 ## E5 - - - Some formulas for sight reduction - - - 10/03/2004

On pages C1 thru C4 there are four methods for solving the navigation triangle in which the distance "D" is measured along the earth from point 1 to point 2. If point 2 is the position directly under an astronomical object then the distance (D) is identical to the angle from directly over the observers position (zenith), to the astronomical object (zenith distance).

This angle is the complement of the elevation angle (e) of the object as measured from the horizontal plane, and in some cases a slight change to the formulas will determine the value of e directly, or the zenith angle (zenith distance) can be calculated and then subtracted from 90 degrees to determine the elevation angle.

```Sight Reduction using The Law of cosines - (ref page C1)
When observing an astronomical object from point one (L1, LO1)

t   =  DLO = the difference in longitude, or local hour angle. (L.H.A.)
Dec = Declination of object
C   = Azimuth angle.
e   = the elevation angle of the astronomical object (degrees)

sin e = sin L1 * sin Dec + cos L1 * cos Dec * cos t
cos C = (sin Dec - sin L1 * sin e ) / ( cos L1 * cos e )
or
sin C = ( cos Dec * sin t ) / cos e    (caution - ambiguity)

Sight Reduction using the Adgeton method (inverted) - (ref page C2)

sin R = sin t * cos Dec      (R is less than 90 degrees )
sin K = sin Dec / cos R      (note 1)
sin e = cos R * cos (K-L1)   (e is less than 90 degrees )
sin C = sin R / cos e        (note 2)

(note 1) If t is greater than 90 degrees then
K is greater than 90 degrees.

(note 2) If L1 is greater than K then C is greater
than 90 degrees.

Sight Reduction using the no-name method - (ref. page C4)

Q   = distance from pole to the perpendicular, measured along the
meridian of point one.
t   = DLO = difference in longitude, or local hour angle (L.H.A.)
Dec = Declination of object
C   = Azimuth angle
e   = elevation angle  (degrees)

tan Q  = (cos t) / tan Dec
tan C  = (tan t) * (sin Q) / cos (L1+Q)
tan e  = (cos C) * tan (L1+Q)

```
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