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____________________________________________________For Heavenly Mathematics: Astrobox ~ Contents
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____________________________________________________For Heavenly Mathematics: Astrobox ~ Contents
1
____________________________________________________For Heavenly Mathematics: Astrobox ~ Contents
Issue 8
|
contents
October 2005
Cover Story:
Celestial Navigation
5 History of Celestial Navigation
9 Forefathers of Celestial Navigation
19 Guide to Celestial Navigation
29 Celestial Navigation Instruments
In conversation:
17 Singapore Naval Officer
reviews:
32 Book Reviews
33 IT section
37 Net Reviews
regualrs:
2 Astrobox
3 Heavenly Edit
trivia:
39 Crosswords puzzle
40 Just for a smile
41 Promotions
Trips
to
telescope,
2
years
answer
to
visit
book
polaris,
vouchers,
subscription,
crosswords
puzzle 41
Astro-jokes 40
1
__________________________________________________For Heavenly Mathematics: Astrobox ~ Your Mails
Astrobox
Celestial Letter of the month
Write In
and win a
set of
celestial
navigation
books!
Blow us away with your
feedback and you might stand
a chance to win a range of
Celestial Navigation Books
courtesy of Astrobooks worth
$300. With all these books in
hand, I am sure you will not
face with cases of lost in the
oceans!
Send in your comments by 15
November, and be in the
running to walk away with
these way-finding books!
Other featured mails will walk
away with a session of
Celestial Navigation Lesson
with our professional tutor
from National University of
Singapore. So do keep your
mails coming in!
2
Your September issue was totally heavenly! It gave me a new insight
on why there are different seasons, leap years, solar and lunar eclipse,
etc. After reading your magazine, I am now able to answer enquiries
post by my kids better. But I have one request here. Can you all have
one issue to talk about astronav or celestial navigation? I have an
uncle, who used to be a sailor. His story on how he found his way out
in the ocean just by looking at the stars always fascinated me. I do
hope to know about celestial navigation hence next time I am out in
the seas with my friends I can show off the new gained skill. Stay
heavenly! SKYE LAW
Well, guess what, we are covering on Celestial Navigation this
issue! Now understand this whole issue and start showing off
your skill to all your friends! Also, your ‘accurate prediction’
mail has earned you an US$200 Sextant to assist you in your
Celestial Navigation! Now go and navigate the world!
***********************************************************
**This is so embarrassing to
tell everybody that I have no
idea how eclipse occurred till I
read your last issue. And I
always thought that leap years
occurred due to some silly
rules set by our ancestors!
Never do I know the long
history behind it! *Applause*
Silly Gal
Right… Now you know it!
There are many more
heavenly secrets that you
never knew existed. Do take
up
courses
in
your
educational institute to know
more about the astronomy! I
know of a few existing
courses about astronomy in
NUS. And the lecturer for
those modules is totally
HEAVENLY!
**I never know Singapore
have such good astronomy
magazine! I am sure it is good
educational material for our
kids nowsaday who have no
idea of the UNIVERSE! I will
continue my support for this
magazine! AstroFanatics
Right we are still currently
the ONLY magazine that
touches on astronomy totally.
And we do need your
continual support to keep us
in heavenly business!
_________________________________________For Heavenly Mathematics: Heavenly Edit ~ the Editorial Page
Heavenly edit
Find
your way!
With the great Casino (uh sorry, ‘Integrated Resort) debate on every
one’s lips currently, I am glad to know that we are not losing our way
in life. With the many voices in bid to stop the social adversity from
happening, I do hope that all of us will still have time to watch the
recent full moon!
This issue we bring you to a lesson on how to find your direction just
by looking at the celestial bodies! I know this is totally heavenly!
This skill was acquired by our ancestor centuries ago! With the
development of technology, radio-transmission, Global Positioning
System, this skill is moving towards EXTINCTION!
But this is the skill that will stay
with us in the event of power
failure or transmission failure!
The stars will never play us out!
Find your way!
Yours Heavenly,
jonathan
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For Heavenly Mathematics: History of Celestial Navigation
5
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For Heavenly Mathematics: History of Celestial Navigation
History of Celestial Navigation
Even before history was
recorded, navigation by means
of following rivers, lakes and
oceans has been widely used.
As transportation was of key
importance of contact with the
world, navigation played a vital
role that bridge historical
people closer that allowed the
progress of civilization.
Humans of early years
had learned that one of the
most convenient and efficient
ways of traveling was by water.
This mode of transport allowed
them to ferry goods to and fro
from other countries to engage
in trading and travel.
This gave birth to the
early
mariners
like
the
Sumerians, Cretans, Egyptians,
Phoenicians and Greeks all of
which were located near the
Mediterranean
Sea
(an
advantage was that they had
many ports near the sea, so
they
possessed
high
accessibility of sea travel). The
Scandinavians in northern
Europe also had the means to
conduct sea travel.
Early mariners did not
have established data on
navigation procedures, they
mainly explored by trial and
error. As nautical charts were
not present and armed with
only a list of directions (know
as periplus by the Romans – it
gave details of landmarks,
places of anchorages and water
hazards like reefs and shoals),
they only ventured areas not
very far from the coasts (mostly
onlyskirting
a list ofthe
directions
(known
just
coastlines).
This
as
periplus
by
the
Romans
it
enabled them to know –the
gave details
of landmarks,
positions
of their
ships by
places
of
anchorages
and water
aligning
themselves
to
hazards
like
reefs
and
shoals),
prominent objects on land that
they only
ventured
areasships.
not
could
be seen
from their
very far
thein the
coasts
Usually
theyfrom
traveled
day
(mostly
just
skirting
and came back to shore the
by
coastlines).
