Geomatics Chapter 2,3

Used to define points and orientation

• Used to define positionand orientation, change in location or relative distance between points on a sphere
• Based on latitude and longitude

Formed by the intersection of a plain bisection of the earth at right angles to the axis of rotation

Formed by the intersection of vertical planes passing through the center of the earth and the sphere

58.1333 Degrees North

106.667 Degrees West

6367272 m

Path made by the Earth traveling around the sun

Closest point to the sun on the ecliptic path

Farthest point from the sun on the ecliptic path

The Vernal and Autumnal equinox are points on interesection between the ecliptic and celestial equator. This plane also pass through the sun

Azimuth is the angle measured clockwise from North

Latitude=h+(90-declination)

The interval between two successive lower transits of the sun's center of the same meridian

1 hour

Sanford Flemming

Imaginary line that seperates two calendar dates

The interval between two successive upper transits of the vernal equinox over the same meridian

0.9973 solar days

• 1'
• 6076.65 feet
• 1852.16 m

Branch of mathematics which determines by obsservation and measurement the exact positions of points and areas of large portions of the Earths surface, the shape and size of the earth, and the variations of terrestrial gravity

Performed on an ellipse as it closely approximates the size and shape of the earth

The geoid coincides with the surface to which oceans would conform over the entire earth of free to adjust to the effects of gravity and centrifugal force

The angle between a plumb line (line perpindicular to the geoid) and a line perpindicular to the ellipsoid

Utilizes measurements and characteristics of the Earths gravity field to deduce the shape of the geoid

If the value of acceleration of gravity can be determined at the point of measurement directly

If only the differences in the value of the acceleration of gravity are measured between two or more points

H=h-N

• H=Orthometric elevation
• h=Height of the ellipsoid measured from Earth's surface
• N=Geodial height (undulation)

• Shape
• Area
• Distance
• Direction

Conformal (orthomorphic)

• Populations per square meter
• Distribution maps (trees, tons of coal etc.)

Projection at the center of the earth. All great ciircles appears as straight lines

• Conical projection with two standard parallels that intersect the zone of interest at 1/6 of the zone width from the North and South zone limits
• Meridians appear as straight lines converging towards the center of the cone

• Projection of a globe onto a cylinder.
• Merdians are equally spaced vertical lines
• Parallels are horizontal line whose spacing increases towards the poles
• Created to show a line of constant bearing on the the globe. Appears as a straight line on the projection known as a rhumb line

Scale at latitude=(Scale at equator) x cos(latitude)

• UTM zones are 6 degrees wide
• Reference ellipsoid is NAD 27 or NAD 83
• Basis for 1:50000 topographic maps
• Origin for latitude (northing) is the equator
• Southern hemisphere given 10,000,000 as false northing at the equator
• Origin for Easting is at the Central meridian of each zone
• False Easting of 500,000 given to central meridian
• North latitude= 84 degrees N
• South latitude= 80 degrees S

• 180 degrees West
• 60 zones (6*60 zones = 360 degrees)

• R_e/(R_e+H)
• R_e = Radius of Earth (Sphere)
• H = Height above geoid

• k=k₀+ (1+x²/2R²)
• k₀ = 0.9996
• x = Easting
• R = Radius of Earth (sphere)

Grid Factor = (Scale Factor) x (Elevation Factor)

Ground distance = Grid Distance / Grid Factor