SOUTHERN ASTRONOMERS and
AUSTRALIAN ASTRONOMY
ELEMENTARY ASTRONOMY FOR SERVICE USE
PART 3
METHODS OF FINDING DIRECTION FROM
ASTRONOMICAL OBJECTS
There are several advantages in being able to find direction by
astronomical means. A compass may not always be available, can only
be seen by one person and is affected by nearness to iron which is an
important component in all vehicles, in many buildings, [*21] and in
the equipment carried by a soldier who would have to lay aside his
tin hat, rifle, and pack and go some yards away to take a bearing.
The magnetic declination {difference of magnetic from true north)
moreover is different in different parts of the world and may be very
capricious in regions where there are deposits of iron ore. The
stars, however, can be seen by everyone in the column and approximate
methods are easy to learn and apply, and are quite satisfactory
since, without special aids, a direction of march maintained within
two or three degrees of the intended line is quite good. A
disadvantage is, of course, that in cloudy weather astronomical
methods cannot be applied.
The bearing or direction of an object from an observer or the
direction in which it is desired to travel may be defined by the
angle which the direction makes with the line pointing due north, and
is measured up to 180° either towards the east or west. Thus the
bearing of north-east is 45° east and of south-west 135°
west. Another method of defining bearing is to number the degrees
from 0° to 360° right round the compass, beginning at north
so that east is 90° south, 180°, and west 270°. This
is the definition most commonly used in the services and is probably
preferable to the first one, which, however, is used in the remainder
of this booklet for the reason that it simplifies the use of the
diagrams provided to calculate the bearing of astronomical objects.
It is quite easy to convert from this to the second method by taking
bearings towards the east as they stand and subtracting bearings
towards the west from 360°. If the divided card on the back of
this booklet is held horizontally with the division marked “0”pointing to
the north, each of the other divisions will define a bearing from
this direction. The interval between consecutive divisions is
2°. This card may be used as an aid in deciding a line of march.
The first thing to do is to decide, possibly from a map, what is to
be the bearing of travel, and then the card may be held horizontally
with the “0” division towards the north and the march
proceeded with in the direction corresponding to the bearing chosen.
if the direction of north is not known, the card may be set in the
correct direction by setting towards an object of known bearing, the
line from the centre of the card to the division corresponding to the
bearing of the object. The known bearing may be towards a landmark,
for example a hill, or an astronomical object such as the rising
Sun.
One way of finding direction in the southern hemisphere by means
of the Sun is to lay a watch horizontally with the twelve o’clock mark pointing directly towards the
Sun, then north will be the direction lying midway between twelve and
the direction of the hour hand. If in the northern hemisphere, point
the hour hand towards the Sun, and south will be the direction midway
between the hour hand and twelve. The watch must be set to standard
time not summer time. It should be remembered that this method is of
no use in the tropics or near them, but outside say 40° either
[*22] north or south it should give fairly satisfactory results or,
except in the summer, outside 30°.
At night the stars may be used to find direction and maintain it.
If you look at Figure A and remember the description given, you will
see that there are two points in the sky labelled CN and CS, which do
not appear to move. The one visible from Australia is the point CS
and is the central point of the south polar map. There are several
ways of locating it approximately. One way is to measure the length
from γ to α in Crux and then go further in the same
direction four times this length. Other ways are to take a point half
way between Achernar and the star β
in Centaurus or one half way between β in Hydrus and β in Chamaeleon or one half way between
ε in Pavo and ε in Carina. The point determined in any
of these ways will always be almost due south. In the northern
hemisphere, fortunately, the star Polaris is very near the north
pole, and its direction may always be taken as approximately
north.
Groups of stars which are close to the line of 0° declination
on the maps are nearly either due east or due west when they are near
the horizon and if the observer is near the equator they may be used
to mark approximately east or west while they are less than half way
from the horizon to the zenith. The three stars near the centre of
Orion (“the belt”) on Map III are an example of this. Anyone
with a reasonable knowledge of the sky will always have a fair idea
of his bearings on a clear night.
A convenient way of finding true north when remaining at one place
for a day or more is by means of the shadow stick. A stick is set up
vertically on a level surface and a circle drawn round it with the
base of the stick at its centre. The end of the shadow of the stick
will touch the circle at two places during the day and, if the angle
between the two lines-joining the base of the stick to these points
is bisected, the true north-south line is obtained. It is worth
keeping in mind that a line half way between the direction of sunrise
and the direction of sunset will run due north and south.
