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Material Type: Notes; Class: Geodesy 1; Subject: Surveying Engineering; University: Ferris State University; Term: Unknown 1989;
Typology: Study notes
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∆λ =0.
∆λ λ 2
λ 1
∆φ =0.
∆φ φ 2
φ 1
w =0.
w A
λ 2
λ 1
C 1 e p
B 1 e p
cos φ 1
2
:= + ⋅
A 1 e p
cos φ 1
4
:= + ⋅
Common equations:
φ 2
:= radians 30.444814320( )
λ 2
:=radians 10.451308964( )
λ 1
φ :=radians 10( ) 1
:=radians 30( )
Given data:
e p
e p
a
2 b
2 −
b
2
second eccentricity squared: :=
b =6356752.31414036 m
f b :=a −a f⋅
a :=6378137 m⋅ :=
The following data refer to a given reference system
dms ang( ) degree ←floor ang( )
rem ←(ang −degree) 60⋅
mins ←floor rem( )
rem1 ←( rem −mins)
secs ←rem1 60.0⋅
degree
mins
secs
radians ang( ) d ←dd ang( )
d
π
dd ang( ) degree ←floor ang( +0.0000000001) :=
mins ←(ang −degree) 100.0⋅
minutes ←floor mins( +0.0000000001)
seconds ←(mins −minutes) 100.0⋅
degree
minutes
seconds
Some useful angle functions:
The Inverse Geodetic Problem using the method by Bowring
s =109999.999633107 m
s
a C⋅ ⋅σ
2
dms α 21
π
α 21
:=G + H+π
dms α 12
π
α 12
H atan
sin φ
B cos φ
⋅ ⋅tan w( )
σ =0.
σ 2 asin E
2 F
2
G :=atan2 E F( , ) G =0.
⋅ sin w( ) B cos φ
⋅ ⋅ cos D( ) sin φ
− ⋅sin D( )
E :=sin D( ) cos w⋅ ( )
∆φ
3 e p
2 ⋅
⋅ ∆φsin 2 φ 1
Inverse Problem: