Gravity's Increasing Gravitas

The importance of gravity in land surveying (part 1 of 2). Click the following links to download the author's original PDF of this article in three PDFs (they're large): Gravity A, Gravity B, Gravity C.

by V. Kelly Bellis, PLS

Gravity’s importance in geodesy has long been recognized. Beginning with Galileo Galilei’s (1564 – 1642) gravity experiments and theories in the late 16th century, gravity’s force and, more over, its global variations continue to play an ever-increasing role for those of us measuring along Earth’s surface. The benefits from physical geodesy (the study of Earth’s gravity field) also extend well beyond the field of surveying to other disciplines including isostasy, seismology, meteorology, oceanography, climatology and others monitoring the health of our planet. And those are just a few examples with an eye on the Earth.

Today we take it for granted, if we think about it at all, that the centrifugal force along the equator from the Earth’s rotation contributes to the decrease in the pull of gravity, and, when combined with its greater distance from Earth’s center, an object at the equator weighs about 0.5% less than it does if it were at one of the poles, though its mass remains unchanged.

The other primary generalized factor shaping the Earth’s gravity field—the irregularity of mass both at the surface and within the Earth—is basically understood (at least in concept) by most of us today who were awake in school when having been introduced to Sir Isaac Newton (1642 – 1727) and the laws of gravity.

While this article isn’t intended to detail the historical developments between Galileo and the current efforts underway by NGS’s Gravity for the Redefinition of the American Vertical Datum (GRAV-D) surveys, there is just too much incredibly cool measuring stuff along the way to leave out and that I think most surveyors will appreciate. So, part one of this article is intended to help introduce the future by explaining just a little as to how we got to the present. In part two, we’ll catch a glimpse of an individual gravity survey being conducted by NGS.
 

Equi-what?!


“So what does gravity have to do with my work in the first place? I’m just a dirt surveyor!” you might ask. Whether we embrace it or not, if we’re surveying with any type of GPS equipment we’re geodetic surveyors, and if our work product is at all concerned with heights and in what direction water is directed then gravity becomes paramount. An imagined ideal surface covering the entire planet, somewhere in the vicinity of mean sea level, but totally calm, smooth, void of the effects of tide, currents, and breezes is the geoid. It is a surface on which no marble will roll of its own accord. It is a surface determined solely by gravity and, more particularly, where the potential energy of gravity is perfectly equal—no matter where on its surface gravity is measured. It is an equipotential surface.
 

Measuring Gravity

The gravity pendulum has historically been used in measuring the Earth’s gravity field during most of the past 400 years. Its amazing development into both relative and absolute gravity measuring devices (gravimeters), with increasing sensitivity and precision, is wonderfully chronicled in the scholarly article written in 1965 by Victor F. Lenzen and Robert P. Multhauf entitled “Development of Gravity Pendulums in the 19th Century.” Thanks to the preservation work accomplished through Project Gutenberg, this excellent article is freely available [eBook #35024].

Concurrent with the geodetic research of the late 16th and early 17th centuries focused in understanding the planet’s size and shape—i.e., spheroid vs. prolate spheroid (greater diameter in the polar plane) vs. oblate spheroid (greater diameter in the equatorial plane)—gravity measurements even then played a significant role in geodesy’s development.

Since about the mid-20th century, spring-based measuring devices have been developed and are widely accepted as the instrument of choice for measuring gravity at a given station relative to another.
The other method employed today in measuring gravity at a given station and determining its absolute value involves the principle of a free-falling object and monitoring its descent with extraordinary precision.
 

Mendenhall Pendulum: An Early Workhorse


The desolate 43-acre piece of rock rising abruptly nearly 300’ above the water in the middle of the Pacific Ocean that native Hawaiians call Mokumanamana was chosen by the Coast & Geodetic Survey to be included in its 1928 survey operations. The gravity station on Necker Island was just one amongst the 342 gravity stations across the United States, Puerto Rico, Alaska, and Hawaii reported in its “Annual report of the Director, United States Coast and Geodetic Survey to the Secretary of Commerce for the fiscal year ended 1928.”