CALCULATION OF THE BEARING OF THE SUN
AT RISING OR
SETTING
Figure I is an alignment diagram which provides a method of
calculating the bearing of the Sun as it is rising or setting. These
diagrams offer a convenient method of calculating a quantity which
depends on two others. The bearings found by means of the diagrams
about to be described should be accurate to within a quarter of a
degree (half a degree very easily) and the method gives a reliable
way of checking the magnetic compass. The compass bearing of the
astronomical object is compared with the computed value and the
difference between the two gives the correction that must be applied
to compass readings to obtain bearings from true north. If, for
example, the compass bearing of the astronomical object is 11°
more than the computed value you know that 11° must be
subtracted from the compass bearing to obtain true bearing. The
rising Sun is particularly useful for this purpose. In this case, if
we know the latitude in which we are situated and the declination of
the Sun at the time, we can calculate the bearing at which the Sun
will rise or set, and the diagram is provided to shorten this
calculation. The meaning of declination has already been explained.
North declination or latitude is plus, and south declination or
latitude is minus, so that these may be designated either by the
signs or by the letters N. and S. The declination corresponding to
the nearest date may be taken from Table IV if an approximate value
only is needed, or the accuracy may be improved by taking a
proportional part of the difference in declination between the two
dates and adding it to the first. Cut the side scales by a taut
thread at points corresponding respectively to the declination and
latitude. The bearing at which the Sun will rise or set is read off
where the thread cuts the middle scale and is measured towards the
east for rising and towards the west for setting. If the declination
is north, the scale value less than 90° is read, and if the
declination is south the scale value greater than 90° is
read.
In using these alignment diagrams, two things ought to be
remembered: firstly, the scale divisions are not always equal in
value; for instance, in Figure I the fight-hand scale is a latitude
scale and, reading from the bottom, the first division is 5° and
the second (which is numbered) is 10°. However, this should
cause no difficulty if it is remembered that the divisions between
the consecutive numbered. ones always represent equal values.
Secondly, the accuracy of the work can be increased if one-tenth of a
division is estimated; for instance, if the bearing of the Sun is
required in latitude S. 23.6°, the thread should cross the scale
six-tenths of the way between the division 23° and division
24° Knowledge of the bearing of sunrise or sunset may prove
useful in two ways: on the one hand it gives a handy method of
finding beating in the early morning or late afternoon, and on the
other hand it may occasionally enable use of the tactical advantage
of approaching an enemy from the sunward side, which may be a
worthwhile one if the sun is low and shining in his eyes. Any
rifleman or motor driver will appreciate this.
Examples of the use of Figure I:
Lat. -- -- 34°S. 33.9° S. 23° N.
Dec. -- -- +17° -23½° -12.4°
B -- -- 69.3° 118.7° 103.5°
Figure I may be used also to find the bearing of rising or setting
of a star or the Moon. If you want to find the bearing of rising or
setting of a star, find it on the maps and estimate its declination.
Then use the diagram as for the Sun. For example, suppose we wish to
find the bearing at setting of Sirius in latitude 34° south.
[*24]
From Map III the declination of Sirius is estimated to be 17°
south. Drawing the thread between 17° on the left-hand scale and
34° on the right-hand scale, the bearing at setting of Sirius is
110° west. If the object is the Moon or a planet, observe its
position among the stars and then use the place it would occupy on
the map to find its declination. If an astronomical almanac is
available the declinations of the Moon and planets may be found from
it.
CALCULATION OF THE BEARING OF THE SUN
AT ANY HOUR
Figure II can be used to carry out the calculation of the bearing
of the Sun at any time during the day. In order to compute this the
information necessary is the date, the longitude and latitude of the
place, the time and the longitude corresponding to the standard time
being kept. The procedure to find the bearing of the Sun is then as
follows:
(1) Take from Table IV the mean time when the Sun is
on the meridian and the declination for the nearest date — for
improved accuracy take the proportional part between the two nearest
dates.
(2) Subtract four minutes from the tabular meridian
passage for every degree east of the standard time meridian, or add
four minutes for every degree west of it, to find the time at which
the Sun will be on your meridian. Table V is a table giving the
standard time meridians for different places likely to be of
interest.
(3) Now take the difference between the actual time
and the time when the Sun is on the meridian. This is called the
“hour angle”, and is east if the time is before transit
time, or west if the time is after the transit time. The hour angle
must be converted from hours and minutes to degrees. This may be done
mentally by converting to minutes and dividing by four; for example
6h. 31m. is 391 min., that is, 97.8°.
