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Geodesy and the Size and Shape of the Planet Earth




 афедра иностранных €зыков

 

 

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”фа 2012

 

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–екомендовано к изданию методической комиссией факультета землеустройства и лесного хоз€йства Ѕашкирского государственного аграрного университета, протокол є ___ от __________ 2012 г.

 

ƒанный сборник текстов предназначен дл€ подготовки бакалавров направлени€ 120100 √еодези€ и дистанционное зондирование. ¬ качестве материала дл€ чтени€ используютс€ аутентичные тексты из различных интернет-источников. “ематика текстов св€зана с будущей профессиональной де€тельностью обучаемых и отражает основные пон€ти€, виды де€тельности, инструменты и методы, примен€емые в геодезических исследовани€х.  роме того, в сборнике представлены тексты, отражающие специфику развити€ данного вида де€тельности в различных странах. “ексты могут быть использованы как дл€ аудиторной работы обучаемых, так и дл€ внеаудиторной работы. –абота над текстами может затрагивать такие аспекты воспри€ти€ и анализа информации, как, например: составление библиографического описани€, аннотации, реферата; смысловой анализ текста, составление плана, определение и формулирование главной мысли текста; лексико-грамматический анализ текста, перевод отдельных фрагментов текста, составление терминологического словар€; обсуждение полученной информации в различных ситуаци€х.

 

—оставитель: ассистент кафедры иностранных €зыков ј.–. ћустафина

 

–ецензент: доцент кафедры иностранных €зыков «.Ќ. »зимариева

 

 

ќтветственный за выпуск: зав. каф. иностранных €зыков к.ф.н., доцент ќ.Ќ. Ќовикова

 

Contents:

Part I  
1.1. Geodesy    
1.2. Geodesy and the Size and Shape of the Planet Earth    
1.3. Measuring Plate Motion    
1.4. Geodetic Datum Overview    
1.5. The Global Geodetic Observing System (GGOS)    
1.6. Surveying    
1.7. Map Reading    
1.8. Topographic Maps    
1.9. Great Circles  
1.10. The Field of Surveying and the Role of the Surveyor    
1.11. Geodetic Surveying    
Part II  
2.1.Geodetic Datums    
2.2. Earth Rotation Studies    
2.3. Future of Paper Maps    
2.4. Map Colors    
2.5. Topographic Maps    
2.6. Map Projections    
References  

Part I

Geodesy

According to the classical definition of F.R. Helmert (A 1880), geodesy is the "science of the measurement and mapping of the earth's surface". This definition has to this day retained its validity; it includes the determination of the earth's external gravity field, as well as the surface of the ocean floor. With this definition, which is to be extended to include temporal variations of the earth and its gravity field, geodesy may be included in the geosciences, and also in engineering sciences, e.g., National Academy of Sciences (1978).

Triggered by the development of space exploration, geodesy turned in collaboration with other sciences toward the determination of the surfaces of other celestial bodies (moon, other planets). The corresponding disciplines are called selenodesy and planetary geodesy.

Geodesy may be divided into the areas of global geodesy, national geodetic surveys, and plane surveying. Global geodesy is responsible for the determination of the figure of the earth and of the external gravity field. A geodetic survey establishes the fundamentals for the determination of the surface and gravity field of a country. This is realized by coordinates and gravity values of a sufficiently large number of control points, arranged in geodetic and gravimetric networks. In this fundamental work, curvature and the gravity field of the earth must be considered. In plane surveying (topographic surveying, cadastral surveying, engineering surveying), the details of the terrain are obtained. In plane surveying, the horizontal plane is generally sufficient.

There is close cooperation between global geodesy, geodetic surveying and plane surveying. The geodetic survey adopts the parameters determined by measurements of the earth, and its own results are available to those who measure the earth. The plane surveys, in turn, are generally tied to the control points of the geodetic surveys and serve then particularly in the development of national map series and in the formation of real estate cadastres. Measurement and evaluation methods are largely identical in global geodesy and national geodetic surveys. Particularly space methods (satellite geodesy) enter more and more into regional and even local surveys. This also implies more detailed gravity field determination on regional and local scale.

