Earth Science: Geodesy

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Earth Science: Geodesy


Geodesy is the science of measuring the shape and size of a planet or moon. Earth itself, because we have easy access to it, is by far the most accurately measured planetary body. Many measurements of Earth's shape and of the precise locations and motions of points fixed to its surface are made using satellites, which, since the late-1990s, have allowed differences as small as 0.4 inches (1 cm) to be measured from space. The motions of continents, the melting of ice caps, changes in Earth's surface wrought by earthquakes, and other phenomena are now routinely detected from space using geodetic methods. Since precision navigation and positioning are increasingly important in today's world, the continuous updating and improvement of geodetic information is crucial in many fields.

Historical Background and Scientific Foundations

The philosophers of ancient Greece were aware that Earth is round. They were also the first people to measure its size. About 250 BC, the Greek philosopher Eratosthenes (384–322 BC) estimated the size of Earth by measuring (with an assistant's help) the lengths of the shadow cast by a stick in Alexandria, Egypt, at the same time of the same day that the sun stood directly overhead in the city of Syrene several hundred miles away, casting no shadows. Applying trigonometry to this information, Eratosthenes calculated that Earth's equatorial circumference (the distance around the planet along the equator) is 25,000 miles (40,233 km)—remarkably close to the true value of 24,901 miles (40,075 km).

Many centuries passed before additional significant fundamental progress in geodesy occurred. Around 1600, as European trade, empire, and warfare expanded and physical science began to advance on many fronts, modern geodesy was born with the widespread application of careful triangulation. Triangulation is the determination of the location of a reasonably fixed point (say, a marker set into bedrock) by measuring the angles to two other points of known location, often termed control points. By applying trigonometry to these measurements, the location of the fixed point can be mapped. The newly mapped point can then be used as a control point for a new triangulation. In this way, networks of triangulation can be spread over entire countries or, ultimately, continents.

In 1660, the Royal Society in London was formed to promote scientific investigation. In 1666, the French formed a rival organization, L'(A)cademie Royale des Sciences. The two bodies soon became embroiled in a patriotic dispute about the shape of Earth. The French maintained that Earth is a prolate spheroid, that is, an almost spherical object lengthened in the direction of its axis (North to South), somewhat like an egg. The English maintained that it is an oblate spheroid, that is, an almost spherical object flattened at the poles and broadened at the Equator, somewhat like a tomato. In the 1730s, to settle the dispute, L'Academie Royales des Sciences mounted expeditions to points near the Equator in South America and relative near the North Pole in northern Scandinavia to measure the curvature of Earth's surface in each region. If Earth is prolate, it must be flatter near the equator; if it is oblate, it must be flatter near the pole. The expeditions showed that Earth is, in fact, oblate. This shape is caused by the rotation of Earth on its axis, which causes an apparent centrifugal force that pulls outward from the spin axis (e.g., along the equator). The fact that such measurements could even be made shows how advanced the science of geodesy had become by that time.

In the 1900s mathematical and instrumental advances allowed more precise geodesy. The meter was defined as one 1/10,000,000 of the distance from the equator to the North Pole through Paris. However, geodetic networks of triangulation remained national affairs: Each national measurement network was a separate creation, so there was no way to precisely relate points in different countries, much less in different continents. This was amended in the first two-thirds of the twentieth century, using precise measurements of local gravity (Earth's surface gravity varies slightly from place to place), observations of the stars, and more precise instruments for conventional triangulation.

In the mid-1980s, geodesists began to use satellite-based geodetic measurement systems. These included laser ranging (bouncing laser light from a satellite off the surface of Earth), very long baseline interferometry (synthetic aperture radar), and the Global Positioning System, a constellation of satellites exchanging radio signals that allows a receiver anywhere on Earth's surface to calculate its position to high accuracy.

Modern geodesy uses several basic concepts to describe the shape of Earth (or any other planet or moon). First is the reference ellipsoid. This is an idealized geometric figure, a perfectly symmetrical oblate spheroid. The reference ellipsoid does not reflect that actual bumpiness of Earth's surface. Its purpose is to give geodesists a reference or standard in comparison to which the variations of Earth's actual shape can be specified.

Second is the geoid. This is also an abstract surface—it does not correspond exactly to the surface of the land or sea, except at certain points—but has a more detailed physical basis than the reference ellipsoid. At sea, the geoid is the surface that would coincide with the surface of the world ocean if it were unaffected by tides, currents, or the like: over land, it is the surface where the sea surface would be found if it were able to send fingers of water to every point. It is, in essence, the idealized global sea level. The geoid is not symmetrical because Earth's gravity field is not symmetrical, but varies from

place to place: Where gravity is stronger, ideal sea level would be higher (more water would be drawn to such spots), and the geoid is higher.

