2. Geodesy :- Geo - Earth desy - The
study of
“The study of the Earth”
Geodesy is the science of the
measurement and mapping of the earth’s
surface
3. Merriam-Webster:a branch of
applied mathematics concerned with the
determination of the size and shape of
the earth and the exact positions of
points on its surface and with the
description of variations of its gravity
field.
4. • 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.
Types of Geodesy
6. Eratosthenes had observed that
on the day of the summer solstice
(20-22 June), the midday sun
shone to the bottom of a well in
the Ancient Egyptian city of
Swenet (known in Greek as
Syene).
Eratosthenes Egypt
about 240 BC
Spherical Model of the Earth
8. •He knew that at the same time, the sun was not
directly overhead at Alexandria; instead, it cast a
shadow with the vertical equal to 1/50th of a circle (7°
12').
•He also knew that Alexandria and Syene were 500
miles apart
•To these observations, Eratosthenes concluded that
the circumference of the earth was 50 x 500 miles, or
25000 miles.
Spherical Model of the Earth
9. •The accepted value along the equator is 24,902 miles,
but, if you measure the earth through the poles the value
is 24,860 miles
•He was within 1% of today’s accepted value
•Eratosthenes' conclusions were highly regarded at the
time, and his estimate of the Earth’s size was accepted
for hundreds of years afterwards.
Spherical Model of the Earth
10. How Do We Define the Shape
of the Earth?
We think of the
earth as a sphere
It is actually a spheroid,
slightly larger in radius
at the equator than at the
poles
11. The Ellipsoid
An ellipse is a mathematical
figure which is defined by
Semi-Major Axis (a)
and
Semi-Minor Axis (b)
or
Flattening (f) = (a - b)/a
It is a simple geometrical
surface
Cannot be sensed by
instruments
b
a
15. Europe
N. America
S. America Africa
Topography
An ellipsoidal-earth model is
no longer tenable at a high
level of accuracy. The
deviation of the physical
measurements refer from the
ellipsoidal model can no
longer be ignored.
The geoid anomaly is the
difference between the geoid
surface and a reference
ellipsoid
The Real Earth (Geoid)
16. What is the Geoid?
• “The equipotential
surface of the Earth’s
gravity field which
best fits, in the least
squares sense, global
mean sea level.”
• Can’t see the surface
or measure it directly.
• Modeled from gravity
data.
17. Ellipsoid and Geoid
Ellipsoid
• Simple Mathematical Definition
• Described by Two Parameters
• Cannot be 'Sensed' by Instruments
Geoid
• Complicated Physical Definition
• Described by Infinite Number of
Parameters
• Can be 'Sensed' by Instruments
20. Which ellipsoid to choose ?
O2
O1
Europe
N. America
S. America Africa
N
Topography
N
Ellipsoid and Geoid
21. Common Ellipsoid
The best mean fit to the Earth
Europe
N. America
S. America Africa
N
Topography
A = 6,378,137.000 m
1/f = 298.2572236
22. Unfortunately, the density of the earth’s crust is not uniformly the
same. Heavy rock, such as an iron ore deposit, will have a stronger
attraction than lighter materials. Therefore, the geoid (or any
equipotential surface) will not be a simple mathematical surface.
Ellipsoid and Geoid Heights
23. Heighting
•The equipotential surface is forced
to deform upward while remaining
normal to gravity. This gives a
positive geoid undulation.
•Conversely, a mass shortage
beneath the ellipsoid will deflect
the geoid below the ellipsoid,
causing a negative geoid
undulation.
Ellipsoid
Ellipsoid
P
P
H
H
Geoid
Geoid
h
h
Topography
Topography
24. h = H + N
h = H + N
h = H + N
h = H + N Ellipsoid
Ellipsoid
h
h
P
P Topography
Topography
H
H
Geoid
Geoid
N
N
N = Geoidal Separation
H = Height above Geoid
(~Orthometric Height)
h = Ellipsoidal height
Heighting
Orthometric Height (h) “ perpendicular vertical distance
between the geoid and land surface”
25. Heighting
The height difference between
ellipsoid and geoid is called the
geoidal undulation
To obtain orthometric heights,
the geoidal undulation must be
accounted for
Ellipsoid
Ellipsoid
P
P
H
H
Geoid
Geoid
N
N
N = Geoidal Separation
h
h
Topography
Topography
26. Latitude and Longitude
Lines of latitude are called “parallels”
Lines of longitude are called “meridians”
The Prime Meridian passes through Greenwich, England
28. Length on Meridians and Parallels
0 N
30 N
∆φ
Re
Re
R
R
A
B
C
∆λ
(Lat, Long) = (φ, λ)
Length on a Meridian:
AB = Re ∆φ
(same for all latitudes)
Length on a Parallel:
CD = R ∆λ = Re ∆λ Cos φ
(varies with latitude)
D
29. Any set of numbers,
usually in sets of
two or three, used to
determine location
relative to other
locations in two or
three dimensions
Coordinate systems
30. Global Cartesian Coordinates (x,y,z)
O
X
Z
Y
Greenwich
Meridian
Equator
•
•A system for the whole
earth
•Non manageable and
difficult to relate to other
locations when translated
to two dimensions
•The z-coordinate is
defined as geometrically
31. Geographic Coordinates (φ, λ, z)
• Latitude (φ) and Longitude (λ) defined using an
ellipsoid, an ellipse rotated about an axis
• Elevation (z) defined using geoid, a surface of
constant gravitational potential
