# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Star identification via Bygrave formulas**

**From:**Paul Hirose

**Date:**2018 Jan 12, 08:48 -0800

In addition to sight reduction, the Bygrave formulas and a slide rule can identify a star (compute its SHA and declination) from its azimuth and altitude if the observer's position and time are approximately known. Simply interchange the pole and observer: latitude retains its usual sense, but use azimuth angle (Z) as LHA and altitude as declination. Then work the problem as a sight reduction. For instance, at 2018 Jan 8 10 h UT, 30S 160E, a bright star is observed at altitude 61° and estimated azimuth 40°. To identify the star, use these parameters: 30 latitude 61 declination 140 LHA Remember that Z is measured from the south in south latitude, so if azimuth = 40 then Z (alias "LHA") = 140. (You should have seen how much time I wasted because I forgot that.) Latitude and declination are "same name" unless altitude is negative. No great accuracy is necessary, so I won't try to interpolate between the graduations on the slide rule. W = arc tan (tan 61 / cos 140) W = 67.0 LHA is between 90 and 270, so replace W with 180 - W: W = 113.0 X = 90 - 30 + 113.0 X = 173.0 Z = arc tan (tan 140 * cos 113.0 / cos 173.0) Z = 18.3 Hc = arc tan (cos 18.3 * tan 173.0) Hc = 6.6 Greenwich hour angle of Aries is 258°. Add east longitude (160), subtract 360, and get 58 as the local hour angle of Aries. Angle Z (18°) from the Bygrave formula is actually the meridian angle of the unknown body. It was observed east of the meridian, so right ascension = 58 + 18 = 76°. Therefore SHA = 360 - 76 = 284. Hc is the declination, -7°. If you search the stars in the Almanac daily table, Rigel is the only one with both coordinates approximately correct. (There are a few degrees of error since I intentionally made the azimuth a little inaccurate.)