Introduction to Geodesy Flashcards
Geodesy in the Geodetic Glossary (NGS 2009)
“The science concerned with determining the size and shape of the Earth” or “The science that locates positions on the Earth and determines the Earth’s gravity field.”
Fundamental Properties of the Earth (3)
(1) its geometric shape,
(2) its orientation in space, and
(3) its gravity field as well as the changes of these properties with time.
Geodesy from the Greek words
“geo” and “desa” means “earth” and “to divide”.
Webster’s definition of Geodesy
That branch of applied mathematics which determines by observation and measurement the exact positions of points and the figure and areas of large portion of the earth’s surface, the size and shape of the earth, and the variations in the terrestrial gravity
Classical definition by F. R. Helmert, 1880
“the science of measuring and portraying the Earth’s surface”
Contemporary definition by Vanicek & Krakiwsky, 1986
“the discipline that deals with the measurement and representation of the Earth’s surface, including its gravity field, in a three-dimensional time varying space”
General ideas or concepts of Geodesy (3)
(1) the size and shape of the earth
(2) the gravity field of the earth
(3) the positioning of points on the surface of the earth
Modern definition of Geodesy (2)
(1) measurement and modeling of the geodynamic
(2) phenomena such as polar motion, Earth rotation and crustal deformation
Branches of Geodesy (4)
(1) Physical Geodesy
(2) Geometric Geodesy
(3) Geodetic Astronomy
(4) Satellite Geodesy
Geodesy Subdivisions (3)
(1) Geometrical geodesy
(2) Physical geodesy
(3) Satellite geodesy
Concerned with describing locations in terms of geometry.
Geometrical Geodesy
One of the primary products of geometrical geodesy.
Coordinate Systems
Concerned with determining the Earth’s gravity field, which is necessary for establishing heights.
Physical Geodesy
Concerned with using orbiting satellites to obtain data for geodetic purposes.
Satellite Geodesy
Homer: 9th Century B.C.
Earth was a flat disk supporting a hemispherical sky.
Pythagoras: 6th Century B.C (2)
(1) Suggested that the earth was spherical in shape
(2) Made on the basis that a sphere was considered a perfect form, and not by deduction from observations
Aristotle: 4th Century B.C. (3)
The earth must be spherical in shape;
(1) Changing horizon as one travels in various directions,
(2) Round shadow of the earth that was observed in lunar eclipses; and
(3) Observation of a ship at sea where m ore (or less) of the ship is seen as the sheep approaches (or goes away)
To settle the issue, they sent out an expedition to confirm the correctness of the claims. The measurements of the expedition in Peru conclusively proved the earth to be flattened.
French Academy of Sciences in 1735
Geoid Development in 1872-1873
Listing introduced the concept of the geoid as the surface of the undisturbed seas and its continuation into the continents. Theellipsoid of previous studies now became an approximation of the earth.
Geoid Development in 1884
Helmert defined more precisely the geoid identifying it with an ocean with no disturbances such as would be caused by tides, winds, waves, temperature, pressure and salinity differences. Etc. This geoid was considered to be an equipotential surface of the earth’s gravity field.
Everyday Geodesy (3)
(1) GNSS navigation system
(2) Web-based mapping services
(3) Ships and aircraft
Why learn about Geodesy? (2)
(1) The need for flatness
(2) Round realities
Units in Geodesy (2)
(1) Angular Units
(2) Linear Units
Angular Units (6)
(1) Degrees, minutes and seconds
(2) Radians
(3) Circles and Semicircles
(4) Grade/grad/gon
(5) Mil
(6) Milli-arc second (mas)
Degrees (3)
(1) 360 divisions of a circle
(2) from the Latin de gradus (suggest a connection with a step on a ladder)
(3) denoted a small circle
Minutes (3)
(1) subdividing the degree into 60 parts
(2) from the Latin par minuta prima, “frist small part”
(3) denoted with a single tick mark
Seconds (3)
(1) subdividing the minutes in sixty parts
(2) from the Latin pars minuta secunda, “second small part”
(3) denoted by two tick marks
An angle might be expressed in (3)
(1) decimal degrees (DD);
(2) degrees and decimal minutes; or
(3) degrees, minutes, and decimal seconds (DMS)
It denotes the degrees of a DMS angle
δ (delta)
It denotes the minutes
μ (mu)
It denotes the seconds
σ (sigma)
Conversion Formula (DMS angle δ°μσ to DD)
DD = δ° + μ/60 + σ/3600
A natural angular unit; they arise from the relationship between a circle and its circumference. The angle such that the arc length of the circle segment subtended by this angle is exactly one unit in length.
Radians
A circle whose radius is exactly one unit in length.
Unit Circle
An angle of one radian
For a unit circle, an angle of one radian creates an arc of length 1.
The definition of Radian
This leads to the observation that 360° means the same thing as 2π radians.
Conversion from radians to DD
Multiply the angle in radians by 180°/π.
Conversion from DD to radians
Multiply the angle in decimal degrees by π/180°
Circles and Semicircles
One circle equals 2π radians, or 360°, and one semicircle equals π radians, or 180°.
Grade/grad/gon
The grade, also known as the grad or gon, is an angular unit dividing the circle into 400 parts, so 400 gon = 2π radians.
Mil
The mil is an angular unit developed by militaries to direct artillery fire.
NATO mil
including Canada, it is 1/6400 circle
One NATO mil equals
0.000 981 748 radians, which is close to one milliradian, and it is from this relationship that the unit gets its name.
NATO mil in one quarter circle
There are 1600 NATO mil in one quarter circle.
Milli-arc second (mas) (2)
(1) A milli-arc second, abbreviated mas, is 1/1000 arc second
(2) It is used in geodesy to describe the extremely small angular rotations needed to transform coordinates between different geodetic reference frames.
Linear Units (2)
(1) Meter
(2) Acres and hectares