Third, two bodies of measurements are specified with respect to the geoid: These measurements define the locations of certain well-characterized points on Earth's surface. Each body of measurements is called a datum. The vertical datum is a set of points with precisely known heights, and the horizontal datum is a set of points with precisely known latitude (north-south location), longitude (east-west location), or both. The two datums are updated every so many years to compensate for movements of Earth's crust. In the United States, datum points are marked by round brass plates set into bedrock and stamped with identifying information. These plates may often be seen on mountaintops. The datums supply a foundation for measuring other points or changes in the landscape. For example, the vertical datum gives a standard against which surveyors can measure subsidence of land, such as is occurring in the vicinity of New Orleans, Louisiana. Or, the horizontal datum allows surveyors to monitor land slippage in the vicinity of the San Andreas fault in California.

Because the geoid is defined as mean (average) local sea level (or what mean sea level would be, if the sea were present), which is in turn affected by how strong Earth's gravity happens to be in a given area, geodesists are interested in measuring variations in Earth's gravity field. In 2002, a pair of U.S. satellites was launched into Earth's orbit on a Russian rocket, forming the Gravity Recovery and Climate Experiment (GRACE). The two GRACE satellites fly about 137 miles (220 km) apart and continually measure the distance between them to high precision using lasers. As the leading satellite passes above an area of higher gravity, it dips slightly, increasing the distance between the satellites: As the second satellite enters the high-gravity area, it dips too and the distance between them decreases. As the satellites move out of the high-gravity area they gain altitude again, first one and then the other. Scientists have been able to build up a detailed gravity map of Earth from these continual slight changes in distance between the two satellites. This information has allowed geodetic measurements of both stable and time-varying features of Earth's mass distribution with unprecedented accuracy. As of 2008, the mission continued.

Modern Cultural Connections

The Global Positioning System is now incorporated in many automotive navigation systems and in millions of miniature devices for surveying, wilderness orienteering, land-sea rescue guidance, and other purposes, including weapons targeting.

The GRACE satellite has performed types of environmental measurement that were hitherto impossible. For example, GRACE has enabled researchers to measure the amount of groundwater contained in the Congo River basin, to discover a large meteor crater hidden under the Antarctic ice, to assist in measuring a subtle gravitational effect called frame dragging (a test of general relativity), and to measure the rate of ice loss from the Greenland and Antarctic ice caps. These ice caps are so large—Greenland, with only a tenth as much ice as Antarctica, contains about 596,000 cubic miles (2.5 million cubic km) of ice—that their gravitational pull can be detected from space. Further, so fast are these giant masses of ice melting—Greenland lost about 19 cubic miles (80 cubic km) of ice per year from

1997 to 2003—that the gravitational change due to this loss can also be detected.

The melting rates of the Greenland and Antarctic ice sheets are significant because melting of land-based ice sheets raises sea level. The degree to which global climate change will raise sea level by melting ice has been a matter of scientific debate, but satellite geodesy data from GRACE and other missions is helping reduce this uncertainty. In 2006, scientists announced that GRACE data had confirmed that Greenland is losing ice at a surprisingly fast and accelerating rate and that Antarctica is losing ice as well. These data were widely reported in the mass media, helping communicate to the public the reality and seriousness of global climate change. Rising sea levels may inundate some coastal settlements over the next century and increase the vulnerability of others to storms. The amount of sea-level rise will determine the amount of damage and displacement of populations that is caused.

Primary Source Connection

Scottish scientist James Hutton (1726–1797) wrote his Theory of Earth in four volumes. Hutton's work included the assertion that Earth's core was hot and that its surface moved and was weathered over time. His theory of deep time claimed Earth was much older than the few thousand years asserted by most of his contemporaries. Hutton's work thus laid the foundation for several modern geologic principles.



THEORY of the EARTH; or an Investigation of the Laws observable in the Composition, Dissolution, and Restoration, of Land upon the Globe.


Prospect of the Subject to be treated.

When we trace the parts of which this terrestrial system is composed, and when we view the general connection of those several parts, the whole presents a machine of a peculiar construction by which it is adapted to a certain end. We perceive a fabric, erected in wisdom, to obtain a purpose worthy of the power that is apparent in the production of it.

We know little of the earth's internal parts, or of the materials which compose it at any considerable depth below the surface. But upon the surface of this globe, the more inert matter is replenished with plants, and with animal and intellectual beings.

Where so many living creatures are to ply their respective powers, in pursuing the end for which they were intended, we are not to look for nature in a quiescent state; matter itself must be in motion, and the scenes of life a continued or repeated series of agitations and events.

