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calculation of δ cont'd

(VN VE VZ)= (-sinLcosθvi-sinLsinθvj+cosLvk
             -sinθvi+cosθvj
             cosLcosθvi+cosLsinθvj+sinLvk)
velocity= (VN, VE, VZ)
[[image 1]] 
ground track
[[image 2]]

tanδ= VE/VN

δ=tan-1(-sinθvi+cosθvj/-sinLcosθvi-sinLsinθvj+cosLvk)

L=nadir latitude 
θ=θg+λE λE= nadir longitude measured east from the prime meridian (if nlong<) λE=18+nlong)
θg=angle between prime meridian and Iaxis (pointing in direction of vernal equinox)
in general, θg=θgo + correction term(s)
θgo= angle between vernal equinox and prime meridian on Jan 1 (Julian date) of year that velocity is measured

Because the shuttle's coordinates are given to us in the B1950 coordinate system, θg is fixed and θg= θgo.

Coordinate system B1950:  ___ vernal equinox direction on Jan 1, 1950. So, to find θ (angle between and nlongitude, we need θ= θgo + λE= (vernal equinox -> Greenwich) + (nlongitude)

Transcription Notes:
Image 1 is a wave graph with the Y axis labeled N and the X axis labeled E Image 2 is a triangle with an angle labeled δ. Opposite side of triangle labeled VE and adjacent side labeled VN.