Content Page :
1) Introduction
2) Why celestial navigation
3) The theory behind celestial navigation
4) Celestial navigation in the past :
Wayfinding (non-instrumental navigation)
Viking navigation (sun navigation)
Columbus navigation (dead reckoning)
5) Navigational Instruments:
-Latitude hook, kamal
-Cross staff & back staff
-Quadrant
-Astrolabe
-Nocturnal
-Sextant
-Simple Celestial Navigation with the sextant
6) Finding the latitude:
- By Polaris
- Taking noon sun sights
7) Global Positioning System (GPS)
8) Navigation in the Singapore Navy
9) Navigation Procedure:
- Sun Run Sun
- Sun Run Merpass & Merpass Run Sun
10) Bibliography
1. Introduction :
The human race has been using the heavens to find their way since the
beginning of recorded history. Some of these methods are actually very
simple while others are extremely complex. In celestial navigation, the
navigator observes the celestial bodies like the Sun, Moon and the stars
to locate his position on Earth. Our group has chosen to do this project
because we believe that celestial navigation is a beautiful form of
human art and the study of it should be continued despite the rise of
GPS (Global Positioning System). And even so, celestial navigation is
still essential, especially when technology fails.
2. Why celestial navigation?




Understanding navigation, emergency & maintaining skills
Tradition
Enjoyment
Perspective of Life
Understanding navigation, emergency & maintaining skills
Instances where electronic failure due lighting strikes, flooding and other
disasters are often documented. Even battery-powered handheld equipment can
fail when the batteries run out. Hence it’s advantageous to have some
knowledge of celestial navigation for back up purposes. Furthermore celestial
navigation is also the only reliable means of checking the gyro at sea. In a
Discovery channel documentary, a navigating officer in one of the world’s
most sophisticated ship was shown taking an evening star sight. When enquired
why, he was quoted as saying, “Everything can fail but not the stars.” Thus
celestial navigation is still important in present day navigation systems.
Tradition
How is it possible to contemplate an 18th century brass and ebony sextant, and
not wonder what it was like to peer through it at the heavens; to bring an
evening star down to a twilight horizon from the deck of a tall ship? To sense
the approval of those who witness this magic-like prowess. To triumph at
landfall well predicted? To know he can navigate any ocean with no help from
anyone? Celestial navigation is one of the oldest of traditional arts and it would
be a tremendous loss if it were to die out.
Enjoyment
Knowing the night sky is like having a giant roadmap overhead. What could be
as satisfying as steering by a star or identifying constellations and planets on a
clear starry night? In addition, it is interesting that one can estimate one’s
latitude in the Northern Hemisphere by measuring the altitude of the pole star.
Furthermore, on a more aesthetic sense, the night sky is breath-takingly
beautiful especially when seen from a place where there is little light pollution.
Perpective of Life
Celestial navigation as a whole provides a wealth of wonderful images and
language to enliven the way we speak about, and understand, the direction of
our lives.
3. The theory behind celestial navigation
The basic theory behind celestial navigation is finding our unknown position from
a known position. If we have some information we can deduce the rest.
Below are several basic rules on which the practice of celestial navigation is build
upon:
a. Celestial navigation is based on the pre-Copernican concept. Its view of
the heavens is that the Earth is the unmoving centre, around which the
sun, moon, stars and planets revolve.
Ptolemy’s pre-Copernican concept
b. Space and time are a continuum. In celestial navigation, time=distance.
Longitude is measured in degrees, and each 15o is represented by 1 hour.
(Since 360o = 24 hour) i.e. One hour of the rotation of the Earth
corresponds to 15o angle of the Earth’s rotation. One second of time is
equal to roughly ¼ mile at the equator.
c. The three coordinate systems:
(It is essential that we are familiar with some of the common terms used in
celestial navigation.)
Earth’s coordinate system :
Equator: is the only great circle whose plane passes through the centre of
the earth and is perpendicular to the polar axis. It is used as a reference point
for setting latitude lines, thereby given the value 0 o
Latitude lines: runs parallel to the equator. It circles the Earth to the
North Pole from 0 to 90 degrees for the North Latitude and from 0 to 90
degrees to the South Pole for South Latitude.
