NavList:

   

Reply

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.)

   

Reply