Geoscience Reference
In-Depth Information
B
l
A
h
2
h
1
s
0
A
0
B
0
l
0
R
R
Ã
0
Fig. 5.14. Reduction of spatial distances
With
2sin
2
ψ
cos
ψ
=1
−
2
,
(5-107)
this is transformed into
h
1
)
2
+4
R
2
1+
h
1
R
1+
h
2
R
sin
2
ψ
l
2
=(
h
2
−
2
;
(5-108)
and with
l
0
=2
R
sin
ψ
2
(5-109)
and the abbreviation ∆
h
=
h
2
−
h
1
,weobtain
l
2
=∆
h
2
+
1+
h
1
R
1+
h
2
R
l
0
.
(5-110)
Hence, the chord
l
0
and the arc
s
0
are expressed by
l
0
=
−
∆
h
2
1+
h
1
l
2
1+
h
2
;
(5-111)
R
R