With the corresponding classifications in the realms of the English and French languages, the concept of "geodesy" (la geodesie, "hoher Geodasie" after Helmert) is to be referred only to global geodesy and geodetic surveying. The concept of "surveying" (la topometrie, Vermessungskunde or "niedere Geodasie" after Helmert) shall encompass plane surveying.

Geodesy and the Size and Shape of the Planet Earth

Earth, with average distance of 92,955,820 miles (149,597,890 km) from the sun, is the third planet and one of the most unique planets in the solar system. It formed around 4.5-4.6 billion years ago and is the only planet known to sustain life. This is because factors like its atmospheric composition and physical properties such as the presence of water over 70.8% of the planet allow life to thrive.

Earth is also unique however because it is the largest of the terrestrial planets (one that is composed of a thin layer of rocks as opposed to those that are mostly made up of gases like Jupiter or Saturn) based on its mass, density, and diameter. Earth is also the fifth largest planet in the entire solar system.

As the largest of the terrestrial planets, Earth has an estimated mass of 5.9736 × 1024 kg. Its volume is also the largest of these planets at 108.321 × 1010km3.

In addition, Earth is the densest of the terrestrial planets as it is made up of a crust, mantle and core. The Earth's crust is the thinnest of these layers while the mantle comprises 84% of Earth's volume and extends 1,800 miles (2,900 km) below the surface. What makes Earth the densest of these planets however is its core. It is the only terrestrial planet with a liquid outer core that is surrounded with a solid, dense inner core. Earth's average density is 5515 × 10 kg/m3. Mars, the smallest of the terrestrial planets by density, is only around 70% as dense as Earth.

Earth is classified as the largest of the terrestrial planets based on its circumference and diameter as well. At the equator, Earth's circumference is 24,901.55 miles (40,075.16 km). It is slightly smaller between the North and South poles at 24,859.82 miles (40,008 km). Earth's diameter at the poles is 7,899.80 miles (12,713.5 km) while it is 7,926.28 miles (12,756.1 km) at the equator. For comparison, the largest planet in Earth's solar system, Jupiter, has a diameter of 88,846 miles (142,984 km).

Earth's circumference and diameter differ because its shape is classified as an oblate spheroid or ellipsoid, instead of a true sphere. This means that instead of being of equal circumference in all areas, the poles are squished, resulting in a bulge at the equator, and thus a larger circumference and diameter there.

The equatorial bulge at Earth's equator is measured at 26.5 miles (42.72 km) and is caused by the planet's rotation and gravity. Gravity itself causes planets and other celestial bodies to contract and form a sphere. This is because it pulls all the mass of an object as close to the center of gravity (the Earth's core in this case) as possible.

Because Earth rotates, this sphere is distorted by the centrifugal force. This is the force that causes objects to move outward away from the center of gravity. Therefore, as the Earth rotates, centrifugal force is greatest at the equator so it causes a slight outward bulge there, giving that region a larger circumference and diameter.

Local topography also plays a role in the Earth's shape, but on a global scale its role is very small. The largest differences in local topography across the globe are Mount Everest, the highest point above sea level at 29,035 ft (8,850 m), and the Mariana Trench, the lowest point below sea level at 35,840 ft (10,924 m). This difference is only a matter of about 12 miles (19 km), which is very minor overall. If equatorial bulge is considered, the world's highest point and the place that is farthest from the Earth's center is the peak of the volcano Chimborazo in Ecuador as it is the highest peak that is nearest the equator. Its elevation is 20,561 ft (6,267 m).

To ensure that the Earth's size and shape is studied accurately, geodesy, a branch of science responsible for measuring the Earth's size and shape with surveys and mathematical calculations is used.

Throughout history, geodesy was a significant branch of science as early scientists and philosophers attempted to determine the Earth's shape. Aristotle is the first person credited with trying to calculate Earth's size and was therefore, an early geodesist. The Greek philosopher Eratosthenes followed and was able to estimate the Earth's circumference at 25,000 miles, only slightly higher than today's accepted measurement.

