STAR FINDER AND IDENTIFIER S-3a
b y Stjepo M. K o t l a r i c
Scien tific Co-worker
H ydrograph ic Institute o f the Y u go sla v N a vy
The n ew Star Fin d er and Id en tifier nam ed S-3a, developed by the
author o f this paper is designed p rim a rily fo r use w ith the Am erican
N autical Alm anac. A short description and exam ples o f its use w ith the
star chart No. 8 given here w ill dem onstrate the sim plicity and accuracy
o f this solution o f star iden tification problems.
SHORT D ESCRIPTION
T h is Star F in d er com prises 57 selected stars taken fro m the d a ily
pages o f the A m erican N autical Alm anac and the rem ain in g 116 stars taken
fro m the star list near the end o f this Alm anac, w ith the addition o f a
fu rther 9 fain ter stars. Thus the stars used fo r celestial navigation, fro m
p ractically all the Nautical Alm anacs in the w orld, are shown in this
Finder. In fact, it is the second varian t o f a Star F in d er developed by the
same author and described in the paper “ N e w Star Fin d er Superseding the
Star Globe ” published in January 1963 edition o f the In terna tion a l H y d r o ­
graphic R e v i e w . T h is has been m o d ified so as to reduce the number o f star
charts fro m 36 to on ly 18, and p rim a rily to enable its direct application
to the A m erican Nautical Alm an ac and other sim ilar Alm anacs (the British,
Brazilian, N orw egian, ate.), w h ile retaining the origin al accurate and sim ple
solution procedure.
A continuous picture o f star positions w ith respect to all values o f
both the local hour angle o f the F irs t P oin t o f A ries and all latitudes o f the
observer is the desired goal fo r all star finders. This, h ow ever, is d ifficu lt
to attain except on a star globe, and on board ship this does not p rove
practical. F o r the Star F in d er under review it is attained b y means o f 9
pairs o f star charts and one tem plate show ing the visible hem isphere
(h orizon system o f coordinates). T h e equatorial stereographic p rojection is
used fo r the construction o f all charts and the tem plate. T h e p lotted parts
o f the star path on both sides o f the plotted star symbol, fo r the in terval
o f the local hour angle o f the F irs t P oin t o f A ries fo r w h ich the star chart
is constructed, give a continuous picture o f star positions w ith respect to
all values o f A rie s L H A in this in terval and all positions o f the observer.
Each p air o f star charts shows the w estern and eastern hem isphere
separately. T h e stars are plotted w ith different symbols, according to their
m agnitude. Selected stars are in black, and other stars in green. T h e stars
in constellation are connected b y a dashed y e llo w line, w h ile the alignm ents
are plotted w ith solid y e llo w lines to make orientation in the sky easier.
B y this d ifferen tiation o f the type and colour in which the star names in
this Star F in d er are printed the user can clearly see where he m ay fin d the
accurate coordinates o f the id en tified star, i.e. either on the daily pages o f
the Am erican Nautical Alm anac fo r the selected star, or in the star list near
the end o f this Alm anac.
The names o f the selected stars are shown in black capital letters,
w h ile all o ilie r stars are shown in green, using capital letters fo r regu lar
names and low er case type for astronom ical (B a yer’ s) names.
F o r other than selected stars it is d ifficu lt to find accurate coordinates
in the star list near the end o f the Am erican Nautical Alm anac since this
list is not com piled in alphabetical order but in the SHA order. T his is w h y
in this Star F in d er an alphabetical Index o f names o f all plotted stars
(both selected and others) has been included. In the Index rounded values
o f S H A and declination are given against the star names in o rd er to
facilitate the fin d in g o f accurate coordinates fo r the identified stars (oth er
than selected stars). T h is is done by using the SH A taken from this Index
and the star name, these being the tw o entering arguments in the star list
near the end o f the A m erican Nautical Alm anac.
