Introduction to Geodesy

Question 1

Geodesy in the Geodetic Glossary (NGS 2009)

Answer 1

“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.”

Question 2

Fundamental Properties of the Earth (3)

Answer 2

(1) its geometric shape,
(2) its orientation in space, and
(3) its gravity field as well as the changes of these properties with time.

Question 3

Geodesy from the Greek words

Answer 3

“geo” and “desa” means “earth” and “to divide”.

Question 4

Webster’s definition of Geodesy

Answer 4

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

Question 5

Classical definition by F. R. Helmert, 1880

Answer 5

“the science of measuring and portraying the Earth’s surface”

Question 6

Contemporary definition by Vanicek & Krakiwsky, 1986

Answer 6

“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”

Question 7

General ideas or concepts of Geodesy (3)

Answer 7

(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

Question 8

Modern definition of Geodesy (2)

Answer 8

(1) measurement and modeling of the geodynamic
(2) phenomena such as polar motion, Earth rotation and crustal deformation

Question 9

Branches of Geodesy (4)

Answer 9

(1) Physical Geodesy
(2) Geometric Geodesy
(3) Geodetic Astronomy
(4) Satellite Geodesy

Question 10

Geodesy Subdivisions (3)

Answer 10

(1) Geometrical geodesy
(2) Physical geodesy
(3) Satellite geodesy

Question 11

Concerned with describing locations in terms of geometry.

Answer 11

Geometrical Geodesy

Question 12

One of the primary products of geometrical geodesy.

Answer 12

Coordinate Systems

Question 13

Concerned with determining the Earth’s gravity field, which is necessary for establishing heights.

Answer 13

Physical Geodesy

Question 14

Concerned with using orbiting satellites to obtain data for geodetic purposes.

Answer 14

Satellite Geodesy

Question 15

Homer: 9th Century B.C.

Answer 15

Earth was a flat disk supporting a hemispherical sky.

Question 16

Pythagoras: 6th Century B.C (2)

Answer 16

(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

Question 17

Aristotle: 4th Century B.C. (3)

Answer 17

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)

Question 18

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.

Answer 18

French Academy of Sciences in 1735

Question 19

Geoid Development in 1872-1873

Answer 19

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.

Question 20

Geoid Development in 1884

Answer 20

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.

Question 21

Everyday Geodesy (3)

Answer 21

(1) GNSS navigation system
(2) Web-based mapping services
(3) Ships and aircraft

Question 22

Why learn about Geodesy? (2)

Answer 22

(1) The need for flatness
(2) Round realities

Question 23

Units in Geodesy (2)

Answer 23

(1) Angular Units
(2) Linear Units

Question 24

Angular Units (6)

Answer 24

(1) Degrees, minutes and seconds
(2) Radians
(3) Circles and Semicircles
(4) Grade/grad/gon
(5) Mil
(6) Milli-arc second (mas)

Question 25

Degrees (3)

Answer 25

(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

Question 26

Minutes (3)

Answer 26

(1) subdividing the degree into 60 parts
(2) from the Latin par minuta prima, “frist small part”
(3) denoted with a single tick mark

Question 27

Seconds (3)

Answer 27

(1) subdividing the minutes in sixty parts
(2) from the Latin pars minuta secunda, “second small part”
(3) denoted by two tick marks

Question 28

An angle might be expressed in (3)

Answer 28

(1) decimal degrees (DD);
(2) degrees and decimal minutes; or
(3) degrees, minutes, and decimal seconds (DMS)

Question 29

It denotes the degrees of a DMS angle

Answer 29

δ (delta)

Question 30

It denotes the minutes

Answer 30

μ (mu)

Question 31

It denotes the seconds

Answer 31

σ (sigma)

Question 32

Conversion Formula (DMS angle δ°μσ to DD)

Answer 32

DD = δ° + μ/60 + σ/3600

Question 33

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.

Answer 33

Radians

Question 34

A circle whose radius is exactly one unit in length.

Answer 34

Unit Circle

Question 35

An angle of one radian

Answer 35

For a unit circle, an angle of one radian creates an arc of length 1.

Question 36

The definition of Radian

Answer 36

This leads to the observation that 360° means the same thing as 2π radians.

Question 37

Conversion from radians to DD

Answer 37

Multiply the angle in radians by 180°/π.

Question 38

Conversion from DD to radians

Answer 38

Multiply the angle in decimal degrees by π/180°

Question 39

Circles and Semicircles

Answer 39

One circle equals 2π radians, or 360°, and one semicircle equals π radians, or 180°.

Question 40

Grade/grad/gon

Answer 40

The grade, also known as the grad or gon, is an angular unit dividing the circle into 400 parts, so 400 gon = 2π radians.

Question 41

Mil

Answer 41

The mil is an angular unit developed by militaries to direct artillery fire.

Question 42

NATO mil

Answer 42

including Canada, it is 1/6400 circle

Question 43

One NATO mil equals

Answer 43

0.000 981 748 radians, which is close to one milliradian, and it is from this relationship that the unit gets its name.

Question 44

NATO mil in one quarter circle

Answer 44

There are 1600 NATO mil in one quarter circle.

Question 45

Milli-arc second (mas) (2)

Answer 45

(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.

Question 46

Linear Units (2)

Answer 46

(1) Meter
(2) Acres and hectares