Geodesy:
Science of earth measurement
•
The earth is
not flat
, but in some cases (very
large-scale mapping) it might as well be
•
The earth is
not a sphere
, but in most cases
it might as well be a spheroid…
•
The earth is a big lumpy loveable mass of
stuff that we can approximate with ellipses
(spheroids), geoids, and datums
Geodesy:
Earth as a sphere
•
Circumference
•
Eratosthenes
•
Alexandria
à
Syene
•
Angle –
7.2
o
(1/50
th
of globe)
•
Distance –
5000 stadia
•
Circ. = 50 x
5000 stadia
= 250,000
stadia
•
39250 km –
52250 km
•
+/- 15% of true
value
Geodesy:
Earth as an ellipsoid
•
GRS 1980
dimensions
•
a = 6,378.13 km
•
b = 6,356.75 km
•
Diff. (a-b) = 21.38 km
•
Circumference
•
Equator = 40,075 km
•
Polar = 39,940.64 km
•
Diff. (Eq. – Pl.) = 134.36
km
b
b
N
S
a
a
= Semi-major axis (equatorial radius)
= Semi-minor axis parallel to the rotational
axis of the earth (polar radius)
(After Dent,
Thematic Map Design,
1990)
Geodesy:
Earth as a geoid
•
Satellites (1958
à
)
•
Large depressions,
bulges
•
Not noticeable, but
affect precise survey
work
•
Geoid affects
cartographer's
reference ellipsoid
Geodesy:
Earth as an ellipsoid vs. geoid
North Pole
7.62 m (25 ft)
7.62 m (25 ft)
7.62 m (25 ft)
7.62 m (25 ft)
15.24 m (50 ft)
15.24 m (50 ft)
Fischer reference ellipsoid
1 / 298.25
South Pole
Geodesy:
Earth as an ellipsoid vs. geoid
North Pole
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
Equator
Latitude
Latitude
+13
+10.2
+7.3
+4.6
+2.4
+2.2
+6.4
+7.1
+5.7
+5.0
–2.7
–2.8
–14.3
–24.5
–30.0
–6.1
–7.6
–3.6
–0.4
South Pole
The Geoid-
Deviation from the
GRS 1980 Ellipsoid
Average deviation
in meters at each
10 degree latitude
Datum: Orients ellipsoid to
geoid
•
Datums:
•
Describe size & shape of earth (ellipsoid)
•
Anchor ellipsoids to earth’s surface
•
Describe origin & orientation of coordinate
systems
•
Ex. NAD 27, NAD 83, WGS84