Longitude lines: runs perpendicular to the equator. They are vertical
circles, beginning at 0 degrees at the Greenwich Meridian running through
Greenwich, England, and circling 180 degrees to the east for East Longitude
and 180 degrees to the west for West longitude. Each degree is further
subdivided into 60 minutes, and each minutes into 60 seconds (3600 seconds
per degree)
With this grid system, we can pinpoint the location of anything on Earth by
giving its latitude and longitude.
Celestial Bodies’ coordinate system:
Celestial Equator: It is the imaginary great circle above the earth’s
terrestrial equator and is located half way between the celestial poles.
Declination: It is the angular distance of the celestial body measured
north or south from the celestial equator (0 degrees). It is analogous to earth’s
latitude.
Right ascension or hour circles: It is the angle between the
meridian of the vernal equinox and the meridian of the star and is measured
eastward from the vernal equinox. It is analogous to the ‘longitude lines’ on
the celestial equator. However, right ascension is measured starting from 0 to
360 degrees, or in hours from 0 to 24 hours (rather than 180 degrees east or
west as in the case of longitude.)
First Point of Aries:
Also known as the vernal equinox. It is also referred as the 0 degree hour
circle (or celestial meridian). It is the base point for calculating right
ascension.
Observer’s coordinate system:
Zenith: the point directly over the observer’s head
Nadir: the point beneath the feet of the observer.
Horizon: The equator of the observer, perpendicular to the zenith.
Altitude: The ‘latitude’ of the celestial body, measuring from the horizon
up to the zenith of an observer (90 degrees). The angle is measured with a
sextant or other navigational instruments.
Azimuth: The number of degrees along the horizon of a celestial body
and it corresponds to the compass direction. It starts due North and increases
clockwise to 90o East, then 180o South and then 270o West and finally back to
0o North.
Observer’s meridian: the imaginary line running from observer’s
zenith due north or south to the observer’s horizon.
d. Hour Angles:
Geographical Position (GP) : The point on Earth’s surface
which passes through the centre of the Earth, through its surface, and into the
centre of the celestial body. This information is in the Almanac for every day,
hour and minute of the year.
Greenwich Hour Angle (GHA): The angle measured at the
pole between the meridian passing through Greenwich and the meridian
passing through the celestial body.
Local Hour Angle (LHA): The angle measured at the celestial
pole between the meridian passing through the observer’s meridian and the
meridian passing through the celestial body.
Sidereal Hour Angle (SHA): The angle measured at the
celestial pole between the meridian passing through the first point of Aeries
and the meridian passing through the celestial body, measured westwards.
The Almanac gives the GHA of everything but the stars because that would
take up too much room, instead it gives the SHA, which we can use to
convert, and worksheets help us figure the LHA by using our longitude.
4. Celestial navigation in the past:
In the primitive era, people had no means of tracking time and location. Thus
people started to study the daily rotation of the heavens and the motions of
the sun and moon relative to stars, for agricultural and civil purposes.
In this project, we’ll be looking into:
A. Way
finding (non-instrumental navigation)
B. Vikings
Navigation (sun navigation)
C. Columbus
navigation (dead reckoning)
Wayfinding:
Wayfinding is the navigation in open seas without any assistant of
navigational instrument of any form. The wayfinders merely observe the stars
overhead, the sun, the swells of the ocean and other signs of nature for clues
to direction and location. This method is used for voyaging for over 1000s of
years before the invention of European navigational instrument.
In wayfinding, the star compass is used. (This may sound a little ironic,
because, technically, NO instrument is suppose to be used in wayfinding)
The star compass is actually a mental construction for navigation, so it’s not
exactly an instrument. Hawaiian names are used of the houses of the stars,
which includes the place where the star comes out of the ocean and go back
into the ocean. The star path also reads the path of birds and the direction of
waves. So, all one has to do to be able to navigate is to memorise, memorise
and memorise!
The navigator cannot look up at the stars and immediately tell his position.
This is only possible if he had memorized where he had sailed. Thus, the
navigator has to constantly observe his surroundings (Like the motion of
birds, fish paths and other behaviours of animals etc.) for clues and
constantly remember his speed, direction and time. NO compass, NO
speedometer, NO watch is used. This technique of navigation requires A LOT
of experience to make it work and a good memory.
