Lecture Notes - Geodesy

GEOSDESY

Lecture Notes

GEODESY

AN AUGMENTED REALITY EXPERIENCED

PREPARED BY
MOHD ROZAIMIN BIN ABDUL HAMID
LAILATUL RAHMAH BINTI NEK2 MAT

GEOSDESY
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LECTURE NOTES - GEODESY

TERBITAN EDISI 2020

HAK CIPTA TERPELIHARA, TIADA BAHAGIAN DARIPADA BUKU INI BOLEH
DITERBITKAN SEMULA, DISIMPAN UNTUK PENGELUARAN ATAU
DITUKARKAN KE DALAM SEBARANG BENTUK ATAU SEBARANG ALAT
JUGA PUN, SAMA ADA DENGAN CARA ELEKTRONIK, GAMBAR SERTA
RAKAMAN DAN SEBAGAINYA TANPA KEBENARAN BERTULIS DARIPADA
BAHAGIAN INTRUKSIONAL DAN PEMBEAJARAN DIGITAL, JPPKK
TERLEBIH DAHULU.

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INSTRUKSIONAL DAN PEMBELAJARAN DIGITAL, JPPKK.

PENULIS
MOHD ROZAIMIN ABDUL HAMID
LAILATUL RAHMAH BINTI NEKMAT

DITERBITKAN OLEH
UNIT PEMBELAJARAN DIGITAL
BAHAGIAN INSTRUKSIONAL DAN PEMBELAJARAN DIGITAL
JABATAN PENDIDIKAN POLITEKNIK DAN KOLEJ KOMUNITI ARAS 6, GALERIA PJH,
JALAN P4W, PERSIARAN PERDANA, PRESINT 4,
62100 PUTRAJAYA

Website : www.celt.edu.my
E-mail : [email protected]



GEOSDESY

GEODESY

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TABLE OF CONTENT

INTRODUCTION TO GEODESY 4
What is Geodesy 5
Definition of Geodesy 5
What is true shape of Earth 6
Historical Development of Geodesy 7-10
!"# F%&'()*& *$ G#*,#- . 11
The Application of Geode sy 22
Discipline of Geodesy 12
Geodesy Structure And Branches 13


!"#"!"$%" &'!#(%"& )$ *"+,"&-
./0 /12 "3245 6//7 6879 :;
What is on the ground 15
Why we need the reference Surf aces 16
Introduction 17
Reference surface 18
Topographic surface 19-20

GEOID SURFACE 21
Geoid has following surface 22-23

E L L I PS OID SUR FAC E !"#!$
Reference Elipsoid ./0.1

Reliationship between reference surf aces 23
Orthometric Height, Ellipsoid Height and Geoid Height 29-31
The Deviation of Vertical 01

ACTIVIT Y 33

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INTRODUCTION TO GEODESY.s

Figure 1 : Ancient Egypt (NASA Goddard)

Geo daisia = dividing the Earth

• One of the oldest professions in the
world.

• Semantically, it comes from the word
“Geo” and “Daisia”.

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uWHAT IS GEODESY ?.

• Geodesy is defined as the science of determining the
size, shape and gravity field of the Earth.
• If you know the size/shape of the Earth, you
should also be able to figure out where you are on the
Earth.
• Study of: -

- size and shape of Earth

- measurements of the position and motion
of points on the Earth’s surface

- configuration and area of large portions
of Earth’s surface



DEFINITION OF GEODESY

Figure 2: F.R. Helmert

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WHAT IS TRUE SHAPE OF THE EARTH

!"

Figure 3 : Beautiful Planet




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HISTORICAL DEVELOPMENT OF GEODESY.A

Various opinions on the form of the Earth prevailed in
the past among others, expressed themselves that the
Earth was a spherical shape.

• Homer’s Iliad, 800 BC
• Thales of Millet, 600 BC
• Pythagoras, 580-500 BC
• Aristotle (384-322 BC)

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Figure 4 : Eratosthenes (http://www.classichistory.net)

Eratosthenes (276-195 BC) calculated the circumference of the Earth
using the following equation: -



Circumference =



s = distance between two points that lie on north and south

= angular distance at the center of the Earth between two points

that lie on north and south of the earth surface.

But he could not get the angle directly from the center of the Earth, so he got
the angle measurement the from rays of the sun. Let’s check it out for more….

