Geodesy

Question 1

Define Latitude and its extents

Answer 1

Φ An angle measured at the centre of the spheroid, from the plain of the equator, to some point on the surface of the spheroid. 90°N to -90°S

Question 2

Define Longitude and its extents

Answer 2

λ An angle measured at the centre of the spheroid, from the plain of the prime meridian, to some point on the surface of the spheroid. -180°W to 180°E

Question 3

Define Meridian

Answer 3

A Line that joins points of equal longitude.

Question 4

Define a Parallel (In terms of geodesy)

Answer 4

A line that joins points of equal latitude.

Question 5

Define Azimuth

Answer 5

α An angle measured clockwise from a meridian, (from true north) to the tangent to the geodesic.

Question 6

What is a Grid Bearing

Answer 6

β An angle between grid north and the tangent to the arc at the point. It is measured from grid north clockwise through 360°

Question 7

What is the Arc to Chord Correction

Answer 7

Angular quantity to be added algebraically to a grid bearing to obtain a plane bearing,

Question 8

What is Grid Convergence

Answer 8

γ Angular quantity to be added algebraically to an azimuth to obtain a grid bearing

Question 9

What is the scale factor for the central meridian of a UTM zone

Answer 9

0.9996

Question 10

What is the input for Vincety’s inverse formulae

Answer 10

Vincenty’s inverse formulae use Latitude and Longitude

Question 11

Define geoid

Answer 11

Equipotential Surface of the Earth’s Gravity field - close to Mean Sea Level

Question 12

Define a Spherical triangle

Answer 12

A spherical triangle is a three sided figure drawn on a sphere. It consists of three intersecting
arcs, each arc being part of a great circle

Question 13

Define Meridian convergence

Answer 13

The change in the azimuth of a geodesic between two points on the spheroid

Question 14

Define Great circle

Answer 14

A Line of Intersection made with the surface of a sphere by a plane passing through the centre of the sphere

Question 15

Define Small circle

Answer 15

A Line of Intersection made with the surface of a sphere by a plane passing through any other point other than the centre of the sphere.

Question 16

Define Geodesic

Answer 16

The shortest distance between two points on the surface

of a spheroid. A line of double curvature

Question 17

Define Spheroidal distance

Answer 17

Distance on the ellipsoid along either a normal section or a geodesic. The difference between the two is usually negligible

Question 18

Define Map

Answer 18

A Representation of part of the earth’s surface on a flat plane

Question 19

Define a Map Projection

Answer 19

The mathematical relationship between a point on the earth’s surface and the corresponding point on the map

Question 20

Define a Graticle

Answer 20

Pattern of Meridians and Parallels on the projection

Question 21

Define a Grid

Answer 21

Eastings and Northings equally spaced and set at Right Angles

Question 22

Define True North

Answer 22

Direction of the tangent to the projected meridian at a particular point (varies
continually)

Question 23

Define Grid North

Answer 23

Direction of the North Axis of the grid system (constant throughout)

Question 24

Define Plane bearing

Answer 24

θ The angle between grid north and the straight line on the grid between the ends of the arc formed by the projection of the ellipsoidal distance; measured clockwise through 360°.

Question 25

Define Plane Distance

Answer 25

L The length of the straight line on the grid between the ends of the arc of the projected ellipsoidal distance. The difference in length between the plane distance (L) and the grid distance (S) is nearly always negligible.

Question 26

Define Point Scale Factor

Answer 26

k Ratio of an infinitesimal distance at a point on the grid to the corresponding distance on the spheroid

Question 27

Define Line scale factor

Answer 27

Ratio of a plane distance (L) to the corresponding ellipsoidal distance (s): K = L/s ≈ S/s. The point scale factor will in general vary from point to point along a line on the grid

Question 28

Define Eccentricity

Answer 28

Defined by the Distance between the centre of the ellipse and the focus divided by the distance of the Semi-Major Axis
Denoted by e
e² = 2f - f²

Question 29

Define Ellipsoid

Answer 29

Mathematical Surface that closely resembles the Geoid used for all Mathematical calculations
When used to represent the earth, the three-dimensional
shape obtained by rotating an ellipse about its minor axis.
This is an oblate ellipsoid of revolution, also called a
spheroid.

Question 30

Define Datum

Answer 30

1. A reference frame defined by a spheroid and the
   spheroid’s position relative to the center of the earth.
2. A set of control points and a spheroid that
   define a reference surface.

Question 31

Define flattening

Answer 31

A measure of how much a spheroid differs from a sphere.
The flattening is the ratio of the semimajor axis minus the
semiminor axis to the semimajor axis. Known as ‘f’ and
often expressed as a ratio. Example: 1/298.3. Also known
as the ellipticity.

Question 32

Describe a Translation of Axes (Origin Shift)

Answer 32

A shift of origin, where the co-ordinate axes of two systems remain parallel to each other, is termed
translation.

Question 33

Describe a Rotation of Axes

Answer 33

If the initial (reference) direction is changed, then all bearings in that system will be changed by the same amount. This change is called a rotation of axes.

Question 34

Describe a Transformation of Co-ordinates

Answer 34

If both rotation of axes and translation of origin are to occur, the procedure is to first effect the
rotation, then the translation. The mathematician terms this dual operation a transformation of coordinates.

Question 35

What are the UTM Prorerties of 1 zone

Answer 35

6° wide with additional ½° overlap between zones
Scale Factor = 1 along two lines in each zone 180km east and west of the Central Meridian
Scale Factor at Central Meridian = 0.9996
Scale Factor at Extremes = 1.0005
Zone = 600kms wide
True Origin = intersection of Central Meridian and Equator
Latitude Limits = 84°N & 80°S