The Vikings
In the North of the Arctic Circle, there is continuous daylight for months in the
summer. Since the Vikings voyaged mostly in the summer (around the
summer solstices) where there are very few stars, they did not rely much on
the stars for navigation. Instead, they looked at the sun.
The amazing thing about the Vikings is that they were able maintain a stable
course to cross the Atlantic Ocean, between 61st to 62nd degrees North on a
due western course from Norway to Greenland. A task that is relatively tough
during that era of time.
How they did it?? Well, they had the "solskuggefjøl" ,a sun shadow board,
and the sun compass.
“ Solskuggefjøl"-a sun shadow board
This device is used to determine latitude. It’s a circular wooden board about
25-30cm in diameter and is kept in a bowl of water to stabilize it. The gnomon
(vertical pole) at the centre can be used to set the time of the year. Concentric
circles are marked on the board to represent different dates. The shadow of
the noon sun is then observed. The shadow should reach a particular desired
ring if the ship is on the correct latitude. If the shadow is over the line, the ship
will be too far north; if it hasn’t reach the line, the ship is too far south.
The bearing dial of a sun compass:
Since the sun’s shadow from the gnomon at the middle of the disk describes
different hyperbola at different times of the year, by rotating the disk till the
shadow of the tip falls on a hyperbola that represent 62 degrees & the four
week around summer solstice, we will be able to find out the general
direction.
However, if the wrong curve is chosen, and the course becomes a little too
north in the morning, it can be corrected by steering to a slightly more south
direction, and the average direction will be right.
Columbus Navigation
(Dead Reckoning):
In the late 15th century, celestial navigation was just budding in Europe,
mainly by the Portuguese. Before this, the Europeans relied largely on
deduced/ dead reckoning.
Deduced/ dead reckoning:
The navigator finds his position by measuring the course and distance he has
sailed from some known point. Then, he measures his course and distance
from that point on a chart, pricking the chart with a pin to mark the new
position.
In the Mediterranean Sea, it is not very useful to navigate celestially, because
the latitude is the roughly the same over that area. In confined water, it is
much easier to use dead reckoning to find one’s latitude and hence navigate.
Columbus was primarily a dead-reckoning navigator. He did experiment with
the celestial navigation technique from time to time, but according to records,
he was not very successful. Perhaps Columbus’ failure was due to a mixture
of bad luck and a general lack of celestial-navigation technique and
instruments.
5. Celestial Navigational Instrument :
In the past, it was almost impossible to determine longitude until 1714, when
John Harrison, an English clockmaker came up with the marine chronometer.
Prior to that, sailors and navigators only manage to determine their latitude with
various navigational instruments. Let's take a look at them now.
1. Latitude Hook and Kamal
2. Cross staff & Back staff
3. Quadrant
4. Astrolabe
5. Nocturnal
6. Sextant
The Latitude Hook and Kamal
The Polynesian Latitude Hook is one of
the simplest methods of traveling by
latitude. It is made of two pieces of
bamboo: One of these was split, with a
hook at the end while the other was a
shorter bamboo stick of a fixed length.
The two sticks were then tied together at
a right angle.
The underlying concept was that the stars revolve around the celestial pole. At
the celestial pole is the North Star, which does not appear to move. Hence at any
given time at night, the North Star would remain fixed in the same location.
By pointing the latitude hook at the North Star at arm’s length and looking
through the hook of the bamboo piece, the seaman would then know that he is
keeping at the same latitude as when he first set sail.
The Arabian Kamal, which means “Guide”, works by a similar mechanism. A hole
is made in the middle of a rectangular piece of wood, whereby a knotted piece of
string is passed through. The knotted string is to be held in the teeth to ensure a
fixed distance. The observer maintains roughly the same latitude by pulling the
rope, until the wooden piece fills his field of vision from the horizon up to the
North Star.
Different lengths of knotted string correspond to different latitudes, perhaps of
the various seaports and waypoints described by previous Arab seafarers.
b. Cross-staff
Cross staff, dated:1571 ;
Wood and gilt brass; 1393 mm in length
British Museum, London.