This
enabled
them
night.
to know the positions of their
ships by
aligning themselves
to
Navigation
advancement
prominent
objectstook
on land
and
development
placethat
as
could
be
seen
from
their
ships.
the Phoenicians and Greeks
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For Heavenly Mathematics: History of Celestial Navigation
Roman Astronomers
became the first of the
Mediterranean sailors who
dared to venture far from the
coastlines and to sail at night.
Through observations of the
position and motion of the Sun
and the North Star (Polaris),
they were able to determine
directions
and
estimated
distances from the time it took
to cover them. Thus they
created simple charts and knew
a basic form of dead reckoning
(see instruments).
Celestial Navigation
For centuries sailors
have safely guided their ships
across the oceans by means of
observations of the Sun, Moon,
stars and planets. This art of
locating position is known as
celestial navigation or nautical
astronomy. During their long
travels, the sailors observed
that the celestial bodies seemed
to change their paths across the
sky which resulted in them
rising and setting at different
points along the horizon. As
the earth is nearly spherical and
that the positions of the
celestial bodies changes with
respect to time, the sailors were
able to determine the location
of their ship by observing the
celestial bodies carefully.
the use of lodestones and this
resulted in the construction of
the greatest navigation aid of
all time, the magnetic compass.
The Italians later developed a
chart called a portolano during
the 13th century that showed
the outline of the coast and the
inclusion of crosslines which
aided in locating directions
during their voyagers. The
Greeks also contributed two
inventions to measure the
altitudes of celestial bodies
known as the cross-staff and
the astrolabe. They were also
widely used by navigators to
obtain
measurements
to
determine the approximate
latitude of the vessel as well as
the approximate local time.
Early Aids of Navigation
The magnetic properties
of lodestone were known to
men for centuries even before
the Christian Era. However it
was only around the 12th
century that navigators began
These early aids of
navigation
helped
great
explorers such as Christopher
Columbus, and
Ferdinand
in their
However
various voyages.
through
the
Christopher Columbus
and
Astrolabe
6
6
Portolando
advancement and complexity
of
navigations,
these
cross
staff
instruments were not efficient
.
For Heavenly Mathematics: History of Celestial Navigation
St. Hilaire, a Frenchman
improvised
Sumner's
trigonometric
calculations
which were later used to
supplement dead reckoning
(method of correcting for drift
using triangular calculations of
velocity).
and were deemed redundant in
the 18th century as there were
no clocks that could keep the
time well enough to aid the
fixation of longitude readings.
Past to Present: The
Pioneers of Navigation
The development of
navigation was dramatically
spearheaded in the 17th century
by powerhouse countries like
Britain and France. This led to
the
establishments
of
astronomical observatories to
provide almanacs. Similarly,
mapmaking and the invention
of
required
navigational
instruments were also greatly
encouraged.
One very fundamental
instrument that proved to edge
on the developments of
navigation was the brainchild
of two individuals; John
Hadley and Thomas Godfrey
who invented a quadrant that
could calculate accurately the
observations
of
celestial
bodies during the early 18th
century. This instrument was
similar to the sextant that is
commonly used by navigators
today.
`
John Hadley
John
Harrison
in
England produced several
chronometers between 1730
and 1763 which solved the
longstanding problems of
longitudinal readings during
the early navigation years.
Furthermore, Captain James
Cook's voyages of discovery
in the Pacific Ocean at this
time proved the accuracy and
reliability of these navigational
instruments and techniques.
Early in the 19th century,
Nathaniel Bowditch of Salem
devised many methods that
improved the art of navigation.
In 1837, Captain Thomas
Sumner
created
a
trigonometric method (Sumner
lines of position) of obtaining
reference lines from celestial
observations. In 1875, Marcq
The advancement of
navigation has come a long
way and electronic devices
such as radar and loran are
widely used in navigation
today. Most vessels nowadays
use an automatic pilot. The
United States Air Force has
created a satellite system
known as Global Positioning
System (GPS) in 1978 that has
been providing worldwide
coverage for determining
accurately the latitude and
longitude to within about 10
meters. Following the use of
GPS, the Navstar Global
Positioning
System
was
introduced in the 1980s
allowing space personnel to
store the course of the space
vessel in a computer system,
which helps to verify the
location and speed of the
spacecraft. Multiple computer
systems are fast becoming the
norm in managing navigations.
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For Heavenly Mathematics: Forefathers of Celestial Navigation
Forefathers of Celestial Navigation
Early documented accounts provided proof that
exploration by sea was most abundant in ancient
civilizations. This was due to religious beliefs, conquest and
the necessity of trade routes establishments as well as the
search for riches.
th
The 14 century opened
a pathway to the age of
exploration which was then
recorded in history books.
However exploration between
Europe and Asia began much
earlier as travels between
Greece and India, for instance,
was frequent during the reign
of Alexander the Great as his
vast empire included territories
of both countries. China’s Han
Dynasty as well as the Roman
Empire also had regular trade
relations. Early explorers had
some idea of their final
destination before they set sail.
Although they were searching
for a specific land or route,
they were surprised at what
they discovered most of the
time.
The captain of the ship is
heavily funded by wealthy
merchants of those times and
often
required
a
huge
manpower before voyaging out
to sea. Most voyages during the
14th century were made in the
name of the royal ruler of a
particular
government.
Ironically, the crewmen on
these long and dangerous
voyages were not the most
experienced seamen. They
were mostly needed in aid of
manning the ship’s sails and to
allow for attrition due to illness
and death. The ships that the
royal rulers gave were rarely
new but the captain took what
was given. The captains were
usually inexperienced seaman,
whose
daily
jobs
were
merchants,
adventurers,
soldiers or political figures.