The work party’s observations, led by Lt. (J.G.) E.J. Brown, also included astronomical measurements in the establishment of a longitude station with precise time ticks broadcast by the Naval Observatory sounded over the radio equipment, also seen in this amazing photo.
 

Measuring Gravity A Timeline

Fun facts to know! 
F = mg
g = gravity’s acceleration and is measured in Gals
1 Gal = 1 cm/sec2
g’s value varies and is both location-and time-dependent
g’s value ranges from about 983 Gals near the poles to about 976 Gals along the equator at high elevations
 

 Year   Notes  Image No.  Gals
 1581 swinging chandalier - Galileo Galilei     
 1644  seconds pendulum - Marin Mersenne    
 1672  Cayenne observations - Jean Richer    
 1673  Horologium (cycloid) - Christiaan Huygens    
 1687  Principia published - Isaac Newton    
 1735  method of coincidences - J.J. Mairan Figure 1   
 1737  invariable pendulum - Bouguer   980.7 
 1792  seconds pendulum (Paris) - J.C. Borda & J.D. Cassini Figure 2  
 1817  convertible compound pendulum - Henry Kater    
 1819  invariable pendulum - Henry Kater    
 1826  Königsberg experiments - Friedrich W. Bessel  Figure 3  
 1830s  in vacuo experiments - Baily, Wikes, Kater, et als    
 1862  Repsold-Bessel Reversable - portable pendulum  Figure 4  
 1872  U.S. Coast & Geodetic - gravity surveys (Pierce)    980.76
 1875  structure flexure study - Charles S. Pierce    
 1881  invariable reversible pendulum - Charles S. Pierce    
 1887  1/2 second w/ chronometer - Robert von Sterneck  Figure 5  
 1890  1/2 second improvements - Thomas C. Mendenhall  Figure 6  
 1932  upgrades to apparatus - E.J. Brown, C&GS  Figure 7  
 1934  zero-unstressed-spring - Luien J.B. LaCoste    980.7654
 1950s  widespread use of spring-based surveys    980.76543
 1970s  development of free-fall absolute meters  Figure 8  980.765432
 1980s  large-scale gravity surveys for NAVD    980.7654321
 2007  NGS announces GRAV-D surveys Figures 9,10  









































Ever-increasing Importance

There is a tremendous weThere is a tremendous wealth of information regarding terrestrial-based gravity measurements and its shaping of our past vertical datums that has been omitted from this piece, not to mention the amazing gravity measurements being conducted from space. The ever-increasing importance of gravity measurements will continue into the immediate future in defining the National Spatial Reference System and in the long term defining a Global Height System. See part two of this series in the next issue.
Many thanks to all who helped with their kind assistance and helpful information, including Vicki Childers (NGS), Dru Smith (NGS), Dan Winester (NGS), Franz Barthelmes (ICGEM), Wolfgang Köhler (ICGEM), and Franz Ossing (GFZ).

V. Kelly Bellis is a professional land surveyor and president of Horizon Surveying Company, Inc. in Ellsworth, Maine. Kelly is also an artist and photographer by avocation. He may be reached at kellybellis@gwi.net.

PSM wishes to thank V. Kelly Bellis for allowing us to reformat his work, “Gravity’s Increasing Gravitas,” to accommodate the spatial and typographic considerations inherent with print magazine format. All imagery published in this article was obtained from the author’s original document, which can be found on our website in its original form.  The following are the author’s comments regarding specific image elements: “All spatial content and its associated mapping (including the illustrations of the geoid!) were created using the software program Global Mapper. Many thanks go out to Mike Childs of Blue Marble Geographics for his unparalleled support. Additional graphic embellishments were made using Adobe’s Photoshop, CS6. Be sure to check out the Geoid Gallery for additional illustrations and content at: http://panocea.us/geoid-gallery/

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