The cross-staff is a mariner’s navigational instrument in the 16th century. It is
also known as ballastella, Jacob’s staff or fore-staff.
Instead of measuring the celestial body (usually, the pole star or the sun) down
from zenith, it measures the angles and altitude of the celestial body from the
horizon (as this is usually a clear cut line on fine days). It has a graduated staff
with one or more perpendicular vanes or cross pieces moving over it.
To measure the altitude of a particular celestial body, the eye-end of the staff will
be placed near the observer’s eye and the other end will be held by the longer
vane, half way between the horizon & the celestial body. The shorter vane or
‘transom’ is then slid along the staff until its upper edge appear to touch the
celestial body while the lower edge touches the horizon.
The altitude can be easily read off the scale on the staff.
In measuring the altitude of the sun, the observer had to face the sun, which may
be quite inconvenient and not to mention bad for the eyes. Hence this led to the
development of the back staff.
The pictures show medieval surveyors using the cross-staff
Back staff
The Back staff or “Davis Quadrant” was invented by an English explorer, John
Davis who was very impressed by the ingenuity of the cross staff. The back staff
is actually an improvement over the cross staff, whereby the observer need not
face the sun directly, but with his back to the sun, can observe the altitude of the
sun by looking at the sun’s shadow. It was composed of three vanes (sight,
shadow, and horizon) and two arcs fastened to a staff and divided in degrees.
The sight vane slides along the sight arc the same time as the shadow vane
slides along the shadow arc. The two arcs are part of two circles with a common
centre, which is located on the horizon vane. The small arc measures 60 degrees
and the large one - 30, thus providing a maximum zenith altitude of 90 degrees.
Quadrant :
Quadrant is a simple tool to measure latitude. Its name was derived from the
quarter circle that is used as a scale.
The Arabs were the first people to use this navigational tool. However, instead of
degrees inscribed onto the circumference, some ancient quadrants had the
names of ports and waypoints carved on the arc. When the plumb line cuts the
arc at the given name, the sailor then knew that he had to turn either east or west
along that latitude to reach that place in question.
To use a quadrant, the plane of the quadrant has to be adjusted to lie in the
plane of the observer's meridian. A plumb line is suspended from the quadrant's
centre to ensure vertical alignment. It measures the angle form the vertical and
the line of sight to the body. (as shown in the diagram on the left)
Astrolabe
The picture on the left: Astrolabe, dated 1594, Brass; British Museum, London
Astrolabe or "star-taker” gave the altitude of a body by measuring its complement
from the zenith down to the line of sight and is used to give a picture of the sky's
view at the observer's latitude and time. It is speculated that it originated in
ancient Greece and was then refined by the Arabs.
It was a disk with degrees of arc engraved around its circumference and has
sight vanes on a rotating pointer called "alidade." It is suspended by a small hook
or "eye" which hung in a vertical plane. It has moveable parts that can be set for
specific dates and times, and interchangeable templates that can set latitude. A
rod of ring's diameter length is pivoted at the center of the ring, carrying sights at
either end. When aligned on a star or planet, an angular scale inscribed on the
armillary ring gives the object's altitude.
Nocturnal
The nocturnal was first conceived in the 1200s and was widely used by early
Europeans and Arabs alike. It was made up of a sight, a pointer (the horizontal
arm), and two disks:- one, which tells the date, and the other that tells the hours.
This device is used to tell time using the positions
of the stars. One disk is set to the date while
Polaris will be seen through the hole in the centre.
The horizontal arm attached to the centre of the
ring is then rotated around and aligned with
pointer stars, such as the Big Dipper, Little Dipper
or Cassiopeia. The point where the arm coincides
with the marked disk will be taken as the time.
It is only used to measure Polaris's distance in minutes of arc from true North;
thus, there are some corrections that need to be applied. Furthermore it cannot
be used in southern latitudes because Polaris will not be visible above the
horizon.
However it was one of the most accurate clocks around, and was used
extensively at sea and on land up until the early 1800s, even after the
chronometer was perfected.
Sextant :
The sextant was invented in the 1800s. Since then, it has become widely
acknowledged as a universal nautical symbol along with the compass.