In order to study the Earth and use geodesy today, researchers often refer to the ellipsoid, geoid and datums. An ellipsoid in this field is a theoretical mathematical model that shows a smooth, simplistic representation of the Earth's surface. It is used to measure distances on the surface without having to account for things like elevation changes and landforms. To account for the reality of the Earth's surface, geodesists use the geoid which is a shape that is constructed using the global mean sea level and as a result takes elevation changes into account.

The basis of all geodetic work today though is the datum. These are sets of data that act as reference points for global surveying work. In geodesy, there are two main datums used for transportation and navigation in the U.S. and they make up a portion of the National Spatial Reference System.

Today, technology like satellites and global positioning systems (GPS) allow geodesists and other scientists to make extremely accurate measurements of the Earth's surface. In fact it is so accurate, geodesy can allow for worldwide navigation but it also allows researchers to measure small changes in the Earth's surface down to the centimeter level to obtain the most accurate measurements of the Earth's size and shape.

Measuring Plate Motion

We can tell from two different lines of evidenceЧgeodetic and geologicЧthat the lithospheric plates move. Even better, we can trace those movements back in geologic time.

Geodesy, the science of measuring the Earth's shape and positions on it, lets us measure plate motions directly using GPS, the Global Positioning System. This network of satellites is more stable than the Earth's surface, so when a whole continent moves somewhere at a few centimeters per year, GPS can tell. The longer we do this, the better the accuracy, and in much of the world the numbers are quite precise by now.

Another thing GPS can show us is tectonic movements within plates. One assumption behind plate tectonics is that the lithosphere is rigid, and indeed that is still a sound and useful assumption. But parts of the plates are soft in comparison, like the Tibetan Plateau and the western American mountain belts. GPS data helps us separate blocks that move independently, even if only a few millimeters per year. In the United States, the Sierra Nevada and Baja California microplates have been distinguished this way.

Three different geologic methods help determine the trajectories of plates: paleomagnetic, geometric and seismic. The paleomagnetic method is based on the Earth's magnetic field.

In every volcanic eruption, the iron-bearing minerals (mostly magnetite) become magnetized by the prevailing field as they cool. The direction they're magnetized in points to the nearest magnetic pole. Because oceanic lithosphere forms continuously by volcanism at spreading ridges, the whole oceanic plate bears a consistent magnetic signature. When the Earth's magnetic field reverses direction, as it does for reasons not fully understood, the new rock takes on the reversed signature. Thus most of the seafloor has a striped pattern of magnetizations, as if it were a piece of paper emerging from a fax machine (only it's symmetrical across the spreading center). The differences in magnetization are slight, but sensitive magnetometers on ships or aircraft can detect them.

The most recent magnetic-field reversal was 781,000 years ago, so mapping that reversal gives us a good idea of spreading speed in the most recent geologic past.

The geometric method gives us the spreading direction to go with the spreading speed. It's based on the transform faults along the mid-ocean ridges. If you look at a spreading ridge on a map, it has a stairstep pattern of segments at right angles. If the spreading segments are the treads, the transforms are the risers that connect them. Carefully measured, those transforms yield the spreading directions. With plate speeds and directions, we have velocities that can be plugged into equations. These velocities match the GPS measurements nicely.

Seismic methods use the focal mechanisms of earthquakes to detect the orientation of faults. Although less accurate than paleomagnetic mapping and geometry, they are useful in parts of the globe that aren't well mapped and have no GPS stations.

We can extend measurements into the geologic past in several ways. The simplest one is to extend paleomagnetic maps of the oceanic plates farther from the spreading centers. Magnetic maps of the seafloor translate precisely into age maps. The maps also reveal how the plates changed velocity as collisions jostled them into rearrangements.

Unfortunately the seafloor is relatively young, nowhere more than about 200 million years old, because eventually it disappears beneath other plates by subduction. As we look deeper into the past we must rely more and more on paleomagnetism in continental rocks. As plate movements have rotated the continents, the ancient rocks turned with them, and where their minerals once indicated north they now point somewhere else, toward "apparent poles." If you plot these apparent poles on a map, they appear to wander away from true north as rock ages go back in time. In fact, north does not change (usually), and the wandering paleopoles tell a story of wandering continents.

