Introduction to Geodesy

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Lecture 3

• Introduction to Geodesy

Geodesy is a 21st Century science making use of
the most advanced space measurement and computer
technologies.
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• Definition of Geodesy
• Geodesy is the study of
• The size and shape of the earth
• The measurement of the position and motion
  of points on
• the earth's surface, and
• The configuration and area of large portions
  of the earth's surface.
• Geodesy serves as a foundation for the mapping
  and referencing of all
• geospatial data, it is a dynamic application of
  scientific methods in support
• of many professional, economic and scientific
  activities and functions,
• ranging from land titling to mineral exploration
  from navigation, mapping
• and surveying to the use of remote sensing data
  for resource management
• from the construction of dams and drains, to the
  interpretation of
• seismic disturbances.

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Applications of Geodesy
Geodesists improve models to enable more precise
determination of satellite orbital positions.
They use radio astronomy to position the earth
and points on or above the earths surface in a
reference system based on quasars. Using
space-borne instruments, geodesists study
variations in mean sea level, mass transports
caused by atmosphere, ocean circulation, ground
water redistribution, and ice sheet
changes. Satellites are also used to mea-sure
earths gravity field and its temporal changes
and to study its role in climate change
phenomena and natural hazards. Geodesists use
new satellite navigation and positioning
capabilities to survey the land more accurately
and more economically to within a centimeter.
They use state-of-the-art navigation systems to
provide precise positions of science platforms
on board aircraft, ships, and satellites. Geodesy
plays an active role in the burgeoning geomatics
industry that includes the disciplines of land
surveying, photogrammetry, remote sensing,
hydrography, cartography, engineering surveying,
geographic information science, and geospatial
computing.
Ohio State University
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Geodetic Surveying

• An accurate means of determining position and
  height.
• Geodetic survey is an effective means of
  providing accurate position and
• height on the earth's surface. Works that
  require geodetic surveys for
• the accurate positioning of control points
  are
• Large mapping projects
• Tunnelling and laying of pipelines
• Precise control positioning for large
  survey works

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Shape of the Earth

• Over limited area treat earth as a plane - simple
• Sometime as as a sphere - spherical trigonometry
• geoid
• Forces generated by the Earths rotation
  flatten the Earth into an ellipse

.
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A Historical Perspective of Geodesy
The Ancient Greeks suspected the Earth was
round. Eratosthenes (276 - 195BC) made the first
attempt to compute the dimensions of the Earth.
He noticed that at the summer solstice (ie sun
directly overhead) the suns rays were reflected
vertically from a deep well in Syene, Egypt. At
the same time, at Alexandria, the suns rays were
measured at an inclination of 7o 12 from the
vertical
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A Historical Perspective of Geodesy
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A Historical Perspective of Geodesy
S distance from Alexandria to Syrene
Sphere radius r circumference C 2?r
S r.Z r S / Z
but assumes Alexandria and Syrene on same meridian
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A Historical Perspective of Geodesy

• Syene not exactly on Tropic of Cancer. Therefore
  Sun not
• directly overhead.
• Syene and Alexandria not on same meridian
• Distance between Syene and Alexandria not
  accurately
• known (10 too long)
• Earth not exactly spherical

Final result gave circumference of the Earth as
16 too big.
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A Historical Perspective of Geodesy

• After Columbus and de Gama discovered earth was
  not flat
• Fernel, 1525 observed the elevation of the sun in
  Paris and Amiens using astro tabls and odometer,
  1 error
• Newtons laws of motion detrmined the earth was a
  prolate ellipsoid.

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A Historical Perspective of Geodesy
centrifugal force at pole 0 centrifugal force
at equator max
resultant force pulls point P towards equator
gravity decreases in magnitude from the poles to
the equator due to the centrifugal force of the
earths rotation
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A Historical Perspective of Geodesy

• Bouguer discovered regional gravity variations
  due to the non uniform density of the earth
• Clairaut and Stokes relationships between gravity
  measurements and the flattening of the earth
• Laplace, Gauss and Bessel, deviation of the plumb
  line

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Relationship Between Different Surfaces
Earth An irregularly shaped planet we have to
work on. Geoid An equipotential surface (a
fancy way of saying the pull of gravity is equal
everywhere along the surface) which influences
survey measurements and satellite orbits. A
plumb bob always points perpendicular to the
geoid, not to the center of the earth.
Ellipsoid An ellipse which has been rotated
about an axis. This provides a mathematical
surface on which we can perform our
calculations. The shape of the ellipsoid is
chosen to match the geoidal surface as closely
as possible.
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Relationship Between Different Surfaces

• AHD coincident with geoid for most practical
  purposes
• geoid departs from a geocentric sphere by 22km
  and from an oblate geocentric spheroid, flattened
  at the poles by 100m
• All conventional survey measurements are made
  relative to the geoid, but geodesists choose a
  spheroid to approximate the geoid for data
  reduction and subsequent mapping

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Relationship between the Geoid and Ellipsoid
geoid - spheroid separation N h - H
H orthometric height approximated by AHD above
the geoid h spheroidal height above the
spheroid N geoid height above the spheroid
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Deflection of the Vertical

• Instrument set up perpendicular to the geoid.
  Because we work with the spheroid. Difference is
  the deflection of the vertical. This can be
  neglected if small.