It has proved itself almost indispensable to every seaman over the centuries, as
it can be used to deduce latitude and longitude. This is very important in pin
pointing one’s location out at sea, especially in modern times where a compass
cannot work on ships, due to the ferrous magnetic nature of the ship’s hull.
An Actual
Sextant
Navigators at work!
The sextant is a double reflecting system that uses 2 mirrors to bring the celestial
body targeted, to the observer's horizon. It measures the angle of celestial
bodies above the horizon from the observer's position. Normally, sextants are
handheld and have a fixed telescope leveled at the observer's horizon.
On the sextant, it has a movable radial arm that slides against an arc scaled in
degrees. The arm is adjusted until a known star's image, which is reflected from
the index mirror to the horizon mirror, lines up with the horizon. The horizon
mirror is half silvered so that the horizon can be seen at the same time the
reflected image of the star can be seen. The radial arm's position on the scale
gives the star's elevation.
Simple Celestial Navigation with the
sextant
We can find out where we are by observing the location of the sun when it is
directly overhead!
1. Firstly, we imagine that the sun is directly overhead at a particular time and
we look up its actual position in the Nautical Almanac.
2. Then, we cross check the accuracy of the Sun's position with a sextant. The
angle should be 90 degrees.
3. However, if the Sun is 1 degree away from the observer's zenith, then we will
be on a circle 60 miles away from the actual position (1 degree = 60 miles). This
is a circular line of position (LOP).
4. When we look at the Sun's position later in the day, we will get another circle,
and our approximate position will be the intersection of the two circles.
5.
To improve accuracy, we draw a third circle.
TATA! We have FOUND our position!
Find latitude by Polaris & taking noon sun sights
Let's assume a position for the observer. In this case,
let the observer's geographical latitude be equals to
'G.L'.
Altitude: The ‘latitude’ of the celestial body,
measuring from the horizon up to the zenith
of an observer (90 degrees). The angle is
measured with a sextant or other
navigational instruments.
Since altitude = 90 degrees - angle Z
(angle Z = angle W)
= 90 degrees -angle W
= geographical latitude 'G.L'
Therefore, altitude of the Polaris above the horizon is the same as the observer's
geographical latitude! And latitude can be measured with a sextant.
Finding Latitude by taking noon sun sights:
E
N
S
Earth
Equator
W
When the Sun is at real noon, (at the highest point on the observer's meridian) , it
is either due North or due South to the observer. The observer's line of position is
then due East or due West. Since East-West line is parallel to the latitude, it is
possible to find the latitude of the observer by means of right triangle.
The principle is identical to finding latitude by the Polaris. The sun's altitude from
the position of the observer is equal to the latitude of the observer. Finding the
sun's altitude with a sextant may be more difficult because of the great light
intensity of the sun. Therefore, the sextant may have to be modified a little by
putting a photograph negative film in front of the index mirror of the sextant to
reduce the light intensity.
Navigation in the Singapore Navy
Concepts
Distinction between the visible horizon and the celestial horizon
The visible horizon is the small circle on the Earth’s surface where the sky
and sea appear to meet. Whereas the celestial horizon is the great circle on
the celestial sphere that passes through the centre of the earth, every point of
which is 90o from the observer’s zenith. This is shown in the figures below.
Visible horizon
Celestial horizon
Hour Angles
 Sidereal Hour Angle (SHA)
 Greenwich Hour Angle (GHA)
 Local Hour Angle (LHA)
As it is physically impossible to tabulate the local hour angles of every
celestial body for all minutes of longitude, a method linking LHA and GHA has
been devised to circumvent this problem. To get the LHA of any celestial
body for any time at any longitude, the following step is needed.
LHA = GHA + East Longitude
or
LHA = | GHA – West Longitude |
W
LHA
Greenwich
Meridian
E
W
LHA
E
Greenwich
Meridian
In addition, the GHA of a particular star can be found by:
GHA star = GHA aeries + SHA star
The Relationship Between the Hour Angles:
These equations are essential
in converting data on a ship and
they are needed in calculating
the exact position of the star.