T w o 20° intervals o f the L H A Aries, d ifferin g by 180°, are used fo r
constructing each p air o f star charts. The circle bordering the star chart
and passing through the celestial poles represents the observer’ s celestial
m eridian. Outside this circle there is a graduation, positive above the
celestial equator and negative b elow it. T his scale is used fo r orientin g the
tem plate o f the visible hem isphere fo r the observer’s latitude, since the
inclination o f the zenith above the celestial equator represents the latitude.
T h e border scale on the righ t hand h a lf is black, and that on the le ft
is red. By selecting the appropriate p air o f star charts according to the
values o f A ries L H A and to the azimuth, shown respectively on each side
o f the upper part o f the star charts, and by p lacing the tem plate over the
selected star chart in such a w a y that their centres coincide and that the
zenith o f the tem plate is placed on the proper latitude value on the black
border scale w h en the azim uth figu res are in black (or on the red border
scale when the azim uth figures are in red), the altitude and azim uth o f
stars can be determ ined, and also vice versa, for, w ith the observed altitude
and azimuth w e can determ ine w hich star is situated in a particular
position.
Star sym bols on all the star charts are plotted fo r odd tens o f degrees
o f the Aries L H A . A part o f the star’s path is plotted to a distance o f 10°
to the left and to the righ t o f the star sym bol’s position. A 10° increase o f
the A ries L H A is plotted as a path in a solid line, and a 10° decrease o f the
A ries L H A is plotted as a dotted line. These portions o f the star paths
facilitate the id en tifica tion o f stars and m ake fo r m ore certainty. In this
w ay, the position o f a star, determ ined b y means o f altitude and azim uth
on the tem plate superim posed on this star chart, m ay be found fro m either
the star sym bol or the accompanying portions o f the star path, and so
any confusion in determ ining the name o f the unknown star observed, one
w hich m igh t be used in navigation, is entirely avoided.
P R A C T IC A L USE
The Star F in d er and Id en tifier S-3a can be used fo r iden tification of
celestial bodies (either stars or planets) as w e ll as fo r m aking an advance
list o f celestial bodies which m ay be observed at a given time. Solutions o f
examples o f all these problems are given in this paper as w e ll as a
reproduction o f star chart No. 8. T h e scale used fo r the star charts and the
tem plate is large enough to give sufficient accuracy fo r identification
purposes. A ll explanations and instructions fo r use are given schem atically
in sim ple and short form in the table printed above each star chart and
on both sides o f the border scale. The main ru le is that red azim uth figures
re fe r to the chart’ s border scale numbered in red, and that black azim uth
figures re fe r to the black numbering, and this rule is clearly printed on
either side o f the star charts.
I f the
other star
using this
additional
observed.
exam ples given in this paper w ere solved b y means o f some
fin d er it would be easy to see w h ich method is preferable. B y
Star F in d er the result is alw ays obtained, directly, w ith ou t any
procedure and w ithout any doubt as to which star has been
Identification of stars
E x a m p le 1. — On 25
50°03'N , L on g. 17° 15' W .
follow s : G M T 19h33m22s,
celestial body b y the Star
February 1965, D R position o f a ship was Lat.
T h e navigator observed an unknown star as
A lt. 37°43', Az. 165°. Id en tify the unknown
Finder S-3a.
Solution :
From the Nautical Alm anac fo r 1965, date 25 February : F o r G M T
18h
A ries G H A ..............................................................
l h33m22s .....................................................................................
65° 23:0
23 24.4
A ries G H A ..............................................................
88 47.4
L o n g ............................................................................. — 17 15.0 W
A ries
LHA
..............................................................