The desire for wealth or
political status was often the
reason in participating on these
dangerous voyages. Under his
command was the pilot also
known as the first mate who
were mainly in charge of the
ships navigations and the crew
that man sails and repairs
during the voyages at sea.
Food supplies were
often limited, consisting of
only pickled or dried meat and
ship's biscuits which were
made from flour with a little
water. Weevils would usually
be found in these biscuits at the
end of the voyages. Their
staple diet also included cheese,
onions, dried beans, salted fish
and recently caught fresh fish.
The absence of fresh fruits and
vegetables caused the sailors to
suffer from a fatal condition
called scurvy due to the lack of
vitamin C. Another major
problem was water supply as
Drawings of Mongols on expedition
fresh water was hard to contain
in barrels and wine turned sour
easily.
The Beginning: Mongols and
Marco Polo
The 4th and 5th centuries
saw barbarians that existed in
large numbers ruled over the
plains of China, India as well
as Europe, thus jeopardizing
the links between these
countries. Furthermore, the
introduction of Islam within
North Africa, the Eastern
Mediterranean, Spain and
France led to the break off of
trade routes as there were
hostilities between Christians
and Muslims.
By the 13th century,
nomadic Mongols had captured
most of Eurasia, Korea, and
Hungary thus opening the
doors that enabled Europeans
to travel to China safely. In the
early 1260s, two brothers from
the city of Venice, Niccolo
Polo (father of Marco Polo)
and Maffeo Polo (uncle of
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For Heavenly Mathematics: Forefathers of Celestial Navigation
Throne ruled the entire South
Pacific and the Indian Ocean
During his reign, numerous
gifts and tributes for the
Emperor
were
collected
throughout a territorial region
that spread over Korea and
Japan to the Eastern coast of
Africa. Admiral Zheng He
began his first of seven
voyages in 1405. The purpose
of his first voyage was to hunt
for the former dethroned
emperor who had escaped. A
fleet of 62 large junks and 255
smaller ships were commanded
by
Admiral
Zheng
He
recaptured
the
deposed,
emperor and also manage to
defeat a large pirate fleet that
had been terrorising the islands
near Sumatra region.
Route taken by Marco Polo
Marco Polo) embarked on their
first journey to China by land
in which they met the Mongol
Emperor, Kublai Khan and
eventually returned to Venice.
In 1271, the Polos made
another journey extending to
about four years, this time
bringing along the young
Marco Polo with them. Kublai
Khan was deeply impressed
with his European visitors that
led them to stay for 17 years
and returned to Europe only in
1292. The route across Central
Asia was lost when the Mongol
Empire fell. Marco Polo's
accounts of travel highly
inspired many Europeans and
thus they were determined
create once again routes of
10
their own to the East in search
of wealth.
Admiral Zheng He
By the 1st century,
many historians claimed that
the
Chinese
had
some
knowledge of the winds and
currents of the Pacific. When
weather prevented the Chinese
from navigating by the sky,
magnetized needles were used
instead to guide them. As the
rocking ship had no level
surface the sailors floated the
needle in a shallow bowl of
water which gave rise to the
modern day instrument, the
compass. Between 1405 and
1433, Emperor Zhu Di's
Treasure Fleet of the Dragon
Over a span of 28 years,
Admiral Zheng He increased
China's trading territory to 37
countries from the Vietnam
coast to the Persian Gulf, the
Red Sea, and eastern Africa.
When Admiral Zheng He died
around 1435, China's economic
domination in the South Pacific
came to and end.
Christopher Columbus
(b. 1451 - d. 1506)
Born in Genoa, Italy, in
1451, young Columbus first
went to sea by the age of 14
and eventually settled Portugal
and married a woman of noble
background. Columbus and his
young son, Diego moved to
Spain in 1485 after his wife’s
death. Columbus knew the
For Heavenly Mathematics: Forefathers of Celestial Navigation
world was round and explained
that as the earth was a sphere,
thus a ship would eventually
reach the Far East traveling in
the opposite direction which
led him to establish trade routes
to Asia.
Drawing of Columbus
Europeans in the 15th
century were not aware of the
existence of the South and
North American continents
thus maps did not portray an
accurate picture and the Pacific
Ocean
remain
unknown.
Columbus seek grant from the
Portuguese king and the
Spanish monarchs to explore
possible trade routes to the
West but was repeatedly turned
down. However after a decade,
Columbus managed to gain
support from King Ferdinand
and Queen Isabella and
promised to bring back gold,
spices and silks from the Far
East. He was also keen on
spreading Christianity thus
leading him on a expedition to
China. In return, Columbus
attained the hereditary title
"admiral of the ocean seas" and
became governor of all the
lands he discovered. This was
done in a series of four voyages.
Before
celestial
navigation was created, sailors
navigated by deduced (dead)
reckoning. This method was
used by Columbus in his
voyages and most other sailors
of his era. Dead reckoning
enables a navigator to plot the
location of the ship at any
given time. As a result, the
journey is already planned out
entirety before the start of the
voyage. In dead reckoning, the
navigator locates his position
by measuring the course and
distance that he has sailed from
a known point which is
recorded down on a chart. A
pin would be used to mark any
new position. At the end of
each day, the ending position
would be the starting point for
the next day's course and
distance measurement.
Quadrant, an equipment used
by Columbus
The most important tool
that Columbus used during his
voyages was the quadrant. This
was a metal plate in the shape
of a quarter-circle. From the
center of the circle hung a
weight on a string that crossed
the opposite edge of the circle.