This globe of the earth is a habitable world; and on its fitness for this purpose, our sense of wisdom in its formation must depend. To judge of this point, we must keep in view, not only the end, but the means also by which that end is obtained. These are, the form of the whole, the materials of which it is composed, and the several powers which concur, counteract, or balance one another, in procuring the general result.

The form and constitution of the mass are not more evidently calculated for the purpose of this earth as a habitable world, than are the various substances of which that complicated body is composed. Soft and hard parts variously combine to form a medium consistence, adapted to the use of plants and animals; wet and dry are properly mixed for nutrition, or the support of those growing bodies; and hot and cold produce a temperature or climate no less required than a soil: Insomuch, that there is not any particular, respecting either the qualities of the materials, or the construction of the machine, more obvious to our perception, than are the presence and efficacy of design and intelligence in the power that conducts the work.

In taking this view of things, where ends and means are made the object of attention, we may hope to find a principle upon which the comparative importance of parts in the system of nature may be estimated, and also a rule for selecting the object of our inquiries. Under this direction, science may find a fit subject of investigation in every particular, whether of form, quality, or active power, that presents itself in this system of motion and of life; and which, without a proper attention to this character of the system, might appear anomalous and incomprehensible.

It is not only by seeing those general operations of the globe which depend upon its peculiar construction as a machine, but also by perceiving how far the particulars, in the construction of that machine, depend upon the general operations of the globe, that we are enabled to understand the constitution of this earth as a thing formed by design. We shall thus also be led to acknowledge an order, not unworthy of Divine wisdom, in a subject which, in another view, has appeared as the work of chance, or as absolute disorder and confusion.

To acquire a general or comprehensive view of this mechanism of the globe, by which it is adapted to the purpose of being a habitable world, it is necessary to distinguish three different bodies which compose the whole. These are, a solid body of earth, an aqueous body of sea, and an elastic fluid of air.

It is the proper shape and disposition of these three bodies that form this globe into a habitable world; and it is the manner in which these constituent bodies are adjusted to each other, and the laws of action by which they are maintained in their proper qualities and respective departments, that form the Theory of the machine which we are now to examine.

Let us begin with some general sketch of the particulars now mentioned.

1st, There is a central body in the globe. This body supports those parts which come to be more immediately exposed to our view, or which may be examined by our sense and observation. This first part is commonly supposed to be solid and inert; but such a conclusion is only mere conjecture; and we shall afterwards find occasion, perhaps, to form another judgment in relation to this subject, after we have examined strictly, upon scientific principles, what appears upon the surface, and have formed conclusions concerning that which must have been transacted in some more central part.

2dly, We find a fluid body of water. This, by gravitation, is reduced to a spherical form, and by the centrifugal force of the earth's rotation, is become oblate. The purpose of this fluid body is essential in the constitution of the world; for, besides affording the means of life and motion to a multifarious race of animals, it is the source of growth and circulation to the organized bodies of this earth, in being the receptacle of the rivers, and the fountain of our vapours.

3dly, We have an irregular body of land raised above the level of the ocean. This, no doubt, is the smallest portion of the globe; but it is the part to us by far most interesting. It is upon the surface of this part that plants are made to grow; consequently, it is by virtue of this land that animal life, as well as vegetation, is sustained in this world.

Lastly, We have a surrounding body of atmosphere, which completes the globe. This vital fluid is no less necessary, in the constitution of the world, than are the other parts; for there is hardly an operation upon the surface of the earth, that is not conducted or promoted by its means. It is a necessary condition for the sustenance of fire; it is the breath of life to animals; it is at least an instrument in vegetation; and, while it contributes to give fertility and health to things that grow, it is employed in preventing noxious effects from such as go into corruption. In short, it is the proper means of circulation for the matter of this world, by raising up the water of the ocean, and pouring it forth upon the surface of the earth.

Such is the mechanism of the globe: Let us now mention some of those powers by which motion is produced, and activity procured to the mere machine.

First, There is the progressive force, or moving power, by which this planetary body, if solely actuated, would depart continually from the path which it now pursues, and thus be for ever removed from its end, whether as a planetary body, or as a globe sustaining plants and animals, which may be termed a living world.

But this moving body is also actuated by gravitation, which inclines it directly to the central body of the sun. Thus it is made to revolve about that luminary, and to preserve its path.

It is also upon the same principles, that each particular part upon the surface of this globe, is alternately exposed to the influence of light and darkness, in the diurnal rotation of the earth, as well as in its annual revolution. In this manner are produced the vicissitudes of night and day, so variable in the different latitudes from the equator to the pole, and so beautifully calculated to equalise the benefits of light, so variously distributed in the different regions of the globe.