These two methods, seafloor magnetization and paleopoles, combine into an integrated timeline for the motions of the lithospheric plates, a tectonic travelogue that leads smoothly up to today's plate movements.

 

Geodetic Datum Overview

A geodetic datum is the tool used to define the shape and size of the earth, as well as the reference point for the various coordinate systems used in mapping the earth. Throughout time, hundreds of different datums have been used - each one changing with the earth views of the times.

True geodetic datums however, are only those which appeared after the 1700s. Prior to that, the earth's ellipsoidal shape was not always taken into consideration, as many still believed it was flat. Since most datums today are used for measuring and showing large portions of the earth, an ellipsoidal model is essential.

Today, there are hundreds of different datums in use; but, they are all either horizontal or vertical in their orientation.

The horizontal datum is the one that is used in measuring a specific position on the earth's surface in coordinate systems such as latitude and longitude. Because of the different local datums (i.e. those having different reference points) the same position can have many different geographic coordinates so it is important to know which datum the reference is in.

The vertical datum measures the elevations of specific points on the earth. This data is gathered via tides with sea level measurements, geodetic surveying with different ellipsoid models used with the horizontal datum, and gravity, measured with the geoid. The data is then depicted on maps as some height above sea level.

For reference, the geoid is a mathematical model of the earth measured with gravity that corresponds with the mean ocean surface level on the earth- such as if the water were extended over the land. Because the surface is highly irregular however, there are different local geoids that are used to get the most accurate mathematical model possible for use in measuring vertical distances.

As previously mentioned, there are many datums in use around the world today. Some of the most commonly used datums are those of the World Geodetic System, the North American Datums, those of the Ordinance Survey of Great Britain, and the European Datum; however, this is by no means an exhaustive list.

Within the World Geodetic System (WGS), there are several different datums that have been in use throughout the years. These are WGS 84, 72, 70, and 60. The WGS 84 is one of the most widely used datums around the world.

In the 1980s, the United States Department of Defense used the Geodetic Reference System, 1980 (GRS 80) and Doppler satellite images to create a new, more accurate world geodetic system. This became what is known today as WGS 84. In terms of reference, WGS 84 uses what is called the "zero meridian" but because of the new measurements, it shifted 100 meters (0.062 miles) from the previously used Prime Meridian.

Similar to WGS 84 is the North American Datum 1983 (NAD 83). This is the official horizontal datum for use in the North and Central American geodetic networks. Like WGS 84, it is based on the GRS 80 ellipsoid so the two have very similar measurements. NAD 83 was also developed using satellite and remote sensing imagery and is the default datum on most GPS units today.

Prior to NAD 83 was NAD 27, a horizontal datum constructed in 1927 based on the Clarke 1866 ellipsoid. Though NAD 27 was in use for many years and still appears on United States topographic maps, it was based on a series of approximations with the geodetic center being based at Meades Ranch, Kansas. This point was chosen because it is near the geographic center of the contiguous United States.

Also similar to WGS 84 is the Ordinance Survey of Great Britain 1936 (OSGB36) as the latitude and longitude positions of points are the same in both datums. However, it is based on the Airy 1830 ellipsoid as it shows Great Britain, its primary user, the most accurately.

The European Datum 1950 (ED50) is the datum used for showing much of Western Europe and was developed after World War II when a reliable system of mapping borders was needed. It was based on the International Ellipsoid but changed when GRS80 and WGS84 were put into use. Today ED50's latitude and longitude lines are similar to WGS84 but the lines do become farther apart on ED50 when moving toward Eastern Europe.

When working with these or other map datums, it is important to always be aware of which datum a particular map is referenced in because often there are large differences in terms of distance between place to place on each different datum. This "datum shift" can then cause problems in terms of navigation and/or in trying to locate a specific place or object as a user of the wrong datum can sometimes be hundreds of meters from their desired position.

Whichever datum is used however, they represent a powerful geographic tool but are most important in cartography, geology, navigation, surveying, and sometimes even astronomy. In fact, "geodesy" (the study of measurement and Earth representation) has become its own subject within the field of earth sciences.





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