Astrolabe used by Columbus
In addition to the
quadrant, an astrolabe was also
used by Columbus in his first
voyage. The astrolabe made of
metal, was a complete circle
and had a moving arm or
alidade that he would sight
along to find the star's altitude.
Columbus used a sandglass to
measure time and a nocturnal
was also used to determine
when midnight would be which
tells the time of the night by the
rotation of stars around the
celestial pole.
Columbus embarked on
his first voyage with three ships,
the Niña, the Pinta and the
Santa Maria. The ship Santa
Maria was nicknamed La
Gallega as she was big and
slow, designed mainly for
storing cargo and not for
exploration The Santa Maria
had three masts (fore, main,
and mizzen) with one large sail
on each mast. The foresail and
mainsail were square while the
sail on the mizzen or rear mast
was a triangular in shape also
known as a lateen. The ship
also carried a small square sail
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For Heavenly Mathematics: Forefathers of Celestial Navigation
on the bowsprit and had a small
topsail on the mainmast above
the mainsail. The Pinta,
captained by Martín Alonso
Pinzón was a leading mariner
from the town of Moguer in
Andalucia. Pinta was a caravel
which is smaller, lighter and
faster than the bulky Santa
Maria. The Niña was the
smallest of the three and it was
captained by Vicente Añes
Pinzón, brother of Martín. The
Niña was another caravel and
may have carried four masts
that include a small countermizzen at the stern equipped
with another lateen sail, thus
making the Niña the best of the
three ships at sailing upwind.
vegetables on board. Feeding
his crew onions and pickled
cabbage every day also kept
other diseases at bay. On top of
this, he made sure that his crew
bathe everyday, wash their
dirty clothes and to also air
their bedding.
James Cook (b. 1728 - d. 1779)
James Cook
James Cook was born
on October 27 in 1728 in
Marton
in
Cleveland,
Yorkshire, England to a farmer
of Scottish decent. Since young,
he was taught by a family in
sea navigations. In 1755, he
joined Great Britain's Royal
Navy and proved himself an
expert navigator. Just after
making officer rank, Lieutenant
Cook was chosen by the Royal
Society of London and made
his first journey to observe the
eclipse of the planet Venus as
well as determining the
location a southern continent in
1768. Cook was one of the first
sea captains to discover the
cure
for
scurvy.
Being
determined to keep his crew
healthy, he ensured that there
were abundant fresh fruits and
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Cook started his first
voyage on August 25 in 1768.
Accompanied by 94 crewmen
and scientist, he departed from
England aboard the Endeavour.
On April 11 in 1769, Cook
arrived and embarked on the
shores of Tahiti, seven weeks
earlier than expected. After
viewing the eclipse of Venus
between the earth and sun for
several weeks, Cook opened a
sealed envelope which he
carried from the Royal Navy.
His mission was to locate the
rumoured southern continent
and claim it for England. Early
mapmakers in the 1570s
assumed there were two major
continents located at the end of
each of the earth's poles. Since
the continents had not yet been
found, the Royal Navy
entrusted Cook with the task of
finding the southern continent
if it existed. On July 13, the
Endeavour left Tahiti and
headed southwest in search of
the southern continent.
Upon reaching New
Zealand on October 6, Cook
discovered the native Maori
people. They were hostile and
Cook had no choice but to fire
on them. The Endeavour
explored New Zealand for a
few
months
and
Cook
concluded that it was not part
of the great southern continent.
Cook would later on explore
and be the first to document the
location of Australia. After
months of studying the
coastlines, he concluded that
this continent was not the great
southern continent that the
Royal Navy wanted him to find.
The Endeavour continued to
journey to Java in the East
Indies. It was here that his crew
became seriously ill with
diseases like malaria and
dysentery. Cook effort to keep
his man healthy was futile as
they were overwhelmed by
these diseases. 30 of his crew
died and this forced Cook to
sign on new crew in South
Africa for his return leg to
England.
Cook's second voyage
began on July in 1772 from
Plymouth, England with two
ships, the Resolution and the
Adventure. His orders were to
find the southern continent. His
For Heavenly Mathematics: Forefathers of Celestial Navigation
plan of searching for the
continent by circumnavigating
the globe and this led him to
the discovery of the continent.
Cook discovered more islands
in the South Pacific during his
second voyage. After reaching
the Antarctic Circle in January
1774, Cook had sailed farther
south than any other explorer.
On his final voyage on
July in 1776, Cook, with a
crew strength of 112, he
boarded the Resolution once
again with a sister ship, the
Discovery. The objective of his
third voyage was to find the
fabled Northwest Passage by
taking a route from the Pacific
side. Cook visited some islands
in the Pacific as well as New
Zealand and Tahiti.
On January 18 in 1778,
Cook saw the Hawaiian Islands
for the first time and named it
after his friend, the Earl of
Sandwhich. It was known as
the Sandwich Islands. The
natives there were very
hospitable as they thought that
Cook was a god and that his
men were supernatural beings.
Cook observed that the people
in the Pacific had a common
language with similar customs
and deduced that these
Polynesians had dispersed over
the many islands in the Pacific.
Things turned ugly as Cook
returned again to the islands the
following year. The natives
were then unhappy about the
presence of the Europeans.
Cook decided to leave the
islands but was forced to return
as they encountered a storm
which damaged the ships. This
angered the natives even more
and they stole one of the ship’s
boats. Cook took things into his
hands and captured the
Hawaiian chief as hostage. As
Cook was heading back to his
ship with his hostage, the angry
natives surrounded him and his
men. Cook then signaled his
boats off shore for backup but
he was stabbed in the back by
one of the natives and was
subsequently killed by the
dozens
of
natives
that
continued to attack him.