Twilight
Navigational officers must know the time of the rising and setting of the sun as
this is important in determining twilight- the period of day when even though the
sun is below the horizon, the observer stills sees light due to refraction by the
upper atmosphere.
Twilight is the time when the altitudes of the stars can be taken because that is
when one can see both the horizon and the stars at the same time. This is due to
the fact that it is extremely dark at sea at night and so it is difficult to see the
horizon even though the stars shine brightly because of minimal light pollution.
Conversely, though it is easy to see the horizon in the day, it is impossible to see
the stars due to the glare of the sun.
Merpass
Merpass is when the celestial body is over the observer's meridian.
The true bearing of the celestial body will be either 000 or 180 and this depends
on 3 factors:
- Latitude of observer
- Declination of the celestial body
- Hemisphere
i.e. In the Northern hemisphere, when latitude and declination have opposite
names, the bearing is 180.
However in the Southern hemisphere, when latitude and declination have
opposite names, the bearing is 000.
The exact time of the merpass can be calculated from the nautical almanac.
The exact latitude of the observer at the time of merpass can be easily found out
by observing the Sun's altitude at the time of merpass.
Latitude = 90o - Altitude + Declination
Naval Procedure:
Daily Procedure:
1) Calculate the morning nautical time (MNT) from the nautical
almanac the night before.
This is the time when we take our readings.
2) At 45 min before MNT, recognise and identify the celestial bodies
and fill up the table under Calculated.
3) At MNT, measure the altitude of the celestial bodies and fill up the
data under the Observed section
For example:
Serial
No.
Calculated
Stars/Planets
Bearing
Observed
Sextant
Gyro
Sextant
alt.
Bearing
alt.
D.W.T
1
Betelgeuse
43.1
66o 04.8’
-
-
2
Canopus
160.6
43 o 41’
44 o 45.4’
05 18 24
3
Jupiter
42.3
45 o 20’
49 o 53.6’
05 28 22
4
Sirius
106.2
61 o 21.5’
68 o 18.2’
05 30 37
5
Formalhaut
241
6 o 37.8’
-
-
A pictorial representation of
the bearing and altitude of the
stars with respect to the ship.
The largest circle represents
the altitude 0 o .
The middle circle represents
the altitude 30 o
and the inner circle represents
the altitude 60 o.
The point above the ship
represents 90 o.
Navigational Stars
Index of Selected Stars - (West to East)
The Nautical Almanac gives the location data for 173 stars, but from this listing 57 stars have
been chosen from amongst these on account of brightness and distribution in the sky; they will
suffice for the majority of observations. The location of a star is given by its sidereal hour
angle (S.H.A.) and its declination (Dec.). The locations given below are rounded off to the
degree of angle and are an aid in finding the star on a star chart, but for sight reduction, more
precise values will be needed from the Nautical Almanac.
No.
Name
Mag. S.H.A.
Dec.
No.
Name
Mag. S.H.A.
Dec.
1
2
3
4
5
Alpheratz
Ankaa
Schedar
Diphda
Achernar
2.2*
2.4
2.5*
2.2
0.6
358
354
350
349#
336#
N.29
S.42
N.56
S.18
S.57
31
32
33
34
35
Gacrux
Alioth
Spica
Alkaid
Hadar
1.6
1.7
1.2*
1.9
0.9
172#
167
159#
153
149#
S.
N.
S.
N.
S.
57
56
11
49
60
6
7
8
9
10
Hamal
Acamar
Menkar
Mirfac
Aldebaran
2.2*
3.1
2.8
1.9*
1.1*
328
316
315
309
291#
N.23
S.40
N. 4
N.50
N.16
36
37
38
39
40
Menkent
Arcturus
Rigel Kentaurus
Zubenelgenubi
Kochab
2.3
0.2*
0.1
2.9*
2.2
149
146#
140#
138#
137
S.
N.
S.
S.
N.
36
19
61
16
74
11
12
13
14
15
Rigel
Capella
Bellatrix
Elnath
Alnilam
0.3*
0.2*
1.7*
1.8
1.8*
282#
281
279#
279
276#
S. 8
N.46
N. 6
N.29
S. 1
41
42
43
44
45
Alpheca
Antares
Atria
Sabic
Shaula
2.3*
1.2*
1.9
2.6
1.7
127
113#
108#
103
97#
N.
