Geodesy Flashcards
Define Latitude and its extents
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
Define Longitude and its extents
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
Define Meridian
A Line that joins points of equal longitude.
Define a Parallel (In terms of geodesy)
A line that joins points of equal latitude.
Define Azimuth
α An angle measured clockwise from a meridian, (from true north) to the tangent to the geodesic.
What is a Grid Bearing
β An angle between grid north and the tangent to the arc at the point. It is measured from grid north clockwise through 360°
What is the Arc to Chord Correction
Angular quantity to be added algebraically to a grid bearing to obtain a plane bearing,
What is Grid Convergence
γ Angular quantity to be added algebraically to an azimuth to obtain a grid bearing
What is the scale factor for the central meridian of a UTM zone
0.9996
What is the input for Vincety’s inverse formulae
Vincenty’s inverse formulae use Latitude and Longitude
Define geoid
Equipotential Surface of the Earth’s Gravity field - close to Mean Sea Level
Define a Spherical triangle
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
Define Meridian convergence
The change in the azimuth of a geodesic between two points on the spheroid
Define Great circle
A Line of Intersection made with the surface of a sphere by a plane passing through the centre of the sphere
Define Small circle
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.
Define Geodesic
The shortest distance between two points on the surface
of a spheroid. A line of double curvature
Define Spheroidal distance
Distance on the ellipsoid along either a normal section or a geodesic. The difference between the two is usually negligible
Define Map
A Representation of part of the earth’s surface on a flat plane
Define a Map Projection
The mathematical relationship between a point on the earth’s surface and the corresponding point on the map
Define a Graticle
Pattern of Meridians and Parallels on the projection
Define a Grid
Eastings and Northings equally spaced and set at Right Angles
Define True North
Direction of the tangent to the projected meridian at a particular point (varies
continually)
Define Grid North
Direction of the North Axis of the grid system (constant throughout)
Define Plane bearing
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°.
Define Plane Distance
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.
Define Point Scale Factor
k Ratio of an infinitesimal distance at a point on the grid to the corresponding distance on the spheroid
Define Line scale factor
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
Define Eccentricity
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
Define Ellipsoid
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.
Define Datum
- A reference frame defined by a spheroid and the
spheroid’s position relative to the center of the earth. - A set of control points and a spheroid that
define a reference surface.
Define flattening
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.
Describe a Translation of Axes (Origin Shift)
A shift of origin, where the co-ordinate axes of two systems remain parallel to each other, is termed
translation.
Describe a Rotation of Axes
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.
Describe a Transformation of Co-ordinates
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.
What are the UTM Prorerties of 1 zone
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