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Deflection of the Vertical

• deflections are unique for each spheroid,
  depending on the fit of the ellipsoid to the
  geoid should be less than 1
• Varies continuously with position due to local
  variations in the geoid
• are related to the differences between astronomic
  and geodetic coordinates
• deflections are resolved into two planes
• components conventionally ve when the gravity
  vertical is deviated to the north or east, of the
  geodetic vertical

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Deflection of the vertical
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Laplace Stations

• Points on a geodetic network where precise
  astronomy obs are taken
• obs used to measure discrepancies between the two
  systems in both position and azimuth
• regional or national ellipsoid datum is defined
  in terms of these differences at a particular
  point eg. Johnston geodetic station

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Deflection of the Vertical

• deflection in the meridian is ve when deflected
  to the north

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Deflection of the Vertical

• deflection is positive to the east and can be
  derived from

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Laplace Equation
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Deviation of the vertical in azimuth a
Unlike the geoid the ellipsoid is not a physical
reality. Its size and position are arbitrarily
chosen and the values of the geodetic coords will
be dependent on this choice. Consequently the
size of the deviation of the vertical a5t a
point is not unique, but is a function of the
chosen reference system
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The Best Fitting Spheroid

• the spheroid is deliberately chosen to be a best
  fit to the geoid, so as to simplify survey data
  reduction. This is achieved by minimizing x,h,N
• 6.3m in geoid-spheroid separation 1ppm
  horizontal scale error

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Coordinate Systems

• Plane Coordinates
• local, possible arbitrary
• z axis vertical throughout
• right handed system
• bearings relative to y axis
• ignores shape of earth
• x,y,z

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The most commonly used coordinate system today is
the latitude, longitude, and height system. The
Prime Meridian and the Equator are the reference
planes used to define latitude and longitude.
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The geodetic latitude of a point is the angle
from the equatorial plane to the vertical
direction of a line normal to the reference
ellipsoid. The geodetic longitude of a point
is the angle between a reference plane and a
plane passing through the point, both planes
being perpendicular to the equatorial plane.
The geodetic height at a point is the distance
from the reference ellipsoid to the point in a
direction normal to the ellipsoid.
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Cartesian Coordinate System
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Relationship Between Cartesian and Geodetic
Coordinate Systems
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Map Grid Coordinates

• derived from geodetic coordinates
• transform 3D to 2D
• scale and line distortions present
• survey observables require corrections
• map projections

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Geodetic Datums

• numerical or geometrical quantity or set of
  quantities which serve as a reference or base for
  other quantities
• The adopted coordinates (after and adjustment of
  measurements comprise the datum)
• The spheroid is a simple geometrical reference
  surface to which the coordinates are referred
• horizontal or vertical, datums
• regional or global different best-fitting
  reference spheroids have been defined in
  different parts of the world because of the
  undulating geoid. Eg. the Australian National
  Spheroid.

NB Difference between spheroid and datum
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Geodetic Datums

• consists of f, l or an initial origin the
  azimuth for one line the parameters of the
  reference ellipsoid and the geoid separation at
  the origin. The deflection of the vertical and
  geoid-spheroid separation are set to zero at an
  origin point eg Johnson in Australia
• geodetic latitudes and longitudes depend on both
  the reference spheroid and coordinate datum
• often the spheroid is implicitly linked to the
  datum, so it has become common to use the datum
  name to imply the spheroid and vice versa eg
  WGS84
• the orientation and scale of the spheroid is
  defined using further geodetic observations

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Horizontal Datum
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Orientation of the ellipsoid to the Geoid
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Orientation of the ellipsoid to the Geoid
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Geodetic Datums

• Local/regional datum
• Approximates size and shape of the earth on a
  local, regional scale
• geometrical centre of the spheroid not
  necessarily coincident with geocentre
• well suited to surveying over the areas they were
  defined for - inadequate for global satellite
• surveying systems.

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Regional Spheroids and Datums

• once the best-fitting spheroid is adopted, all
  geodetic observations are reduced to this
  spheroid, adjusted in a least squares sense,
  which forms the geodetic datum.

eg the Australian Geodetic Datum (AGD) is based
on ANS
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Global Spheroids and Datums

• satellite geodesy provides us with spheroids that
  are geocentric, where their geometrical centre
  corresponds with the Earths centre of mass since
  the satellite orbits are close to the geocentre
• orientation achieved by aligning its minor axis
  with the Earths mean spin axis at a particular
  epoch eg WGS84
• a modern global network of accurately coordinated
  ground stations comprises a global datum called
  the International Earth Rotation (IERS)
  International Terrestrial Reference Frame (ITRF)

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Global Spheroids and Datums

• ITRF is positioned relative to the geocentre
  using a variety of space geodetic techniques,
  such as Satellite Laser Ranging (SLR), Very Long
  Baseline Interferometry (VLBI) and GPS.
• The ITRF is considered to be a more reliable
  datum than WGS84 and will form the backbone of
  the GDA 10cm difference between them

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Effect of Using Different Datums

• Datum and spheroid must be specified to define
  horizontal position not just f, l
• Without this information a single point can
  refer to different positions