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Eratosthenes found that at the
time of the summer solstice,
the rays of the sun descended
vertically into a well in Syene.
Whereas in Alexandria, from
the length of the shadow
produced from the sunrays,

Figure 5 : Source of image Kriginal created by
EASA Blueshift

he can estimate the
distance(s) from Syene to
Alexandria. With h and s

known, can be solved.
Then, the circumference of
the Earth can be measured
by using the following
equation:



Circumference of the Earth Figure 6 : Source of image from https://
= www.youtube.com/watch?v=7C2IMv6_ENI

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Hsing (eighteenth century)

• Buddhist Monk who also mathematician and
astronomer
• Organizing observation over an arc of the

earth.
• His value of the earth’s circumference is
128,300 li (Chinese unit for distance) or
56,700 km
Gemma Frisius and Snellius (1533)

• Introduced the principles of triangulation.
Jean Picard (1669)
• Introduced the telescope for observing star
altitudes and angles of triangulation.
Isaac Newton (1643-1727) and Christian Huygens
(1629-1695)

• Developed earth models flattened at the poles
and founded on principles of physics.
• Maupertuis and Clairaut (1713-1765)
• Confirmed the polar flattening through the
scientific expedition from Sweden and Finland
to Peru (now Ecuador)

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THE FUNCTION OF GEODESY.u

- Determine horizontal points on Earth’s surface
- Determine distances and directions between points on the Earth’s surface , and
- Determine the heights of points on the Earth’s surface.

ITHE GEODESY APPLICATION.

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DISCIPLINE OF GEODESY

Figure 7 : Source of image from Vanicek and Krakiwsky

GEODESY STRUCTURE AND BRANCHES

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GEODESY STRUCTURE AND BRANCHES

• Geometrical geodesy is concerned with describing
locations in terms of geometry. Consequently,
coordinate systems are one of the primary products
of geometrical geodesy.

• Physical geodesy is concerned with determining
the Earth’s gravity field, which is necessary for
establishing heights.

• Satellite geodesy is concerned with using orbiting
satellites to obtain data for geodetic purposes.

• Geodetic Astronomy, is described as [Mueller,
1969] the art and science for determining, by
astronomical observations, the positions of points
on the earth and the azimuths of the geodetic
lines connecting such points. When referring to its
use in surveying, the terms practical or positional
astronomy are often used.

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REFERENCE SURFACES IN GEODESY

HOW OUR EARTH

Figure 8 : Our Earth

LOOK LIKE ?

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WHAT
IS ON
THE
GROUND.

S

Figure 9 : GPS Satellite (ESA and CNES, 2016)

Figure 10 : Flying in a low orbit 830 miles above the Earth (https://www.nesdis.noaa.gov/
content/celebrating-one-year-anniversary-launch-jason-3)

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WHY WE NEED…..

Figure 11 : Selection of a reference surface (https://kartoweb.itc.nl)

REFERENCE
SURFACE?

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INTRODUCTION.s

Any geoinformatics data should be processed and presented in the
form of coordinates numerical value or graphical format such as
plans or maps.

 The earth’s surface is so complex to be modeled for data
processing and measurement to be carried out.

 Any surveying works done by geomatic engineer on a small area
(≤ 18 km2) can assumed the earth’s surface is flat (plane) to
make calculation simple. (the curvature of the earth’s surface is
not taken into account)

 On the other hand, astronomers and navigators, need a reference
surface that similar to earth’s shape, (i.e. the curvature of the
earth surface is taken into account). They used sphere shape to
ease calculation (it needs only one parameter i.e. radius).

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REFFERENCE SURFACE.L

Figure 12 : Geocentric Ellipsoid (URS Corporation)

For the geodesist, the earth’ s surface is divided
• Topographic sur
face
• Geoid Surface
• Ellipsoid or
Spheroid Surface

Figure 13 : Topographic Surface (DFHRS)

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TOPOGRAPHIC.7

SURFACE

• the nature of the earth surface
• here is none mathematical expression to

repres ent th e e arth surface

Figure 14 : Metropolitan area

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Figure 15 : Model of the Earth (https:// www.peterverdone.com)

Anyhow, the shape of the
topographic surface is in
the form of an ellipsoid.s

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GEOID SURFACE.A

- It is the equipotential surface at mean
sea level

- In Torge’s book, Geodesy (p. 44),
description of the geoid:

We consider the waters of the ocean Figure 16 : Water of the ocean
as freely moving homogeneous mat- (https://www.e-education.psu.edu)
ter, which is subject only to the force
of gravity of the Earth. Upon attain-
ing a state of equilibrium, the surface
of such idealized oceans assumes
a level surface of the gravity field;
we may regard it as being extended
under the continents (e.g., by a sys-
tem of communicating tubes). This
level surface is termed the geoid.

