Earth measurement
The earth measurement (also: earth survey ) is a subdiscipline of geodesy , especially the higher geodesy , and a form of surveying . It includes those measurements , models and calculations that are necessary for the precise determination of the earth's shape and the earth's gravity field .
The term “ geodesy” translates well into English with geodesy  in contrast to national and engineering surveys , which are summarized there under surveying .
Earth measurement and its methods
Up until around 1960, earth measurements were based almost exclusively on terrestrial measurements on and between points on the earth's surface ( survey points , levels , leveling , gravimetry and vertical deviation points); the most important of these methods are listed below.
With the start of the first artificial earth satellites , the geodetic working method changed. Even the orbital disruptions that were detected during the few days of operation of the Explorer 1 (1958) increased the accuracy of two sizes of the gravitational field by a factor of ten. The successor Vanguard I offered several years of operation thanks to its solar cell operation, during which the measurements could be significantly refined.
Until the 1960s, the global figure of the earth could only be determined with an accuracy of a few tens of meters because the oceans make up 71% of the earth's surface. Thereafter, a few meters could be reached using geometric methods of satellite geodesy , and from the 1990s even a few centimeters. At the same time, dynamic satellite geodesy was developed , with which today the earth's gravity field can be determined more precisely than 1: 10 million.
"Classic" methods of earth measurement
 Triangulation (exact angle measurement)
 Basic measurement, electronic distance measurement and
 from 1950/70 also trilateration with light and microwaves
 Azimuth and time measurement
 Astronomical “location”: latitude and longitude, and
 Degree measurement (the above exactly in northsouth or eastwest direction)
 Leveling , especially as precision leveling
 trigonometric height measurement
 Altimetry and level measurement with hose scales
 Solar eclipses and parallaxes to the moon

Gravimetry (measurement of gravity) and
 Gradiometry (from around 1920 with the rotary balance )
From around 1960 and increasingly from 1985 onwards, earth measurements made use of other methods, especially those of satellite geodesy .
Earth measurement methods from around 1970
 Satellite triangulation with satellite cameras and other sensors
 Trilateration to satellites  especially to laser reflectors on satellites such as GEOS , LAGEOS , Starlette , as well as to the moon
 Doppler measurements of radio signals (NNSS, transit, etc.)
 Radio interferometry to satellites and VLBI to quasars
 Pseudoranging to GPS and GLONASS satellites
 Satellitetosatellite tracking (SST, e.g. GRACE probes)
 Gradiometry in satellite orbits (in development)
 Modern calculation methods such as collocation , FFT , etc.
Subareas of earth measurement
The theory of earth measurements is usually assigned to three areas:
 Astronomical geodesy: inertial or reference system of global and local coordinates , determination of the mean earth ellipsoid , modeling of the vertical deviation , etc.
 Mathematical geodesy: definition of different coordinate systems and images (often somewhat blurred called " projections "), differential geometry , calculation methods on the ellipsoid and on surfaces of higher order, etc.
 Physical geodesy: modeling of the earth's gravitational field , geoid determination , gravity reductions and anomalies , transition to geophysics and geodynamics , as well as to
 Satellite geodesy and partly for navigation .
History of Earth Measurement
Greek antiquity and Arabs
An important finding for the earth measurement is that the earth has a round shape. Already Pythagoras of Samos declared around 600 BC that the earth had a spherical shape. Two hundred years later, Aristotle discussed the surface shape of the earth in his work Περὶ οὐρανοῦ ( About the Sky , Volume 2, Chapters 13 and 14) and came to the conclusion that it must be spherical for three different reasons.
The Alexandrian scholar Eratosthenes is commonly regarded as the "ancestor" of earth measurement, but he probably had some ancestors from Ionia or even Babylonia . He measured the different zenith distances of the sun in Alexandria and Syene and determined the circumference of the earth to be 252,000 stages, which probably corresponds to an accuracy of 7.7% (for details see Eratosthenes # Determination of the circumference of the earth ) . Posidonius used around 100 BC A similar method in which he determined not the vertical angles of the sun, but those of the star Canopus over the island of Rhodes and in Alexandria, whereby he came to a result similar to that of Eratosthenes with 240,000 stages.
There are also some “ world maps ” from antiquity , which of course could only include the “ Old World ”. From today's point of view, their representations are heavily distorted (around 20 to 40%), which is due to the extensive lack of astrogeodetic measurements. Most of the underlying data is likely to come from coastal shipping .
Technically superior measurements were developed a few centuries later by the Arabs , through which the most important written evidence from Greek natural philosophy was passed down. The nautical charts of this time (socalled portolanes ) and nautical manuals are extremely accurate along busy coasts , they have hardly any errors that are more than 10%. This seems to mean that the size of the earth was known to within 20 percent.
Earth measurement in the advanced cultures of America
(Sources in progress, but sparse)
Earth measurement in modern Europe
At the dawn of the Age of Discovery , scholars were by no means agreed on the size of the earth and the extent of Asia and Africa. After numerous discussions , Columbus was only able to make his planned western route to “India” plausible because he underestimated the Earth's radius and overestimated the size of Asia.
The size of the earth, which had previously been derived by Arab astronomers to be better than 10%, only became more precisely determinable when Snellius developed the method of triangulation in 1615 . From his degree arc measured in Holland, he obtained the earth's radius by 3% too small, while the degree measurement carried out by Jean Picard in 1669/70 in the much longer Parisian meridian was already accurate to 0.1%. Followup measurements by Jacques Cassini to clarify the question of whether the earth's ellipsoid was flattened or elongated at the poles , however, led to contradictions, which Isaac Newton decided in favor of flattening on the basis of theoretical considerations.