John Harrison
(b. 1693 – d. 1776)
Harrison was born in
Foulby, near Wakefield, in
Yorkshire in 1693. When he
was a young boy, his family
moved
to
Barrow,
in
Lincolnshire. He followed his
father’s footsteps and became a
carpenter. In 1713, he built his
first longcase clock with a
mechanism that was made
entirely of wood at a young age
of 20. Three of Harrison's early
wooden clocks are still present
today and are located at the
Worshipful
Company
of
Clockmakers' Collection in
Guildhall in London, the
Science Museum and Nostell
Priory in Yorkshire.
His first wife, Elizabeth
died just eight years after their
marriage in 1718 and took on a
second wife who was also
named Elizabeth. Working
with with his younger brother
James, they came up with a
revolutionary turret clock that
required no lubrication. This
was a breakthrough as clocks in
the 18th century had poor oil
lubrication that caused them to
fail as Harrison designed a
clock which did not need it. It
was this radical thinking that
was deemed important in
tackling the problem of
designing a marine timekeeper
later on.
In his later years and
through
numerals
tries,
Harrison had devised a portable
clock which kept time to the
same accuracy as precision
regulators.
The
longitude
problem that bothered all
mariners at that time was
eventually solved by Harrison
as he took on the scientific and
academic establishment of his
time and won the longitude
prize through extraordinary
mechanical insight, talent and
determination.
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_________________________________________For Heavenly Mathematics: Place To Go ~ Zheng He Exhibition
Place To Go
Duration: 13 Aug 2005 – 10 Feb 2006
Venue: National Library, Level 10
Opening Hours: 10 am – 9 pm daily
Closed on Public Holidays
Admission: Free
Organiser: National Library Board
The Zheng He & Maritime Asia Exhibition, held
at the National Library (Level 10) Victoria
Street, will run for 6 months from 13 August
2005 to 10 February 2006. It aims to enhance
public's interest in learning about Zheng He
and his influence on the maritime history of
Southeast Asia.
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_________________________________________For Heavenly Mathematics: Place To Go ~ Zheng He Exhibition
Why should we go ?
Admiral Zheng He commanded seven great expeditions to more than
30 countries between 1405 and 1433. With the available technology
then, it is an amazing feat to be able to find his way from China to
Africa and back. He made used mostly of Celestial Navigation along
with some simple navigation equipments. In this exhibition, they
showcase some of the equipments he used to navigate.
What to see there ?
Qianxingban is used by Admiral Zheng He to determine the latitude
using the position of constellations. It is a measuring board made up
of 12 pieces of square wood. Navigators aligned the qianxingban
with the horizon and then used the length of their arms to calculate
the position of marker stars. Degrees were measured with finger
widths.
Who should go ?
Anybody who is interested in early navigation expedition! For
readers who have know so much of Celestial Navigation, it will be
good for them to know more of one the greatest forefather of the
Celestial Navigation. They will be able to get more in depth
knowledge on how Celestial Navigation was put into good use during
his expedition.
When to go ?
Date: Saturday 22 October 2005. Time: 3.00 –5.00pm.
Why? Because there is a discussion on “What does it mean to be an
Explorer in Singapore?” The panel discussion includes Stefen Chow
from the NUS Mountaineers who recently returned from Everest,
Wilfred Tok who has climbed the highest peak in the Americas,
Anaconda; and Dr. Chan Yew Wing, who has led and coordinated
numerous expeditions to remote areas. Ask them how they navigate
using the modern technology and whether they have used any
Celestial Navigation during their exploration.
15
_____________________________________For Heavenly Mathematics:In Conversation: Singapore Naval Officer
17
_____________________________________For Heavenly Mathematics:In Conversation: Singapore Naval Officer
In conversation
Singapore naval officer, 2LT Jerry Lui
In this issue, we
interview a naval
officer from Republic
Singapore
Navy
regarding
celestial
navigation and his
experiences. Celestial
navigation is one of
the most widely used
forms of navigation
in the olden times.
Today, it has been
replaced by many
advance technologies
such
as
Global
Positioning
System
(GPS).
To your knowledge, what are
the types of navigation used in
the Republic Singapore Navy
(RSN)?
Oh. There are a few types of
navigation methods that we
employ. From my knowledge,
we use coastal navigation,
astro-navigation,
also
otherwise known as celestial
navigation, pilotage and ocean
navigation. On top of that, we
also use GPS to find out our
current location if we are out at
sea.
As celestial navigation is the
topic of the month for our
magazine, we would like to
know more about the extent to
which celestial navigation is
used in RSN.
Actually, with all the advance
technologies on board the ship,
we do not really use celestial
navigation often. The only
time in which we usually
employ celestial navigation is
either during training of new
naval officers or when all
other
modern
navigation
instruments fails and celestial
navigation is deployed as a last
resort.
How was the learning process
like?
It was really really tough
17
_____________________________________For Heavenly Mathematics:In Conversation: Singapore Naval Officer
(Laughs) we really had to
study very hard to pass the
tests as it was rather hard to
grasp the concepts and to
differentiate the stars. Actually
I made so many mistakes
while I was learning it, but we
all learn from mistakes don’t
we?
Oh I see. I understand that in
celestial navigation, stars are
used as reference points. Since
it is so difficult to differentiate
the stars from one another, is
there any software that is used
to calculate the stars that will
be seen on any particular day?
Oh yes! Definitely. There is
this software called PC
Sightmaster that we use. It is
actually used quite widely on
board cargo ships etc. This
software is really accurate. All
we have to do is to key in
certain values such as time and
date and place, it will calculate
and actually churn out a list of
stars that will be visible at the
specific time and date.