S.
S.
S.
S.
27
26
69
16
37
16
17
18
19
20
Betelgeuse var.*
Canopus
-0.9
Sirius
-1.6*
Adhara
1.6
Procyon
0.5*
271#
264#
259#
256#
245#
N. 7
S.53
S.17
S.29
N. 5
46
47
48
49
50
Rasalhague
Eltanin
Kaus Australis
Vega
Nunki
2.1
2.4
2.0
0.1*
2.1*
96
91
84#
81
76#
N.
N.
S.
N.
S.
13
51
34
39
26
21
22
23
24
25
Pollux
1.2*
Avior
1.7
Suhail
2.2
Miaplacidus1.8
Alphard
2.2
244
234#
223
222#
218#
N.28
S.59
S.43
S.70
S. 9
51
52
53
54
55
Altair
Peacock
Deneb
Enif
Al Na'ir
0.9*
2.1
1.3*
2.5
2.2
63#
54#
50
34
28#
N.
S.
N.
N.
S.
9
57
45
10
47
26
27
28
29
30
Regulus
Dubhe
Denebola
Gienah
Acrux
208#
194
183#
176
174#
N.12
N.62
N.15
S.17
S.63
56 Fomalhaut
57 Markab
1.3
2.6
16#
14
S. 30
N. 15
1.3*
2.0
2.2*
2.8
1.1
* = Stars that are prominent for observers in the Northern hemisphere.
# = Stars that are prominent for observers in the Southern hemisphere.
Var. = Variable star, mag. = 0.1 to 1.2
- Note that many stars are visible North and South of the equator.
Taken directly from http://www.angelfire.com/nt/navtrig/F1.html
4) Using the sun’s course to map out location on earth
A position-plotting chart is needed to find out the ship's direction and the ship's
eventual course.
Time
Event
Sunrise
Measure sun’s bearing
0830
Measure morning sun’s altitude
1000
Calculate morning sun and plot Observed position (Sun Run Sun)
1115
Prediction of merpass of the sun
Merpass-15min
Measure merpass sun’s altitude (Sun Run Merpass)
1400
Measure afternoon sun’s altitude and bearing (Merpass Run Sun)
1530
Sun Run Sun
Sunset
Measure sun’s bearing
5) Predict the Evening Civil Time (ECT)
6) Identify the stars 15 min before ECT
7) At ECT, measure the altitude of the celestial bodies
8) Prepare the next day’s MNT
Sun Run Sun
Method: (An Example)
This is just a rough sketch as seen from a position-plotting chart.
No scales are given.
Stage1
1) Using the bearings of three of the stars observed, draw the bearing lines.
- Your estimated position will be the circle enclosed within the 3 lines
Stage 2
1) Plot your position using dead reckoning
- From a given position (the centre of the circle), the ship travels 20km/h for 2 hours at
bearing 100o
- Hence a line of bearing of 100o, whose length is determined by the scale of the map,
is drawn.
(eg 4cm = 40km)
- At the end of 2 hours, the estimated position of the ship on the map is the end of the
4cm line and is called the dead reckoning point 1 (DR1)
2) At the same time, plot the celestial position of the sun (CP1)
- this will give you your actual position on the map
(eg it is actually 1 km from the estimated position and slightly to the north)
3) Draw the bearing of the sun and form the position line (PL1)
4) From DR1, drop a perpendicular line to PL1
Stage 3
1) After another 2 hours, find your position using dead reckoning again.
- label the new point DR2
2) Find the celestial position of the sun at this time and draw the position line (PL2)
3) Transfer PL1 through DR2
- Something like drawing a line parallel to PL1 that passes through DR2
4) The point of intersection of PL1 and PL2 is observation point. This is where you are most
likely to be found.
Sun Run Merpass
The procedure is similar to that of sun run sun
1) Starting from a dead reckoning point (DR), calculate the time of merpass at DR.
2) With that time (converted to Greenwich Mean Time :GMT), find out the declination of the
sun from the nautical almanac.
3) Find the altitude of the sun at the time of merpass.
