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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
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