(4) Working on Figure II, pull the thread taut to
cross the point on the X scale corresponding to the declination of
the Sun and the point on the Z scale corresponding to the hour angle
and read the angle indicated where the thread crosses the Y scale.
This angle is called N. N is the same sign as the declination and is
less than 90° when the hour angle is less then 90° and is
greater than 90° when the hour angle is greater than
90°.
(5) Next calculate the angles (Latitude-N) and
90°-(Latitude-N). Be careful of signs, for example, if latitude
= 33.9° and N = +26° (Latitude-N) is &minus 59.9° and
90°−(Latitude-N) is 149.9°
(6) Pull the thread taut between the point on the X
scale corresponding to the hour angle and the point on the Z scale
corresponding to the angle 90°−(Latitude−N). The
angle R (arbitrarily taken less than 90°) may be read from the Y
scale. [*24]
(7) Next pull the thread taut to cross the Y scale at
the same point as in the last step (that is, the point where we read
off R) and the Z scale at the point corresponding to the angle N. The
bearing of the Sun may then be read on the X scale. If the angle
(Latitude − N) was plus, the bearing will be the angle greater
than 90°, and if (Latitude − N) was minus, the bearing
angle less than 90° will be read. When the hour angle is west
the angle is measured westwards from the north point, and if the hour
angle is east the bearing is measured eastwards.
It may not always be convenient to make a calculation
of this kind while on the march but it would be quite good enough to
assume a longitude and latitude corresponding roughly to the centre
of the day“s march and calculate the
bearings of the Sun at various hours. This could be done the night
before and a note made of the results so that bearings could be kept
by watching the Sun during the march.
TABLE III.
Examples of the Use of Figure II
1 Date January 10. June 1. September 8.
2 Standard time longitude 150° 150° 150°
3 Longitude 151° 151° 152°
4 Meridian transit (Table IV) 12h 08m 11h 57m 11h 59m
5 Sun on meridian 12h 04m 11h 53m 12h 11m
6 Time 18h 35m 09h 33m 13h 35m
7 Hour angle h.m. W. 6h 31m E. 2h 20m W. 18h 11m
8 Declination -22.0° +22.0° +7.5°
9 Hour angle, degrees W. 97.8 E. 35.0 W. 17.8
10 90-(Lat.-N) +15.2 +149.9 +80.8
11 Latitude -34.0 -33.9 +17.0
12 N -108.8 +26.0 +7.8
13 R 82.5 39.0 63.2
14 (Lat -N ) +74.8 -59.9 +9.2
15 Bearing W. 112.2 E. 36.0 W. 117.0
16 Zenith distance 84.1 64.9 19.5
Note: - 8 on X scale and 09 on Z scale give 12 on Y scale.
9 on X scale and 10 on Z scale give 13 on Y scale.
13 on Y scale and 12 on Z scale give 15 on X scale.
14 on X scale and 15 on Z scale give 16 on Y scale.
After several practice calculations it was found possible to work
out a bearing of the Sun in about four minutes and a complete set of
computations for a day may be greatly shortened by the fact that
lines 1, 2, 3, l, 5, 8, and 11 are the same for all the computations
of a given day. Taking advantage of this a complete set giving
bearings every half hour of the day for an imaginary march from
Sydney to Penrith was worked in 18 minutes. In making these
calculations it will be a help to prepare a form with abbreviations
of the steps named on the left-hand side of Table III. This will
enable use to be made of the alignment diagram without confusion or
reference to the text. The results obtained by this graphical method
should be within half a degree of the truth.
The same diagram may also be used to find the altitude of the Sun
by adding the following step:
(8) Pull the thread taut to cross the X scale at the point
corresponding to {Latitude-N) and the Z scale at the point
corresponding to the bearing and read the zenith distance of the Sun
on the Y scale. If the Sun is visible this angle is always less than
90°. The altitude is then 90° — zenith distance.
MAINTAINING DIRECTION AT NIGHT
When the direction of march is decided upon a star near the
horizon in this direction may be selected and used as a mark towards
which to proceed. It must be remembered that the star is moving and
that it will be necessary occasionally to check the bearing and
perhaps change the object being used. If the march is in certain
directions the selected star may be moving relatively quickly,
particularly unfavourable cases being stars to the north when in
south latitudes, or stars to the south when in north latitude. If
there is an object, for instance a planet, whose right ascension and
declination are known, it may be easily found by plotting it on the
maps and then looking at that part of the sky. When once planets are
located in the sky they may be used in the same way as stars.
Last Update : 13th August 2012
Southern Astronomical Delights ©
(2012)
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