Geoscience Reference
In-Depth Information
Table 5.11 Sample computation for the inverse solution of the geodetic problem
Given data
Ellipsoidal parameters
Computational results
90
00
0
00.11
00
L
1
ﾼ
Krassowski Ellipsoid
S
ﾼ
15 000 000.330 m
35
00
0
00.22
00
100
00
0
00. 321
00
B
1
ﾼ
A
1
ﾼ
215
59
0
04.34
00
290
32
0
53. 392
00
L
2
ﾼ
A
2
ﾼ
30
29
0
20.96
00
B
2
ﾼ
GRS75 Ellipsoid
S
ﾼ
14 999 751.047 m
100
00
0
00. 228
00
A
1
ﾼ
290
32
0
53. 329
00
A
2
ﾼ
GRS80 Ellipsoid
S
ﾼ
14 999 744.004 m
100
00
0
00. 229
00
A
2
ﾼ 290
32
0
53. 329
00
A
1
ﾼ
Review and Study Questions
1. Why do we choose a reference ellipsoid as the reference surface on which
geodetic surveying computations are performed? What are the requirements for
the reference surface selected for geodetic computations?
2. Explain the concepts of the Earth ellipsoid and the reference ellipsoid.
3. Given the flattening ʱ and eccentricity e, can we define the shape and size of the
reference ellipsoid and why?
4. What is the difference between astronomical longitude and latitude and the
geodetic longitude and latitude?
5. Construct a sketch to derive the formulae for transformations between L, B,
H and X, Y, Z.
6. Construct and derive the formulae for transformations between the geocentric
coordinate system O-XYZ and the topocentric coordinate system P-xyz (list the
formulae that include rotation matrices and translation vectors will do).
7. Which point on the ellipsoid has an R
A
independent of directions? Please
illustrate.
8. Write out a set of formulae for the radius of curvature of the meridian, the
radius of curvature in the prime vertical, and the mean radius of curvature,
using V, c and W, a, and specify the relationship between the values of their
results.
9. Analyze the laws of changes of the meridional radius of curvature and radius of
curvature in the prime vertical with the changes of latitude (trajectory of the
center of curvature when 0
90
).
10. Construct and derive the integral of the meridian arc length.
11. Construct and derive the formula for the length of a parallel arc.
12. Why does the length of the meridian arc of the unit difference in latitude in the
northern hemisphere turn out to be longer in the north and shorter in the south?
Why is the arc length along a parallel of the unit difference in longitude shorter
in the north and longer in the south?
B
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