these questions you may try:

http://feature.geography.wisc.edu/sco/maps/m_anomal.html

http://greenwood.cr.usgs.gov/pub/fact-sheets/fs-0239-95/fs-239-95.pdf

http://www.mines.edu/fs_home/tboyd/GP311/MODULES/GRAV/NOTES/gravforce.html

2. Complete the following table by using the formula:

where q is the latitude, h is the sea level elevation (in meters) and a is the anomaly (in milligals). Total gravity will be given in milliGals. Finally, convert milliGals to m/s².

3. Mark the locations given in the table above on a U.S. map and indicate the gravity. Note that latitudes for the U.S. are denoted as positive but longitudes are denoted as negative.

4. At which of these locations would you weigh the least? The most?

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1. Choose a search engine and type in "gravity values" and milligals. Browse some websites to answer the following questions.

a. Define a Gal.

1 Gal equals 1 cm/sec²

b. Define a milliGal.

A milliGal is 1/1000 Gal = 0.001 Gal = .001 cm/sec²

Or 1 Gal = 1000 mGal

c. Using dimensional analysis, convert 3321.78 milliGals to m/s².

d. What is a gravity anomaly?

Gravimeters measure all effects that make up the Earth’s gravity field. Many of these effects are caused by known sources, such as the Earth’s rotation, distance from the Earth’s center, latitude, tidal effect, topographic relief or gravimeter fluctuations. The observed gravity reading is the value measured by the gravimeter after corrections have been made for tidal variation and gravity instrument fluctuation. This is the value of "g" that is usually reported for a particular location. (The value of "g" should not depend on the hourly changes in tides nor on "instrument drift"—variation in the response of the gravimeter over time.)

If one subtracts the effects of one or more known effects from the observed gravity reading, the result is called a gravity anomaly. There are many types of gravity anomalies. The "latitude corrected" anomaly subtracts the effects of the elliptical shape of the earth and its rotation. The "free air" anomaly then subtracts the effects of altitude. "Bouguer" and "isostatic" anomalies further subtract effects of the mass underlying observation points or of variations in topography.

e. Why are gravity anomaly maps useful?

Gravity anomaly maps are very useful to geologists when they try to determine what kind of minerals or rock exists below the surface of the earth. For example, sedimentary rocks have low densities and are characterized by gravity lows on anomaly maps. Mafic rocks, which contain high-density minerals, often are associated with gravity highs. Anomaly maps also contain information about the distribution of different underground materials. They can mark edges of rock units or faults, showing where the underground material changes.

If you are having trouble finding sites to answer these questions you may try:

http://feature.geography.wisc.edu/sco/maps/m_anomal.html

http://greenwood.cr.usgs.gov/pub/fact-sheets/fs-0239-95/fs-239-95.pdf

http://www.mines.edu/fs_home/tboyd/GP311/MODULES/GRAV/NOTES/gravforce.html

2. Complete the following table by using the formula:

where q is the latitude, h is the sea level elevation (in meters) and a is the anomaly (in milligals). Total gravity will be given in milliGals. Finally, convert milliGals to m/s².

3. Mark the locations given in the table above on a U.S. map and indicate the gravity. Note that latitudes for the U.S. are denoted as positive but longitudes are denoted as negative.

4. At which of these locations would you weigh the least? The most?

 I would weigh the least at location (27, -99); the most at (45, -68).

More anomaly and gravity values are given in the following table.

The Excel formula used to compute the Gravity in milliGals was the following.