18
You previously mentioned that
one of the difficulties in
celestial navigation is the
spotting of specific stars in the
night sky. So are there any
other difficulties or barriers
faced while applying celestial
navigation?
Celestial navigation is a very
tedious process as we need to
refer to many charts and books
at the same time just to do our
calculations. Thus it takes
quite some time just to get our
calculations done. Not only
that, locating of the predicted
stars as stated by the software
PC Sightmaster is not easy as
the stars may be too dim to be
seen by the naked eye or the
sky may be too cloudy. In
addition to that, if the waters
are too rough, it makes the
measuring of the declination of
the stars really difficult. Hence,
celestial navigation is not as
easy as it seems.
Personally, what is your
opinion of celestial navigation?
Although celestial navigation
is not easy to master, however
I find it really interesting as an
ancient art of sea-faring
navigation. I feel that with
proper training and sufficient
practice, it is the most accurate
form of navigation known to
man. It is pretty amazing how
celestial navigation is still
being used in this time and
date after enduring through
decades
of
technological
advances. In some parts of the
world today, especially Indian
Navy and Royal Navy, it is
still being used frequently as a
form of primary navigation.
Last but not least, is there any
memorable moments that
occurred while using celestial
navigation that you would like
to share with our readers?
Certainly! There was this
particular training session on
board ship in the middle of the
South China Sea where we had
to calculate the ship’s position
using celestial navigation.
After much calculation, I
finally got the coordinates of
the ship’s position. To my
horror, the coordinates was
actually a point in mainland
China! (Chuckles) That really
proved to me that I should
buck up.
(Laughs) Thank you for you
time, Sir. We certainly gained
many insights.
For Heavenly Mathematics: Cover Story: Guide to Celestial Navigation
Guide to Celestial Navigation
How did sailors manage to navigate themselves in a vast
featureless ocean centuries ago? Sophiscated equipments
like Global Positioning System (GPS) and radars were all
not invented then. Without this modern electronic
equipment, sailors still managed to make their way across
the ocean safely.
Our forefathers had great
knowledge on the celestial. They
were able to find their way n
direction through the position of
the celestial bodies. Skilled
navigators were recruited on
board ships during ancient
voyages to help ships find their
way out in the sea. They used
angular measurements between
the horizon and a common
celestial object. During the day,
when stars cannot be seen, the
Sun was most often used. At
night, the Moon, planets or one
of the navigational stars were
Able to find their way and
direction through the
position of the celestial
bodies.
_____________________
used. These celestial bodies are
constantly
changing
their
positions with respect to
observers.
Hence,
nautical
almanacs
were
important
references for the sailors.
19
For Heavenly Mathematics: Cover Story: Guide to Celestial Navigation
The Nautical Almanac
The Nautical Almanac is a publication describing the positions and movements of celestial bodies that are directly
overhead to the Earth’s surface at any hour of the day. The Sun, Moon and planets 'move' independently and
hence are specified separately. However, for the stars, only Aries is specified, with the other stars having a set
angular distance from that. The 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.
20
For Heavenly Mathematics: Cover Story: Guide to Celestial Navigation
How Celestial Navigation Works
The fundamentals of celestial navigation are as follows.
Angles
The most common type
of number used by a celestial
navigator is angles, which can
be used to describe the position
of the celestial bodies and
points on the surface of the
earth. A common instrument
used to measure angles is the
sextant. Angles are usually
measured in degrees, minutes
and seconds. The complete
circumference has 360 degrees
(360°), with each degree
equivalent to 60 minutes. The
seconds of arc are not used in
the celestial navigation, because
the sextant is not precise
enough to measure them. The
smallest unit of angle used by
navigators is the tenth of minute,
until
recently,
with
the
emergence of GPS devices, the
1/100 of minute is added.
To
make
the
conversions between angles n
distances easier, a unit called
the nautical mile, which is
equivalent to 1852 m is selected.
One nautical mile corresponds
to an arc of one minute on the
surface of earth. Hence, angles
on the surface of the Earth are
equivalent
to
distances.
However, an exception is the
minute of longitude, which is
equivalent to one mile only near
the Earth’s Equator. Another
important
equivalence
is
between time and degrees of
longitude. Since the earth goes
one complete turn (360°) in 24
hours, each hour corresponds to
15° of longitude or 900 nautical
miles (NM).
21
For Heavenly Mathematics: Cover Story: Guide to Celestial Navigation
The Earth and the Celestial Sphere.
Imagine that the Earth is the center of the universe, surrounded by a larger outer
circle, centered at the same point. This larger outer circle is named the Celestial
Sphere. The stars are fixed on the Celestial Sphere, as if they were painted in its
internal surface.
We use a system of latitude and longitude to specify a position on the Earth’s
surface. Latitude is the angle measured from the Equator in the North-South
direction. Longitude is the angle in the Pole between the Meridian of
Greenwich and that of the considered position.
A similar system called the celestial coordinate system is used for
the Celestial Sphere. The angle analogous to the latitude in the
celestial sphere is declination and its is measured in the plane
North-South, from the Celestial Equator. The analog to the
longitude is named Right Ascension or RA, which is measured
from an arbitrary Meridian, called the Vernal Equinox.
Apparent movement of the stars
The stars have nearly
fixed positions in the Celestial
Sphere. The Sun, Moon and
planets move around during the
year, but when compared to their
apparent movement due to the
rotation of the Earth, their
movement is slow. Consider for
now that the celestial objects
(stars, planets, Sun and Moon)
are fixed in the Celestial Sphere.
22
Using
the
Celestial
Sphere model, imagine the Earth
is stationary and the celestial
sphere is turning around it,
completing a turn every 24 hours.
