Tuesday, June 9, 2015

Modern Haversine Sight Reduction

The cosine haversine Doniol sight reduction formula can be written as an all haversines formula to create the Modern Haversine Method of sight reduction. Only a single haversine table is needed and there are no special case rules.

http://fer3.com/arc/m2.aspx/Haversine-how-derive-it-Bernecky-jun-2015-g31663


Formula:

hvZD = n+[1-(n+m)](a)

Same Name
n = hv (L-d)
m = hv (L+d)

Contrary Name
n = hv (L+d)
m = hv (L-d)

L = Latitude
d = Declination
t = Meridian Angle
a = hv(t)
hv = Haversine
ZD = Zenith Distance
Hc = (90 - ZD) Calculated Altitude




Precision is 1' when done longhand to 4 places using natural haversines (see attached example). Azimuth is quickly done using the Ix graph (attached)