Gravitation, and the vis infita of matter, thus form the first two powers distinguishable in the operations of our system, and wisely adapted to the purpose for which they are employed.

We next observe the influence of light and heat, of cold and condensation. It is by means of these two powers that the various operations of this living world are more immediately transacted; although the other powers are no less required, in order to produce or modify these great agents in the economy of life, and system of our changing things.

We do not now inquire into the nature of those powers, or investigate the laws of light and heat, of cold and condemnation, by which the various purposes of this world are accomplished; we are only to mention those effects which are made sensible to the common understanding of mankind, and which necessarily imply a power that is employed. Thus, it is by the operation of those powers that the varieties of season in spring and autumn are obtained, that we are blessed with the vicissitudes of summer's heat and winter's cold, and that we possess the benefit of artificial light and culinary fire.

We are thus bountifully provided with the necessaries of life; we are supplied with things conducive to the growth and preservation of our animal nature, and with fit subjects to employ and to nourish our intellectual powers.

There are other actuating powers employed in the operations of this globe, which we are little more than able to enumerate; such are those of electricity, magnetism, and subterraneous heat or mineral fire.

Powers of such magnitude or force, are not to be supposed useless in a machine contrived surely not without wisdom; but they are mentioned here chiefly on account of their general effect; and it is sufficient to have named powers, of which the actual existence is well known, but of which the proper use in the constitution of the world is still obscure. The laws of electricity and magnetism have been well examined by philosophers; but the purposes of those powers in the economy of the globe have not been discovered. Subterraneous fire, again, although the most conspicuous in the operations of this world, and often examined by philosophers, is a power which has been still less understood, whether with regard to its efficient or final cause. It has hitherto appeared more like the accident of natural things, than the inherent property of the mineral region. It is in this last light, however, that I wish to exhibit it, as a great power acting a material part in the operations of the globe, and as an essential part in the constitution of this world.

We have thus surveyed the machine in general, with those moving powers, by which its operations, diversified almost ad infinitum, are performed. Let us now confine our view, more particularly, to that part of the machine on which we dwell, that so we may consider the natural consequences of those operations which, being within our view, we are better qualified to examine.

This subject is important to the human race, to the possessor of this world, to the intelligent being Man, who foresees events to come, and who, in contemplating his future interest, is led to inquire concerning causes, in order that he may judge of events which otherwise he could not know.

If, in pursuing this object, we employ our skill in research, not in forming vain conjectures; and if data are to be found, on which Science may form just conclusions, we should not long remain in ignorance with respect to the natural history of this earth, a subject on which hitherto opinion only, and not evidence, has decided: For in no subject, perhaps, is there naturally less defect of evidence, although philosophers, led by prejudice, or misguided by false theory, may have neglected to employ that light by which they should have seen the system of this world.

But to proceed in pursuing a little farther our general or preparatory ideas. A solid body of land could not have answered the purpose of a habitable world; for, a soil is necessary to the growth of plants; and a soil is nothing but the materials collected from the destruction of the solid land. Therefore, the surface of this land, inhabited by man, and covered with plants and animals, is made by nature to decay, in dissolving from that hard and, compact state in which it is found below the soil; and this soil is necessarily washed away, by the continual circulation of the water, running from the summits of the mountains towards the general receptacle of that fluid. The heights of our land are thus levelled with the shores; our fertile plains are formed from the ruins of the mountains; and those travelling materials are still pursued by the moving water, and propelled along the inclined surface of the earth. These moveable materials, delivered into the sea, cannot, for a long continuance, rest upon the shore; for, by the agitation of the winds, the tides and currents, every moveable thing is carried farther and farther along the shelving bottom of the sea, towards the unfathomable regions of the ocean.

James Hutton

hutton, james. theory of the earth, volume 1 (of 4) edinburgh: 1795. available at project gutenberg, july 9, 2004. (accessed march 5, 2008).

See Also Astronomy and Cosmology: Setting the Cosmic Calendar: Arguing the Age of the Cosmos and Earth;



Gordon, Richard G., and Seth Stein. “Global Tectonics and Space Geodesy.” Science 256 (1992):333–341.

Heiskanen, W.A. “New Era of Geodesy.” Science 121 (1955): 48–50.

Meade, Charles, and David T. Sandwell. “Synthetic Aperture Radar for Geodesy.” Science 273 (1996):1181–1182.

Smalley, R., Jr. “Space Geodetic Evidence for Rapid Strain Rates in the New Madrid Seismic Zone of Central USA.” Nature 435 (2005): 1088–1090.

Web Sites

National Ocean Service (US). “Welcome to Geodesy.” March 8, 2005. (accessed February 9, 2008).

Larry Gilman