71° 32:4
F or the A ries L H A value approxim ately 71? 5 and azimuth 165° the
star chart No. 8 w ill be used. T h is star chart, w ith the tem plate already
superimposed and oriented fo r Lat. 50° N, is shown in the illustration
attached to this paper. In the id en tification procedure, however, b efore
placin g the tem plate over it, w e can see fro m the explanation given in the
table above the star chart that fo r A ries L H A 70° the star position w ill be
fou nd on the plotted sym bol o f a star; fo r A ries L H A 80° it w ill be at the
end o f the solid line o f the star’ s path, and fo r Aries L H A 60° at the
beginning o f the dotted line o f the star’ s path. T h is leads us to the conclu­
sion that fo r A ries L H A 71?5 the position o f the star w ill be a little rem oved
fro m the star sym bol at the begin n in g o f the solid lin e o f the path. A s the
azim uth figu res shown on the top o f the star chart and the tem plate are
black (eastern), the zenith o f the tem plate should be placed on the black
border scale o f the star chart in such a w a y as to cover the value o f the
latitude, i.e. -j- 50°.
T h e intersection o f the vertical circle fo r azimuth o f 165° w ith the
altitude p ara llel o f 37?7 (the grid o f the tem plate is shown in blue) was
fou nd to be at the beginning o f the solid lin e path o f the star A L N IL A M .
Thus the star iden tified is A ln ilam . A s its name is shown in black capital
letters, we see from the table above the star chart that it is a selected star
and, accordingly, its accurate coordinates m ay be found on the daily page o f
the A m erican N autical Alm an ac i f these are requ ired fo r sight reduction.
E x a m p le
2. —
T h ree unknow n stars w ith the follo w in g data w ere
observed :
a ) Lat. 50°07' N, A ries L H A 70°, Az. 28% A lt. 22°48',
b ) L at. 50°02' N, A ries L H A 66?5, Az. 29?5, A lt. 25°00'.
c) Lat. 50”03' N, A ries L H A 61°, Az. 152°, A lt. 26°16'.
S olu tion :
a ) F o r A ries L H A 70" and Az. 28° the star chart No. 8 w ill be used
(see A n n ex ). F ro m the explanation in the table above the star chart w e see
that fo r A ries L H A 70° the star’ s position w ill be found to be on the star
sym bol. As the azim uth figures 28° are in black, the zenith o f the tem plate
m ust be placed on the black num bered border scale to cover the latitude
o f + 50°. A t the intersection o f Az. 28° and A lt. 22?8 w e found the sym bol
o f the star M IZ A R . T his name is shown in green, th erefore it is not a selected
star and its accurate coordinates are shown not on the d aily page o f the
A m erican Nautical Alm an ac but in the star list near the end o f this
Alm anac. F o r the easier use o f this list (i.e. to fin d the star at once) we
w ill firs tly fin d in the Star F in d e r’s Alphabetical Index o f Stars the
approxim ate value o f S H A fo r M iza r; by means o f this and the star name
w e shall easily fin d the accurate coordinates SH A and the declination fo r
M izar requ ired fo r sight reduction, w ith ou t w asting tim e in searching for
its name in the A m erican N autical Alm an ac list.
b ) F o r A ries L H A 66?5 and Az. 29?5 the star chart No. 8 w ill also be
used. The explanation in the table above the star chart shows that fo r
A ries L H A 66?5 the position o f the star w ill be found to be on the dotted
lin e o f the star path ap p roxim ately between the star sym bol and the
m idpoin t o f that dotted line. Because the azim uth figures are in black the
zenith must be placed on the black figures + 50° on the chart’s border
scale. T h e intersection o f Az. 29?5 and Alt. 25° is found to be between the
dotted line path o f the star A lio th and the solid line path o f the star Mizar.
As w e have already stated in the table that the star’ s position w ill be found
to be on the dotted line o f the star path, the observed star is w ithout doubt
A L IO T H , since fo r M izar the position on the solid line path corresponds to
a value o f A ries L H A greater than 70° (i.e. approxim ately 72°), w hilst our
value fo r Aries L H A was 66?5.
