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					       EAS-450 – Physics and Chemistry of the Earth

                                 LAB 2 - Gravity
Objective: Make precise gravity measurements, understand sources of measurement errors,
compare measurements to a model.

The Lacoste&Romberg Model G gravimeter

 The Lacoste&Romberg Model G gravimeter. Right: the instrument on its leveling plate. Left:
                schematic representation of the inside of the gravimeter.

Model "G" Gravity Meter Specifications
   RANGE: 7000 mGal
   DATA RESOLUTION: 0.005 mGal
   ACCURACY: 0.04 mGal or better
   REPEATABILITY: 0.01 to 0.02 mGal
   DRIFT: 1.0 mGal per month or less
   LENGTH: 7-3/4 inches (19.7 cm)
   WIDTH: 7 inches (17.8 cm)
   HEIGHT: 9-7/8 inches (25.1 cm)
   WEIGHT: 7 pounds (3.2 kg)
   Weight of suitable battery: 5 pounds (2.3 kg)
   Weight of meter, battery and carrying case: 22 pounds (10.0 kg)
Operating a Lacoste&Romberg Model G gravimeter:
1. Remove the gravimeter from case and connect it to a power source (the gravimeter requires
   two hours to reach operating temperature but we keep it constantly connected to power).
2. Place the gravimeter on its circular plate.
3. Turn on reading and level light switch.
4. Level the gravimeter, first roughly by sliding it on its circular plate, then fine tune using the
   black leveling knobs.
5. Turn arrestment knob counterclockwise to its furthest extent.
6. Peer through the eyepiece and locate the beam. Turn the nulling dial while looking through
   the eyepiece so the left side of the beam matches the left side of the 2.3 reading line.
7. Record the number on the counter. The last digit on the counter is in tenth. It should match
   the last digit on the dial. Estimate one more digit (hundredth) from the nulling dial.
8. The meter reading in milligals is obtained by finding the highest tabled value lower than the
   new reading. Record the value of the table value in milligals. Subtract the table value from
   the meter reading and multiply this difference by the tabled interval factor to convert this
   difference to milligals. Add the tabled milligal value to the calculated value. Example:
                     Meter reading: 3721.21
                     Highest tabled value: 3700
                     Difference: 21.21
                     Interval factor: 1.05655
                     Difference x Interval Factor = 21.72 mGal
                     Highest tabled value in milligals: 3901.43 mGal
                     Sum: 3923.15 mGal
9. After taking a reading, be sure to TURN ARRESTMENT KNOB CLOCKWISE TO ITS
   instrument to case.

                  View of the top of a Lacoste&Romberg Model-G gravimeter.
Lab problems
1. Starting with g=GM/r2, derive the formula that gives the variation of gravity as a function of

2. The Civil Engineering Building is about 30 meters high (?). Calculate the expected variations
   of gravity between the basement and the 4th floor. Is this detectable with the type of
   gravimeter used for this lab? Justify your answer using the characteristics of the instruments
   given above.

3. Gravity survey:
      a. Perform gravity measurements at 5 stations in the Civil Engineering Building:
          basement, 1st, 2nd, 3rd, and 4th floors. Once you reach the 4th floor, close the loop by
          measuring the same stations in reverse order (3r, 2nd, 1st, basement).
      b. During your 2 stations in the basement, have each student in your group take his/her
          own reading. Turn gravimeter off , lock the arrestment knob, and take the gravimeter
          off its leveling plate between each reading.
      c. Once you are back, convert your readings to mGals.
      d. Plot your measurements on a graph, together with the theoretical values.
      e. Comment your results.
      f. Use the repeated measurements at the basement station to calculate the standard
          deviation of the measurements. Comment.
      g. In general, how do your measurement compare, in terms of precision, with the
          specifications given by the manufacturer? Comment.
      h. What could you do to check the accuracy of your measurements?

4. If you wanted to make a profit in buying gold by weight at one altitude and selling it at
   another altitude for the same price per weight, should you buy or sell at the higher altitude

5. Ellipsoid conversion:
  Download “madtran.zip” from http://www.eas.purdue.edu/~calais/teaching, under
  Create a new directory, and unzip madtran.zip into that directory.
  Run madtran.exe to calculate the following conversions:
           o West Lafayette, Indiana, coordinates on the WGS84 ellipsoid:
                  Latitude: 40.438039 N
                  Longitude: 86.908700 W
                  Convert to NAD27 ellipsoid, calculate the approximate horizontal
                      difference between the 2 sets of coordinates in meters.
                  Same with Liberia 1964.
           o Off the French Riviera, coordinates on the ED50 ellipsoid:
                  Latitude: 43 E
                  Longitude: 7.5 W
                     Convert to NAD27 ellpsoid, calculate the approximate horizontal
                      difference between the 2 sets of coordinates in meters.
                     Same with Liberia 1964.

6. Geoid:
  Use http://www.ngs.noaa.gov/cgi-bin/GEOID_STUFF/geoid99_prompt1.prl
  Your GPS gives you an ellipsoidal height of 300 m in Indiana (latitude 40N, longitude
    87W). What is the geoid height for that location? What is the height with respect to mean
    sea level?
  Same question for a 300 m ellipsoidal hehight reading on your GPS in northeastern
    Wyoming (latitude 45N, longitude 105W).

7. What is the gravitational potential at the Earth’s equator? At the pole?
   What is the gravitational potential energy of a 1 kg mass at the Earth’s equator? At the pole?
   If this mass was to fall toward Earth from a large distance where it had zero velocity, what
   would be its velocity at the Earth’s surface?
   (use Requat = 6,378 km, Rpole = 6,357 km)

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