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Introduction to GeodesyIntroduction to GeodesyIng. Hana StaIng. Hana Staňňkovkováá, Ph.D., Ph.D.

IGDM, HGF, VIGDM, HGF, VŠŠBB--TU OstravaTU Ostravahana.stankovahana.stankova@@vsb.czvsb.cz

A911, 5269A911, 5269

1/11/1GeodesyGeodesy

-- a scientific field involved in measuring the Eartha scientific field involved in measuring the Earth’’s s surface, in determining the relationships between surface, in determining the relationships between points of the Earthpoints of the Earth’’s surface, both horizontally and s surface, both horizontally and verticallyvertically

GeodesyGeodesy

GenerallyGenerally

ConcernedConcerned withwith measuringmeasuring thethe EarthEarth on a on a globalglobal scalescale

Takes the curvature of the Earth into accountTakes the curvature of the Earth into account

not not takentaken into account when measuring into account when measuring the curvature of the Earththe curvature of the Earth

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AdvancedAdvanced

Other fields involved with geodesyOther fields involved with geodesy

• CartographyCartography –– ddocumentsocuments the results of geodesythe results of geodesymapsmaps, , plansplans

-- ddescribesescribes illustrative procedures and illustrative procedures and methodsmethods

•• AstronomyAstronomy –– The science of the universe, of The science of the universe, of

cosmic bodies and their movementscosmic bodies and their movements

•• PhotogrammetryPhotogrammetry –– Using photographic images and Using photographic images and geodetic images to determine, under certain geodetic images to determine, under certain

conditions, the size, shape and position of an object conditions, the size, shape and position of an object in a spatial environmentin a spatial environment

DivisionDivisionterrestrialterrestrialaerialaerial

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Photo of Vladislav Hall

Trap Trap vectorvector andand rasterraster vaultvault

Plan of Countor Lines andDMT

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SurveyingSurveying ofof GreatGreat OmyavadOmyavad MosqueMosque in in AleppAlepp inin SyriaSyria

Photo of mosque with a minaret Photo of mosque with a minaret

Vector EvaVector Evalluationuation

Digitální pozemní fotogrammetrie na ČVUT v Praze

GIS Ostrava 2001GIS Ostrava 2001

Ing. MiluIng. Milušše Valentove Valentováá

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http://http://vilemwaltervilemwalter.cz/mapy/.cz/mapy/http://http://brnobrno..tucnacektucnacek.cz/2005122301.cz/2005122301

Historic ortHistoric orthhophotomapophotomap of Brno Cityof Brno City (1930)(1930)

Map with marked of direction seeding axes by aircraft

Hill of Palacky

Comparison of Comparison of the same area the same area about 70 years about 70 years later.later.

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2

NewNew fields involved with geodesyfields involved with geodesy1/71/7

•• Physical GeodesyPhysical Geodesy

Based on knowledge of the EarthBased on knowledge of the Earth’’s gravitational fields gravitational fieldConcerned with the EarthConcerned with the Earth’’s interior composition, s interior composition,

determination of its shape and dimensions of the Earthdetermination of its shape and dimensions of the Earth

GravimetryGravimetry

•• Geodetic AstronomyGeodetic AstronomyField of practical astronomyField of practical astronomy

Determination of latitude, longitude and astronomical Determination of latitude, longitude and astronomical

azimuthazimuth

•• Spherical AstronomySpherical Astronomy

Determines the position of stars and their changes Determines the position of stars and their changes

and astronomical coordinateand astronomical coordinate systemssystems

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•• Space GeodesySpace Geodesy

Concerned with phenomena in space for the Concerned with phenomena in space for the

purpose of solving basic geodetic tasks for purpose of solving basic geodetic tasks for

determining the size and shape of the Earthdetermining the size and shape of the Earth

•• Satellite GeodesySatellite Geodesy

Solves tasks of Solves tasks of advancedadvanced geodesy using terrestrial geodesy using terrestrial measurements on artificial satellitesmeasurements on artificial satellites

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Earth Earth –– physical body, difficult to definephysical body, difficult to define

Formation of terrestrial body Formation of terrestrial body –– impact of two forcesimpact of two forces

The result of both these forces is The result of both these forces is GGravitationalravitational force Gforce G

Magnetizing force „F“

Centrifugal force„P“

LawLaw ofof GravityGravity

EarthEarth´́s s rotationrotation

EarthEarth’’s gravitational field s gravitational field

space where the effect of space where the effect of the Earththe Earth’’s gravity is felts gravity is felt

REFERENCE BODIES OF THE EARTHREFERENCE BODIES OF THE EARTH (1)(1)1/101/10

LevelLevel SurfaceSurface –– closed surface where each point is closed surface where each point is perpendicular to the direction of gravity perpendicular to the direction of gravity

their intersection with the Earth's surfacetheir intersection with the Earth's surfacecontour lines in topographic mapscontour lines in topographic maps((ImageImage) )

The most important The most important levellevel surface for geodesy surface for geodesy

GEOIDGEOIDJ.B. J.B. ListingListing (1872)(1872)

•• ThroughThrough thethe Zero Zero Point,Point,•• Mean ocean and sea surface level, Mean ocean and sea surface level, •• ExtendedExtended bellowbellow the continents by an the continents by an

endless number of canals.endless number of canals.