In this exam ple w e m ay see that, even fo r closely-situated stars in the
star chart, id en tification b y this Star F in d er m ay be made easily and w ith
great certainty. T h is is p rim arily because o f the application o f the special
system o f showing a continuous picture o f a star’s position by means o f
plotted portions o f the star path, a system not used before fo r any other
star finder. Secondly, greater accuracy is obtained b y the use o f a larger
scale fo r the star chart (the distance on the chart fro m the celestial pole
to the celestial equator is 98 m illim etres), and also b y the selection o f the
equatorial stereographic projection instead o f the polar one. Thus fo r the
same star chart dimensions this Star F in d er has a scale nearly tw ice as
large.
c)
F o r A ries L H A 61° and Az. 152° the star chart No. 8 w ill again be
used. F ro m explanations given in the table above this chart w e see that
fo r A ries L H A 61° the star’ s position w ill be found to be at the beginning
o f the dotted line o f the star path. Black azim uth figures correspond to
black latitude scale figures, and the zenith o f the tem plate is placed over
the black + 50°. T h e intersection o f Az. 152° and A lt. 26?3 is found to be
at the beginning o f the dotted line o f the path o f the star S A IP H (k O rion is),
whose accurate coordinates we shall fin d in the star list near the end o f
the Am erican Nautical Alm anac as w e did fo r the coordinates o f thé star
M izar in exam ple a ).
Identification of planets
E x a m p le 3. — On 30 A p ril 1965, at the latitude 5 0 °0 2 'N a navigator
observed an unknown celestial body w ith the fo llo w in g data : A ries L H A
75°, Az. 86?5, A lt. 10°20'. Id en tify the body.
Solution :
F o r Aries L H A 75° and Az. 86?5 the star chart No. 8 w ill be used
(see A n n ex). T h e intersection o f Az. 86?5 and A lt. 10?3 is found to be below
the star Regulus and approxim ately 1 m illim etre above the right-hand edge
o f the letter “ R ” in the name Regulus. In relation to the position o f
Regulus fo r A ries L H A 75° (i.e. to the position on the m idpoint o f the solid
line o f its path) the position o f the observed celestial body (above the
letter R ) has a S H A about 10° less than Regulus (to the le ft), and declination
about 2° less. Coordinates fo r Regulus are obtained fro m the Nautical
Alm anac, and by subtracting the estim ated differences (— - 10° S H A and
— 2° dec.) w e fin d the fo llo w in g coordinates fo r the observed body :
Regulus :
SHA
SHA
208?4
1 0, 0
dec.
198?4
dec.
+ 12?1
2,0
—
+ 10?1
F ro m the d a ily page in the Nautical Alm anac for 30 A p ril takin g the
above coordinates S H A 198?4 and dec. + 10?1 w e fin d that the observed
b od y is the planet M AR S.
In practice h ow ever the procedure is considerably shorter. A fte r
ap p roxim ately estim ating that the position o f the observed body is in the
v ic in ity o f the star Regulus, a glance at the d aily page o f the N autical
A lm an ac fo r 30 A p ril shows the approxim ate coordinates o f R egulus; then
w ith these coordinates a search is made to find w h ich o f the fou r
navigational planets has coordinates closest to those o f Regulus. W e see
that on ly M ars has coordinates close o f the values o f those o f Regulus
(M ars SH A 199“ and dec. + 10°), w h ilst Venus is not visible and the S H A
o f Jupiter is 301° and o f Saturn 14° w hich means that they cannot be
considered in this case. T h is shortened and easy procedure fo r id en tifica ­
tion o f planets w as achieved by the insertion in this Star F in d er o f a large
num ber o f stars (182), i.e. p ractically all stars which m ight be used in
celestial navigation. T h e result in practice is that the position o f a star
determ ined b y means o f Az. and A lt. on the tem plate is never to be found
on an em pty space on the star chart, except w hen one o f the planets is
observed or when an error has been made. But i f a small number o f stars
(o n ly selected stars) are plotted in a star fin d er then w henever the star’ s
position is found to be on an em pty space on the star chart there w ill be
doubt as to w hether the observed celestial body is a non-charted star or
else one o f the planets. This creates uncertainty and the necessity o f
em ployin g yet again the length y procedure fo r identification o f stars and
planets.
