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Determining the Size and Shape of the Earth
Richard J. Pulskamp

Mathematics Topic: Calculus, Trigonometry 
Application Areas: Geodesy 
Prerequisites: Sophomore mathematics majors
Plane trigonometry, firstyear calculus, scalar product
of vectors, and the method of least squares. 

 ©2012 by COMAP, Inc.  UMAP Journal 33.2  30 pages 

There is a long history of attempts to measure the size
and shape of the Earth. During the 17th century, theoretical
work predicted its shape to be that of an oblate
spheroid. Later empirical work challenged this result.
In the 18th century, to settle the question, measurements
of arcs of meridian were made at various locations.
This Module shows how, under the assumption that
its shape is wellapproximated as an ellipsoid of revolution,
both the size and shape of the Earth can be
deduced from the known lengths of arcs of meridian
measured at various latitudes.
Table of Contents
1. INTRODUCTION
2. THE EARTH AS A SPHERE
3. LENGTH OF AN ARC OF A GREAT CIRCLE
4. EARLY MEASUREMENTS OF THE EARTH
5. LENGTH OF AN ARC OF AN ELLIPSE
6. ARCS ON THE EARTH
6.1 Latitude
7. TRIANGULATION
8. DETERMINING THE SHAPE OF THE EARTH
9. FURTHER ARC MEASUREMENTS
10. ANALYSIS
11. SOLUTIONS TO THE EXERCISES
12. APPENDIX
REFERENCES
ACKNOWLEDGMENTS
ABOUT THE AUTHOR