The Earth's and Celestial
Sphere's axes of rotation are in
the same line. Both equators are,
therefore, in the same plane. The
stars are fixed on the celestial
sphere and turn around the earth.
The Celestial poles, being in the
axis of rotation, remain fixed in
the sky. Therefore, a star located
near a Celestial pole will appear
to be stationary in the sky.
Hence, Polaris, a star that is
near the North Celestial Pole (its
declination is 89°05' N) is
always in the north direction, a
fact known by every navigator.
Unfortunately
there's
no
corresponding bright star near
the South Celestial Pole.
For Heavenly Mathematics: Cover Story: Guide to Celestial Navigation
Finding the Earth position by observing the stars
Consider a line connecting the center of a star and the center of the Earth.
The point where this line crosses the surface of the Earth is the
Geographical Position (GP) of this star. An observer positioned in the GP
of a star will see it directly vertically overhead.
Because stars move with the celestial sphere, their GPs also move. The
GPs of stars move quickly along the Earth’s surface, for example, the
Sun's GP travels a mile every four seconds. However, the GPs of other
stars, closer to the celestial poles, move more slowly, for example, Polaris.
Since both the Earth’s equator
and Celestial equator are in the
same plane, the latitude of the
GP is equal to the declination of
the star. The longitude of the GP
is known as Greenwich Hour
Angle (GHA) in a reference to
the correspondence between
hours and longitude.
With the use of a Nautical
Almanac, the GP of a star (its
GHA and declination) in any
moment of time can be
determined. Of great importance
is the exact time of the
observation. As we have seen, 4
seconds may correspond to one
mile in the GP of a star. Hence,
Fig. 4- Geographical Position of a Star
the importance of having a
watch or chronometer with the
correct time for the celestial
navigation.
Another important point is the Zenith, which is the point in the celestial sphere located in the
vertical, over the head of the navigator. The line that connects the Zenith and the center of the
Earth crosses the surface in the position of the navigator. Hence, the following correspondence
between points:
Surface of Earth
Geographical Position of a star
Position of the navigator
Celestial Sphere
Center of the star
Zenith
In this figure, the GP of the star is represented by X and the Zenith
by Z. The distance XZ, from the GP of the star to the point Z of the
navigator is called Zenith Distance and it can be expressed in miles
or degrees, since it is an arc on the surface of the Earth.
23
For Heavenly Mathematics: Cover Story: Guide to Celestial Navigation
The angle that XZ makes with the True North (i.e. the "bearing" of the
star) is called Azimuth (Az ).
The stars are at a great distance from the earth hence their light rays
that reach the Earth are parallel.
Therefore, as illustrated, the distance XZ, measured as an angle, is
equal to the angle that the navigator observes between the star
and the vertical.
However, it is difficult to determine the Zenith
distance precisely due to surrounding factors and
environment, for instance it is difficult to find
the vertical direction in a rocking boat. It is,
however, a lot easier to measure the angle
between the star and the horizon, also known as
the altitude (H) of the star. The altitude of a star
is taken with the sextant held in the vertical
plane, measuring the angle between the horizon
and the star.
The Zenith Distance and the GP of a star, however, are not enough
to determine our position. With this data we can only say that our
position is in a big circle, with the center in the GP of the star and
radius equal to the Zenith Distance. This is known as the Circle of
Position. Point X in the figure is the GP of a star.
Any observer located on this
circle will see the star at the
24
same altitude, but different
azimuths. Suppose the navigator
observes the star with an altitude
of 75°, the Zenith Distance
For Heavenly Mathematics: Cover Story: Guide to Celestial Navigation
would be 90°-75° = 25°. To
determine this distance in miles,
multiply by 60, since one degree
is equivalent to 60 nautical miles
(NM). Hence, the Zenith
Distance or the radius of our
circle is 1500 NM.
If the exact direction where the
GP of the star is known, it would
establish where in the circle the
navigator is. Unfortunately, the
compass cannot be used for this
purpose, as it is not precise
enough, with an error of just 3°,
common when reading a
compass, corresponding to 78
miles of error, which is not
acceptable.
the expected altitude for the
star at a given time can be
calculated using the Nautical
Almanac.
Hence, the way to find the
position is to draw two or more
circles for two or more celestial
bodies and see where they
intercept each other. However,
drawing these circles would
require large charts! This
problem can be solved by
making a guess at our position.
Using this assumed position,
This Calculated Altitude can
then be compared with the
Observed Altitude (the actual
altitude, measured with the
sextant). The difference is the
error of our assumed position
(also known as Delta ) in the
direction of the star.
The Geographical Position of a star,
normally being thousands of miles from
our position, causes the circle of position
to very large. Hence, the small piece that
interests us - the one near our position may be considered a straight line,
orthogonal to the Azimuth of the star.
This line is called the Line of Position or
LOP.
From the
star at a
assumed
position
measured altitude of a
certain time and our
position, a line of
can be drawn. The
navigator’s actual position is
somewhere along this line. To
determine this point, another line
for another star can be drawn.
The point were they intercept
each other is the navigator’s
position
or
Astronomical
Position.
Normally, for better accuracy, the navigator
should repeat this procedure for yet another star.
Due to minor imprecisions during the
measurement, the three lines will probably not
intercept in a single point, resulting in a small
triangle. The navigator’s position is within this
triangle, hence, the smaller the triangle, the more
accurate. It is usually assumed that the
Astronomical Position is in the center of the
triangle.
In the figure above, we can see how three circles of position determine 3 Lines of Position r1, r2 and r3.
