# For the Classroom: Modeling GRACE

The primary gravity measurement is made by recording changes in the speed and distance between the two GRACE satellites. The two satellites fly in formation over the Earth and the precise speed of each satellite and the distance between them is constantly communicated via a microwave K-band ranging instrument. As the gravitational field changes beneath the satellites – correlating to changes in mass of the surface beneath - the orbital motion of each satellite is changed. This change in orbital motion causes the distance between the satellites to expand or contract and will be measured using the K-band instrument. From this, the fluctuations in the Earth’s gravitational field can be determined.

# Materials needed

5-20 magnets of varying strengths, cardboard or foam board, magnetic want, spring scale, two ring stands, rod, 2 clamps, grid of graph paper marked in 5cm squares, and masking tape.

# Procedure

1. Set up two ring stands. Attach each end of the rod to a ring stand so it is suspended between the two ring stands. Attach the spring scale from the rod so the scale slides freely on the rod. Attach the magnetic want to the spring scale and adjust the height so that the scales and wand hang freely. Record the starting weight in Newtons.
2. Tape the grid of graph paper to the top of the card or foam board.
3. On the desktop, between the ring stands, place 5 to 20 magnets of varying strengths, randomly in a space slightly smaller than the size of the foam board.
4. Place the card or foam board on top of the magnets and tape all around the sides.
5. Distribute graph paper to each student the same size of the card or foam board.
6. Slowly slide the spring scale/magnetic wand over each column of the graph paper. For each grid, have students record observed changes in the spring scale. Move the ring stand so the scale/magnetic wand covers the next column of the foam board until the entire board has been mapped.

# Questions

• What was the starting weight in Newtrons? This represents the mass with standard gravity
• For each grid reading that is different from the starting weight, subtract this standard gravity reading. Divide this number by the starting weight. This represents the percent change in gravity. Negative values will represent less gravity than the standard. Positive values show an increase in gravity.
• Where does the model’s gravity increase? Decrease?
• On Earth, what types of things might account for an increase or decrease in gravity?

GRACE will obtain a gravity field map by looking at how the Earth’s mass varies from place to place on the surface as the twin satellites pass over. Mass and gravity are positively correlated-that is to san an increase in mass relates to an increase in the gravitational force exerted. Mass is also related to the density and amount of materials located in any one place.

# Extension

1. Using four equal sized containers, fill the first with rocks, second with water, third with plastic bag of air, and fourth with sand.
2. Weigh each container and record the weight.

# Questions/Analysis

·        Which container weighed the most? The least?

·        Based on the demonstrations would you expect the Earth’s gravitational pull to be constant?

·        Describe geographic features on earth that will cause GRACE to detect changes in gravity

# Discuss with students

• Scales may read in pounds or kilograms but weight in the metric system is correctly recorded in Newtons.
• The difference between acceleration due to gravity and the gravitational force.
• Difference between gravity field and magnetic field
• Why models are used in science.

For more information on the ESSP Program, visit http://essp.gsfc.nasa.gov/

For more information on GRACE, visit http://www.csr.utexas.edu/grace/ 