REFERENCE BODIES OF THE EARTHREFERENCE BODIES OF THE EARTH (2)(2)

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EarthEarth, Geoid , Geoid –– irregularirregular bodiesbodies

--complex shapes unsuitable for complex shapes unsuitable for mathematical evaluations of mathematical evaluations of the acquired measurementsthe acquired measurements

Rotational Rotational EEllipsoidllipsoid

SimplySimply mathematicallymathematically definedefine surfacesurface

Suitable dimensionSuitable dimension–– Earth's ellipsoidEarth's ellipsoid

GeneralyGeneraly Earth's ellipsoidEarth's ellipsoid

Ellipsoid, the parameters of which represent the Ellipsoid, the parameters of which represent the geoidgeoid as a whole as a whole with a center of mass Swith a center of mass S00, likewise with the center of the Earth S, likewise with the center of the Earth SZZ

and with a polar radius identical to the Earthand with a polar radius identical to the Earth’’s axis of rotation.s axis of rotation.

REFERENCE BODIES OF THE EARTHREFERENCE BODIES OF THE EARTH (3)(3)1/121/12

An ellipsoid for the Earth that An ellipsoid for the Earth that approximates the approximates the GGeoideoid only in certain only in certain regions of the Earth. Its center of mass regions of the Earth. Its center of mass SSrr is not identical to the center of the is not identical to the center of the Earth Earth andand its polar radius is parallel to its polar radius is parallel to the Earththe Earth’’s axis of rotation.s axis of rotation.

Reference Reference EllipsoidEllipsoid

•• body flattened at the polesbody flattened at the poles

•• defined by two parametersdefined by two parameters

EquatoralEquatoral radiusradius aa

PolarPolar radiusradius bb

TheThe parametersparametersusedused

flatteningflattening

abai

2

222

abae

firstfirst eccentricityeccentricity

abai

REFERENCE BODIES OF THE EARTHREFERENCE BODIES OF THE EARTH (4)(4)

3

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Reference Reference EllipsoidsEllipsoids

•• BesselBessel (1841)(1841) SS--JTSK (Civil Geodetic Service)JTSK (Civil Geodetic Service)

•• HayfordHayford (1910)(1910)

Recommended IUGG in 1924 at the Recommended IUGG in 1924 at the international ellipsoid.international ellipsoid.

Not suitable for Europe, parameters are Not suitable for Europe, parameters are meant only for the USAmeant only for the USA

•• KrasovskiKrasovski (1940)(1940) SS--42 ( S42 ( S--42/83) 42/83) Military Topographical Military Topographical ServiceService

•• WGS84 (1984) WGS84 (1984) WGS84, WGS84, global geocentric geodetic global geocentric geodetic reference systemsreference systems (GPS)(GPS)

•• GRS80 (1989)GRS80 (1989) ETRS89, ETRS89, European terrestrial reference European terrestrial reference system for the epoch 1989.0, spread system for the epoch 1989.0, spread out along the Eurasian plateout along the Eurasian plate

REFERENCE BODIES OF THE EARTHREFERENCE BODIES OF THE EARTH (5)(5)1/141/14

1/298.257222101/298.2572223561/298.31/297.01/299.153i[m]

6356752,3146356752.3146356863.0196356911.9466356078.963b[m]

6378137.0006378137.0006378245.0006378388.0006377397.155a[m]

19891984194019101841year

ETRS89WGS84KrasovskijHayfordBessel

Tab. Tab. ParametersParameters ofof reference reference ellipsoidsellipsoids

•• ParametersParameters

•• Position and orientation to the Position and orientation to the GGeoideoidDifferencesDifferences: :

REFERENCE BODIES OF THE EARTHREFERENCE BODIES OF THE EARTH (6)(6)

1/151/15REFERENCE BODIES OF THE EARTHREFERENCE BODIES OF THE EARTH (7)(7)

If we replace the geoid with a rotational ellipsoid:

• Geoid plumb line t and ellipsoid normal n form a small angle at various points – deflection of the vertical θ .

OthersOthers reference reference bodiesbodies::

•• Earth'sEarth's sphere sphere (R=6382 km)(R=6382 km)

MeanMean radiusradius ofof curvaturecurvature

••FlatFlat surfacesurface

1/161/16SYSTEM OF GEODETIC GEOGRAPHIC COSYSTEM OF GEODETIC GEOGRAPHIC CO--ORDINATESORDINATES

•• Used to determine location points on the reference ellipsoidUsed to determine location points on the reference ellipsoid

•• Polar radius connects PPolar radius connects Pss and Pand PJJ

EquatorEquator A plane passing through the center of the ellipsoid A plane passing through the center of the ellipsoid S, perpendicular to the polar axis with the plane of S, perpendicular to the polar axis with the plane of the ellipsoidthe ellipsoid

ParallelsParallelsPlanes parallel to the plane of the equator, small Planes parallel to the plane of the equator, small circles with a radius that decreases moving from circles with a radius that decreases moving from the equator to the polesthe equator to the poles

Bundle of planes passing through the axis of rotation, Bundle of planes passing through the axis of rotation, intersecting the surface of the ellipsoid intersecting the surface of the ellipsoid atat

MeridiansMeridians

which are ellipses of semiwhich are ellipses of semi--axes a, baxes a, b

SYSTEM OF GEODETIC GEOGRAPHIC COSYSTEM OF GEODETIC GEOGRAPHIC CO--ORDINATESORDINATES1/171/17

Geodetic latitude Geodetic latitude φφ

The angle at which the The angle at which the geodetic normal led by geodetic normal led by point P to the plane of point P to the plane of the ellipsoid intersects the ellipsoid intersects with the plane of the with the plane of the equatorequator

Geodetic longitude Geodetic longitude λλ

The angle at which the plane of the line of longitude The angle at which the plane of the line of longitude led led by point by point P intersects the plane of the prime meridian P P intersects the plane of the prime meridian P

P(P(φφ,,λλ))