φA=37∘01′ N; -the geographical latitude of position A
λA=9∘00′ W; -the geographical longitude of position A
φB=36∘11′ N; -the geographical latitude of position B
λB=6∘02′ W; -the geographical longitude of position B
Δσ=arccos(sin(φA)sin(φB)+
+cos(φA)cos(φB)cos(λB−λA))=
=arccos(sin(37∘01′)sin(36∘11′)+
+cos(37∘01′)cos(36∘11′)cos(6∘02′−9∘00′))=
=arccos(0.6020⋅0.5904+
+0.7985⋅0.8071⋅cos(−2∘58′))=
=arccos(0.3554+0.6445⋅0.9986)=
=arccos(0.9990)=2.52∘ - the central angle between A and B;
the great-circle distance between two points AB=60⋅2.52∘=151.2 nautical miles,
or AB=R⋅2.52∘180∘π=6371⋅0.0440=280.3 km, where R=6371 km - the mean earth radius.
α=arccos(cos(φA)⋅sin(Δσ)sin(φB)−sin(φA)⋅cos(Δσ))=
=arccos(cos(37∘01′)⋅sin(2.52∘)sin(36∘11′)−sin(37∘01′)⋅cos(2.52∘))=
=arccos(0.7985⋅0.04390.5904−0.6020⋅0.9990)=
arccos(−0.3137)=108.3∘ - bearing from point A to point B
Answer: the distance between positions is about 151.2 nautical miles (280.3 km),
course (bearing from point A to point B) is about 108.3⁰.
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