Geography Reference
In-Depth Information
Proof (( 16.48 ): l 1 ).
Ω )= A 2
tan( L
A 1 cos i tan α,
(16.60)
d α = A 2
dtan( L
Ω )
1
cos 2 ( L
d L
cos i
cos 2 α ,
=
A 1
d α
Ω )
1
1+tan 2 ( L
1
cos 2 ( L
Ω )=
Ω ) =
1+ A 2
cos 2 i
A 1
tan 2 α
d α = A 2
d L
cos i
cos 2 α =
1
=
(16.61)
A 1
1+ A 2
cos 2 i
A 1
tan 2 α
A 1 A 2 cos i
A 1 cos 2 α + A 2 cos 2 i sin 2 α
l 1 := d L
=
d α ( α 0 ) .
End of Proof.
Proof (( 16.47 ): b 2 ).
d 2 B
d α 2 = A 2 A 1 (1
E 2 )sin i
×
sin α [ A 1 (1
E 2 ) 2 + E 2 A 2 sin 2 i sin 2 α ] 1
[ A 1 +( A 2 cos 2 i − A 1 )sin 2 α ] 1 / 2
×
2 E 2 A 2 sin 2 i sin α cos 2 α
×
E 2 ) 2 + E 2 A 2 sin 2 i sin 2 α ] 2 [ A 1 +( A 2 cos 2 i
A 1 )sin 2 α ] 1 / 2
[ A 1 (1
×
(16.62)
( A 2 cos 2 i
A 1 )sin α cos 2 α
×
A 1 )sin 2 α ] 3 / 2
[ A 1 (1
E 2 ) 2 + E 2 A 2 sin 2 i sin 2 α ] 1 [ A 1 +( A 2 cos 2 i
×
2 b 2 := d 2 B
d α 2 ( α 0 ) .
End of Proof.
 
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