The first really accurate earth measurement goes back to the Paris Academy , founded in 1666 , which decided around 1730 to send two geodetic expeditions to Peru (today's Ecuador , 1735–1744) and to Lapland (1736–1737). The two meridian arcs of 3.1 ° and 1.0 ° in length resulted in a significant decrease in curvature to the north, which resulted in an earth flattening of 1: 215. Their excessively high value (partly because of rust on the fathom rules in Lapland) was later corrected to 1: 304 by combining it with the French meridian. The true value (see GRS80 ellipsoid) is 1: 298.25 or 21.385 km difference between the equatorial and polar earth radius.
The measured lengths of these 3 meridians served not least to define the meter , in that the distance equatorpole should be exactly 10 million meters (in fact, it is 10,002,248.9 m).
Other significant works on earth measurement include Clairaut's theorem of 1743, which establishes a relationship between the ellipsoidal shape and the flattening of the gravity of the earth's gravity field, and Delambre's extension of the Paris medidian from Barcelona to Dunkirk (1792–1798). The results of this over 1000 km long degree arc were included in the final meter definition.
Of the numerous 19th and 20th century performed level measurements is still that of Gauss (GöttingenAltona, from 1821 to 1825) and the nearly 3000 km long ScandinavianRussian Struve Arc called (18161852), as well as wrong to Meridian extending Prussia arc of Bessel and Baeyer 18311838. It is also essential  to this day  to include the adjustment calculation developed by Gauss , which minimizes the effect of the inevitable small measurement errors .
Most important results of earth measurements since 1800
Size and shape of the earth figure
In mathematics and geodesy since Carl Friedrich Gauß , the “mathematical figure of the earth ” is the one that corresponds to sea level on average over the seasons and years . The name geoid was coined around 1870 for this level surface with constant potential  meaning the potential energy in the earth's gravity field .
Bessel ellipsoid
Even before the French degree measurements at the end of the 18th century to define the meter , not only was the earth's radius better than 1% known, but also the fact that the earth was flattened . Around 1900 most of the country's surveys were based on the dimensions of the earth determined by Friedrich Wilhelm Bessel , the " Bessel ellipsoid " which is still used today :
 Equatorial radius a = 6,377,397.155 m
 Flattening f = 1: 299.1528
The length of the second semiaxis b results from b = a · (1 − f) to 6,356,078.962 m. It is "too small" by almost 800 meters compared to the values assumed worldwide today (see below), but this is not due to any errors in measurement or calculation, but rather to the greater curvature of the earth in the Eurasia continent block (the Bessel ellipsoid is therefore better for terrestrial surveying systems as a world ellipsoid). The wellknown German geodesist Friedrich Robert Helmert pointed out around 1900 that the global earth ellipsoid must be 700–800 meters larger and have a flattening of around 1: 298 to 298.5.
Influences of gravity
Around 1910, American geodesists tried to model the influences of gravity and, in particular, isostasis more precisely. From the work of Hayford those values in 1924 by the "resulted International were recommended Geodesy" as Standardellipsoid:
 a = 6,378,388 m, f = 1: 297.0
Satellite geodesy
After the first reliable results of the satellite geodesy , the IUGG General Assembly in Lucerne decided in 1967 on the "international ellipsoid 1967", which was based primarily on geometric measurements. The flattening was, however, already verified on 5 places (20 cm) by the analysis of satellite orbits :
 a = 6,378,160 m, f = 1: 298.25
However, with the first precise dynamic methods of the Doppler satellites, discrepancies of 20 to 40 meters (6,378,120  140 m) came to light, partly also with the gravity formula decided at the same time . Although soon afterwards the first world triangulation with the 4000 km high balloon satellite PAGEOS the values of
 a = 6,378,130 m, f = 1: 298.37 ( Hellmut Schmid , ETH Zurich)
resulted, it was decided to wait about 10 years before further defining the reference system .
GRS 80
In 1981 the IAG General Assembly (in coordination with the IAU ) defined the "Geodetic Reference System 1980" ( GRS 80 ), with about 10 parameters characterizing the earth, of which those of the earth ellipsoid are:
 a = 6,378,137.0 m, f = 1: 298.2572, b = 6,356,752,314 m (accuracy ± 1 m or 0.001).
This currently (still) binding earth ellipsoid, including its geophysical parameters, has been incorporated into the GPS database as WGS84 . The “exact” value of the equator axis a would only have to be changed by a few decimeters  which of course no longer has any practical effects in view of the geoid undulations of ± 50 meters along the equator.
Gravitational field and structure of the earth
Preliminary keywords: Earth's gravity field , gravimetry , dynamic satellite geodesy , seismology , geodynamics , interior of the earth and earth models ... ...
See also
 Surveying , astrogeodesy
 Earth sciences , geometry , applied geophysics
 Institute for Earth Measurement (Bamberg)
 Meridian arch , Struve arch
 Earth measurement in antiquity with the gnomon
Web links
Institutes for Earth Measurement
 Research at the Institute for Earth Measurement, University of Hanover
 Satellite astrogeodesy / VLBI / Earth System , Vienna University of Technology
 Research on earth measurements / geodynamics, ETH Zurich
Others
 Bavarian Commission for International Earth Surveying
 Austrian Geodetic Commission  ÖGK  Organ of International Earth Surveying for Austria
 Basic geographic data  Federal Office for Metrology and Surveying, Vienna
 Website on the methods of Eratosthenes
 Like Eratosthenes around 200 BC Measured the earth
 International Association of Geodesy (IAG  International Association of Geodesy )