- It serves as a reference surface for
defining height systems

Figure 17 : Reference surface for defining height system
(https://www.o.quizlet.com)

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Geoid has following properties.0

- real (physical) surface.
- An equipotential surface of gravity.
- Gravity vector (vertical) at any points perpendicular to the surface.
- Closely agrees with mean ocean surface.
- Determined by observations.
- Used as a datum for elevations.
- Cannot be represented mathematically, and therefore cannot be used as a
horizontal datum.

The direction the earth’s gravity field is normal to the geoid surface

Figure 18 : Level (equipotential) surfaces and plump lines near
the earth (https://www.pobonline.com)

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Figure 19 : The Earth’s true shape (Nasa)

Geoid Model for Peninsular Malaysia

Earth’s

Figure 20 : Geoid Model - Penisular Malaysia (JUPEM Malaysia)

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ELLIPSIOD.......L

- Is a solid generated by rotating an ellipse about
the minor axis
- The geometry shape and size of an ellipsoid is
determined by the semi major (a) axis and
flattening value (f)
- The shape of an Ellipsoid is nearest to the shape
of the physical earth (topographic) and can be
defined mathematically.

Ellipsoid d

Figure 21 : Earth’s Topographic and Ellipsoid

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Figure 22 : Earth’s diameter (https://herbzinser60.files.wordpress.com/)

DIAMETER OF THE EARTH.!

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REFFERENCE ELLIPSIOD.A

- There are several ellipsoids used to ‘best fit’ an
area /country for surveying purposes.
- So, each country chooses an ellipsoid whose sur
face corresponded closely to the geoid within
their area of interest. These local ellipsoids have
different shapes and different positions
and orientations.
- Our previous Reference Ellipsoid (Malaysia) was
‘Modified Everest’ (a.k.a Malaysian Ellipsoid):
a = 6377304.063 m

f = 1/300.8017
• What is our new Reference Ellipsoid?

Figure 23 : Reference Ellipsoid (https://unstats.un.org)

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Figure 24 : Selected Reference Ellipsoids (Peter H. Dana)

Figure 25 : Fitting Differencent Ellipsoids to Different Area ( James R Smith )

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RELATION BETWEEN REFERENCE SURFACE.]

Figure 26 : Earth, Ellipsoid and topographic Surface ( James R Smith )

 GPS gives height values related to an ellipsoid (h), thus to
turnGPS(ellipsoid)valuesintotheirequivalentOrthometric
Height (H), requires a correction called Geoid Height (N).

 If ellipsoid height is represented by h and orthometric
height by H, the relationship between the two is
determined by the equation, h = H + N or conversely
H=h-N

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Figure 27 : Earth, Ellipsoid and topographic Surface ( James R Smith )

Orthometric Height, Ellipsoid Height and

Figure 28 : Orthometric and Ellipsoid Height (http://www.dfhbf.de)

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ELLIPSOIDAL HEIGHT

• Ellipsoidal Heights, (h) are measured along the normal to the ellipsoid.
• Thus, height found via GPS are ellipsoid values related to the normal to the

ellipsoid.

ORTHOMETRIC HEIGHT

• The Geoid is that equipotential surface (equal gravity) that best equates to
Mean Sea Level.

• Orthometric heights, (H) are referenced to a Datum which is typically called as
M.S.L.

• M.S.L approximates the Geoid.
• The Orthometric height are obtained when using a normal level instrument

GEOID HEIGHT OR GEOID SEPARATION

• The differences between ellipsoid surface and geoid surface, which is the height
of the geoid measured from the ellipsoid is called geoid height, N.

• Geoid height can be determined with varying degrees of reliability.

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Figure 29 : Geoid Undulation (http://www.kartoweb.itc.nl)

Ellipsoidal height above the reference ellipsoid and the
orthometric height H above the Geoid for two point on the
earth surface. The ellipsoidal height is measured orthogonal
to the ellipsoid. The orthometric height is measured
orthogonal to the geode.

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The Deviation
of The
Vertical.

I

Figure 30 : Deviation of The Vertical (http://www.kartoweb.itc.nl)

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ACTIVITY

Answer the following questions. You may discuss the answer with a friend next
to you in pairs.

1. What does equipotential surface mean?
2. Our previous reference ellipsoid (Malaysia) was “modified Everest. So

what is the reference ellipsoid used now?
3. What kind of height does “level” instrument obtained?
4. And, what about GPS, what kind of height does it gives?
5. Which kind of height that we used for mapping purposes?
6. Differentiate between vertical line and ellipsoid normal?

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