Viewing page 41 of 63

This transcription has been completed. Contact us with corrections.

CALC ΔLAT, ΔLONG        GOOD COPY ΔLAT, ΔLong

[drawing] 
                                             Θ=90-Θ*
FOR SPHERICAL COS:                           dΘ=-dΘ*
dlΘ=rdΘ=-rdΘ*
dlΘ=rsinΘdΦ
[arrow to above] GRIFFITH'S INTRO TO E&M

Notice dΘ*=ΔLAT
       dΦ=ΔLONG

SUBSTITUTE dΘ*,dΦ
dlΘ=-rdΘ*=-rΔlat
dlΦ=rsinΘdΦ=rsin(90-Θ*)Δlong=-rsin(Θ*-90)Δlong
                            =rcosΘ*Δlong

Δlat*,Δlong* ARE DISTANCES, Δlat,Δlong ARE ANGLES.

[drawing]

Δlat*=Xsin(Π-β1-δ)
     =Xsin(β1+δ)
Δlong*=Xcos(Π-β1-δ)
      =Xcos(β1+δ)

For α<<1; sinα~α
x=rsinα~rα

[drawing]

Δlat*~rαsin(β1+δ)
Δlong*~-rαcos(β1+δ)

NOTICE Δlat*=dlΘ
       rαsin(β1+δ)=-rΔlat   => Δlat=-αsin(β1+δ)

NOTICE Δlong*=dlΦ
       -rαcos(β1+δ)=rcosΘ*Δlong   => Δlong= -αcos(β1+δ)/cosΘ* =  -αcos(β1+δ)/cos(nlat)

DEGUELLE, M. FRIEDEL