4) Find the latitude using the formula : Latitude = 90o - Altitude + Declination
5) Draw this latitude on the chart.
6) Transfer the previous position line to the DR of merpass.
7) The point of intersection between these two lines is the observed position at the time of
merpass.
Merpass Run Sun
It is exactly the same as Sun Run Merpass, except that the sequence of events is the
opposite.
1) Calculate the time of merpass and note the DR
2) With that time (converted to GMT), find out the declination of the sun from the nautical
almanac.
3) Find the altitude of the sun
4) Calculate the latitude with the 2 values of altitude and declination
5) Draw the latitude on the chart
6) With the DR from merpass, drop a perpendicular line on the latitude line to get an
intercept.
7) Find the observed point in the usual way stated in Sun Run Sun.
Bibliography:
Texts:
Telescopes and Techniques: An Introduction to Practical Astronomy
By C.R. Kitchin
ref pages: 59-77, 80-81, 83
Eye Witness Handbooks: Stars and Planets:
The visual guide to the night sky viewed from around the world
By Ian Ridpath
ref pages: 16-21
Astronomy Through the Ages: The story of the human attempt to understand the
universe.
By Robert Wilson
Longitude:
The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of
His Time
By Dava Sobel
ref page: 90,91
Websites:
Heavenly Mathematics: Highlights of Cultural Astronomy
http://www.math.ns.edu.sg/aslaksen/teaching/heavenly.shtml
Celestial Navigation; How it works
http://www.seatape.com/303doc.htm
Introduction to Celestial Navigation
http://www.nav.gov/cel/introduction.html
XTant project- Build your own sextant
http://www.tecepe.com.br/nav/XTantProject.htm
Interactive sextant
http://www.tecepe.com.br/nav/sextantflash.html
NOVA Online | Shackleton’s Voyage of Endrance | How a Sextant Works | PBS
http://www.pbs.org/wgbh/nova/shackleton/navigate/escapeworks.html
NOVA Online | Shackleton’s Voyage of Endrance | Navigation by Sextant | PBS
http://www.pbs.org/wgbh/nova/shackleton/navigate/escapenav.html
Celestaire – Navigation Instruments: How does celestial navigation work?
Http://www.celestaire.com/page7.html
Eric Weisstein's World of Astronomy
http://scienceworld.wolfram.com/astronomy/EclipsingBinary.html
Astronomy On-Line Measuring the Altitude of the North Pole Star
http://eso.org/outreach/spec-prog/aol/market/information/finevent/finevent/polar.html
http://eso.org/outreach/spec-prog/aol/market/information/finevent/finevent/polmath.html
celestial navigation for dummy
http://home.tiscalinet.be/asna/Text/celnav1.htm
Celestial Navigation Net
http://celestialnavigation.net/
http://celestialnavigation.net/instruments.hml
http://celestialnavigation.net/practice.html
http://celestialnavigation.net/theory.html
Navigationhttp://www.irbs.com/directory/Navigation/
General Sight Reduction
http://www.info.gov.hk/mardep/javascpt/sight.htm
explanatory articles
http://www.mhs.ox.ac.uk/epact/articles.asp
http://mhs.ox.ac.uk/epact/article.asp?article=Astrolabe
http://mhs.ox.ac.uk/epact/article.asp?article=Armillary$32Sphere
Selected Stars, Listed from West to East
http://www.angelfire.com/nt/navtrig/F1.html
Spherical Coordinates
http://www.angelfire.com/nt/navtrig/E3.html
medieval nag instru
http://www.humboldt.edu/~rap1/EarlySciInstSite/Instruments/RepInst.htm
Epact Scientific Instruments of Medieval and Renaissance Europe
http://www.mhs.ox.ac.uk/epact/catalogue.asp?enumber=96868
Astronomical Instruments
http://members.tripod.com/~worldsite/astronomy/astroinst.html
The History of Sextant
http://www.mat.uc.pt/~helios/Mestre/Novemb00/H61iflan.htm
http://www.cogtech.com/EXPLORER/sextant.htm
Find latitude by Polaris
http://www.eso.org/outreach/spec-prog/aol/market/information/finevent/polmath.html