Unit 1: Locating Buried Objects Using Gravity

Sarah Kruse, University of South Florida (skruse@usf.edu)

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Initial Publication Date: June 23, 2023

Summary

This in-class/lab/homework activity introduces students to the idea that the gravitational acceleration g varies across the surface of the earth and is sensitive to buried features. Students are asked to "read" and and run interactive animations of Newton's Law g = GM/r2 to understand how measured gravity profiles are sensitive to the mass and depth of buried objects.

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Learning Goals

Students will be able to:

  • explain that gravimeters operate on the general principle that gravity acts on a mass on a spring
  • describe situations where underground features have missing mass or extra mass that could be measured by a gravity survey
  • define each of the variables in the Newton's Law for gravitational acceleration
  • describe how the mass and depth of the buried feature each influence gravitation acceleration measured at the surface
  • verify that the equation for Newton's Law matches the results of both numerical calculations and an animation of a gravity profile
  • give a simple explanation for why gravity is described as a potential field
  • demonstrate why elevation corrections are necessary

Context for Use

This unit is designed at a very basic level for introductory college classes in which students may not have thought about detecting buried objects. The tools and activities are designed to

  • provide motivation for the gravity method
  • get students to "read" an equation by describing the meaning of the variables with sketches, words, and plugging in numerical values
  • check their understanding of the equation against simulations of gravity profiles

Description and Teaching Materials

This unit consists of a 5-minute video animation, an interactive gravity profile simulator, and a sequence of three worksheets. The unit is designed so that it can be done outside of a classroom, but would be more efficient if students worked in class or lab with an instructor available to answer questions in real time. Students simply watch the video animation, and work through the worksheets.

Part 1: What Kinds of Buried Features can you Detect by Measuring Gravity? student_worksheet_unit1_part1.docx (Microsoft Word 2007 (.docx) 1.5MB Sep15 24)

This worksheet can be done by hand. Students should have watched the gravity video animation.  The worksheet also points students to a YouTube video showing sinkhole subsidence. One question requires an internet link to answer.

Part 2: "Reading" and Visualizing Newton's Equation for Gravity  student_worksheet_unit1_part2.docx (Microsoft Word 2007 (.docx) 994kB Sep15 24)

This worksheet requires a calculations on a computer or phone.

Part 3: How do the Mass and Depth of a Buried Object Affect Gravity Readings Over the Object?  student_worksheet_unit1_part3.docx (Microsoft Word 2007 (.docx) 887kB Sep15 24)

This worksheet requires students to run the gravity profile simulator.

Teaching Notes and Tips

To beta testers: I would be very grateful if you could get an idea from students on how long it takes them to work through each of the worksheets (skruse@usf.edu).

The worksheets can be done on paper or electronically. On paper is easier for the sketch question in Part 2, but harder for showing the simulation results in Part 3. Electronically is harder for the sketch, but the simulation results can be cut and pasted. Part 2 requires calculations that could be done on a phone.

The gravity profile simulator has not been tested on phones.


Assessment

The worksheets test all the learning goals above, except for the concept that gravimeters operate on the concept of a spring. They could be done individually or in pairs.

References and Resources