Geoscience Reference
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13. In astro-geodetic surveying, the mean square errors of the astronomical deter-
minations of latitude and longitude are respectively
0.3
00
and
0.02 s (equiv-
45
, what are the arc lengths along an ellipsoidal
meridian and along a parallel and what are these mean square errors equivalent
to?
14. Why can we transform the solution of ellipsoidal triangles to the solution of
plane triangles? Please explain Legendre's theorem by which ellipsoidal tri-
angles are solved.
15. What are the reasons for the formation of reciprocal normal sections? Please
describe the rules of position of the normal section and the reverse normal
section. Under what condition do the reciprocal normal sections between two
points on the ellipsoid coincide?
16. What is the geodesic? Please describe the relationship between positions on the
geodesic and reciprocal normal sections.
17. Which normal sections on the ellipsoid are geodesics? Are parallel and prime
vertical geodesics?
18. Derive the differential equations for geodesics.
19. Derive Clairaut's equation for geodesics and illustrate the meaning of this
equation.
20. Given the formula for correction of the vertical deflection:
0.3
00
). So if B
alent to
ﾼ
ʴ
1
ﾼ
R
R
1
ﾼʾ
ð
sin A
ʷ
cos A
Þ
cot z
1
,
, A, and Z
1
on the auxiliary sphere.
21. Construct and explain the meaning of skew normal correction.
22. Draw a diagram of correction for skew normals with the azimuth values of
sides lying in the I, II, III, and IV quadrants, respectively and specify the sign of
the correction for skew normals
mark out the quantities
ʴ
1
,
ʾ
,
ʷ
ʴ
2
.
23. Explain the meaning of correction from normal section to geodesic.
24. Account for the meaning of reduction of the observed zenith distance.
25. What are the data that should be given to calculate the three corrections, i.e.,
correction for deflection of the vertical, correction for skew normals, and
correction from normal section to geodesic? Under what conditions do the
three corrections equal zero, respectively.
26. Account for the basic process of slope distance reduction.
27. Derive the approximate formula for the reduction of slope distance:
S
ﾼ
R
A
˃
,
is given by D
2
(R
A
+ H
1
)
2
+(R
A
+ H
2
)
2
where
˃
ﾼ
2(R
A
+ H
1
)(R
A
+ H
2
)
.
28. What is gravimetric deflection of the vertical and astro-geodetic deflection of
the vertical? What are the two factors that affect the value of deflection of the
vertical?
cos
˃
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