Making an advance list of celestial bodies which could be observed at a given
time
E x a m p le 4. — On 28 F eb ru ary 1965 during the evening tw ilig h t fo r
G M T I9 h26m31s at the D R position, Lat. 5 0°04'N , Long. 15»00' W , fin d the
approxim ate azim uth and altitude o f each first magnitude star and any
navigational planets between altitudes 20" and 60° in the eastern h em i­
sphere.
Solution :
F rom the N autical A lm an ac fo r 1965, date 28 Febru ary : F o r G M T
18h
A ries G H A
l h26m31s ..................
68°20'4
21 41.3
A ries G H A
L o n g ...........
90 01.7
— 15 00.0 W
A ries L H A
7 5 ° 0 l 'J
Selection of stars
F or Aries LHA approx. 75° and eastern (black) azimuths the star
chart No. 8 will be used. The zenith o f the template must be placed on the
black + 50° o f the latitude scale. Then between altitude parallels 20° and
60”, Az. and Alt. have to be taken out for each first magnitude star for the
position o f Aries LHA 75" i.e. for the m idpoint o f the solid line o f the star
path. From the appended star chart we fin d in this way :
Pollux ..............................................
P rocyon .........................................
Betelgeuse .....................................
Sirius ................................................
Rigel ..................................................
Az.
Alt.
110?0
130.0
161.5
154.0
176.0
52?5
34.5
4 6.0
19.5
31.7
Selection of planets
From the Nautical Almanac for 28 February 1965 we find the follow ing
coordinates for planets and their nearest selected stars :
Planets
Venus
+ 7“ Regulus
Aldebaran
+ 17
SHA
Dec.
SHA
208°
292
+ 12°
+ 16
— 22°
+ 21
Dec.
0
not
visible
186°
313
not
visible
Dec.
Difference
from nearest
selected star
1+
Mars
Jupiter
Saturn
SHA
Nearest
selected
star
If the differences in SHA and Dec. found above are added to the
coordinates o f the stars mentioned, then from the star chart No. 8 with
the template oriented for latitude we find the follow ing :
— Mars is about 5" south o f Regulus (approxim ately 6 millimetres
below Regulus) and about 22° left o f Regulus (i.e. somewhat more
than twice the dotted line path’s length to the left o f Regulus).
Accordingly Mars is in the vicinity of the horizon and has an
altitude o f less than 20° and thus it does not come into consider­
ation.
— Jupiter has a SHA about 21° to the right o f Aldebaran (i.e. for
about the full length o f the dotted and the solid star path lines to
the right). This means that Jupiter is not on this particular star
chart (eastern hemisphere) but on the star chart No. 7, and thus
does not com e into consideration.
In this way, by means o f estimated coordinates of the planets, and
without precise plotting, it can be ascertained whether or not any o f the
fou r planets comes into consideration. The plotting o f the position o f a
planet can then follow , as well as the portions o f its path on both sides for
+ and — 10" o f SHA according to the estimated length o f these lines of
the nearest plotted stars. W ith the planets plotted in this w ay the
approxim ate Az. and Alt. coordinates can be read in order to find the
planets easily in the sky in the same way as has been done in the example
for the stars.
CONCLUDING NOTE
This Star Finder and Identifier S-3a has not yet been issued. It can be
printed either on the paper used for nautical charts, with an additional
plastic template, or else on 10 white opaque plastic sheets for star charts,
including appropriate technical facilities such as a small centre hole in
the star charts and a small peg in the centre o f the template fo r setting
and rotating the template m ore easily. The fashion in w hich such a manual
tor star identification will finally be issued will depend on arrangements
made between the author o f the Star Finder and the publisher interested
in it. Regarding a Nautical Alm anac differing from the American Alm anac,
this Star Finder could be further m odified in order to make the use o f the
Star Finder m ore convenient.