25
For Heavenly Mathematics: Cover Story: Guide to Celestial Navigation
In traditional celestial navigation, the determination of a Line of Position
involves the computation of the GP of the star (GHA and declination) using
the Nautical Almanac and the solution of the Position Triangle PXZ,
which is formed by the terrestrial pole (P), the GP of the star (X) and the
assumed position of the navigator (Z).
This solution yields the Calculated Altitude and the Azimuth of the star,
with the help of tables. The difference, in minutes of degree, between the
calculated altitude and the altitude of the star measured with the sextant is
the distance between the line of position and our assumed position - the
error Delta of our estimate. This can be away or towards the star.
The GP of a star and the triangle of Position are solved by computerized formulas in Navigator software. All that
is required is the sextant reading (date, time and altitude), name of the star and the assumed position (latitude and
longitude).
Determination of the Astronomical Position
It is not necessary to draw the lines of position when using Navigator software. Instead, its can be done using
pencil and paper:
1.
Plot your assumed position.
2.
Using a parallel ruler, draw a line passing on the assumed position, in the direction of the Azimuth
of the star.
3.
Over this line, measure the error Delta of the estimate - in the direction of the star or contrary to it
- according to the sign of the Delta.
4.
Draw the line of position, orthogonal to the Azimuth, at this point.
Detailed Nautical Charts are usually only available for places near the shore. When in high seas, charts with the
adequate scale to plot the navigator’s position are not available. instead, special plotting paper is used instead.
When navigating using Navigator software, the computer determines the altitude lines interceptions and
calculates the astronomical position. A simplified map is drawn, showing the parallels, meridians, lines of altitude
and the astronomical position.
Altitude corrections
But before we can use this apparent reading in our calculations, some corrections must be made, in order to obtain
the true observed altitude. These corrections are:
1) the height of the eye
2) semi diameter of the body (only for Sun and Moon)
26
For Heavenly Mathematics: Cover Story: Guide to Celestial Navigation
3) instrumental error
4) atmospheric refraction
5) parallax (only for the Moon).
Most of these corrections depend only on the selected celestial object and altitude, hence they are performed
automatically by Navigator software. The only information required by the program is the height of the eye
(Dip) and the instrumental error. The application of these corrections to the instrumental altitude give the
corrected altitude, the one used in calculations.
An observer located in a high place will see a star with an altitude bigger than
that at sea level, in the same location. This error is called height of the eye (Dip).
Due to a small misalignment of the scale of the sextant, there is a sextant
index error (IE). To read the index error, adjust the scale to 0°00.0' and
point towards the horizon. Turn the drum until the horizon forms a single
line. Then the index error can be read.
The index error can be positive or negative. The index correction has
opposite signal (i.e. must be subtracted from altitude if positive and viceversa).
Since the navigator is not in the Earth's center, but at its surface, the
apparent object position is below the true geocentric position, resulting
in parallax error.
Parallax is only meaningful for the Moon. Since other celestial bodies
are so far, their parallax is very small.
Nautical Almanac data is tabulated for the centers of the celestial objects.
However, it is easier to measure the altitude of the lower part of the body, for
the Sun and the Moon, as illustrated. This is known as the lower limb. A
correction, called semi diameter must also be applied in order to obtain the
altitude of the center of the body. Sometimes, the upper limb is also used.
27
For Heavenly Mathematics: Cover Story: Guide to Celestial Navigation
Other Methods of Celestial Navigation
Lunar Distance
This older method was refined in
the 18th century. Although it is
an old method, it is a sound one,
and can be used when a
timepiece is not available or its
accuracy is suspected during a
long sea voyage. The navigator
precisely measures the angle
between the Moon and a body
like the Sun or a selected group
of stars lying along the ecliptic.
That angle, after it is corrected
for various errors, is the same at
any place on the surface of the
earth, facing the moon at a
unique instant of time. The
navigator could search through
the almanac to find the angle
measured, and thus know the
time
at
Greenwich.
The
calculation in minutes can be
done using simple calculators,
allowing the navigator to use
other acceptable celestial bodies
than the old nine listed in the
almanac. Knowing Greenwich
Time, the navigator can work
out longitude.
half-second per day. If it is worn
constantly, keeping it near body
heat, its rate of drift can be
measured with the radio, and by
compensating for this drift, a
navigator can keep time to better
than a second per month.
Traditionally, a navigator set his
chronometer from his sextant, at
a geographic marker surveyed
by a professional astronomer.
This is now a rare skill, and
most harbor masters cannot
locate their harbor's marker.
Traditionally,
three
chronometers were kept in
gimbals in a dry room near the
center of the ship. They were
used to set a watch for the actual
sight, so that no chronometers
were ever risked to the wind and
salt water on deck. Winding the
chronometers was a crucial duty
of the navigator, logged as
"chron. wound." for checking by
line officers. Navigators also set
the ship's clocks and calender.
The Use of Time
The considerably more popular
method was (and is) to use an
accurate timepiece to directly
indicate the time of a sextant
sight. The need for accurate
navigation
led
to
the
development of progressively
more accurate chronometers in
the 18th century. Time is
measured with a chronometer, a
quartz watch, or a short wave
radio broadcast from an atomic
clock. A quartz wristwatch
normally keeps time within a
Modern Celestial Navigation
Modern celestial navigation
methods, developed in the
19th century, allow navigators
to measure latitude as part of a
fix, by sighting 2 or 3 bodies
within a few minutes of each
other. When the celestial line
of position concept was
discovered in 1837, leading to
the modern mathematical
28
"intercept
method"
of
reducing sextant sights later in
the 19th century, navigators
were finally able to obtain
both latitude and longitude at
once from their celestial
observations, giving them a
position "fix", rather than
viewing these two properties
as separate entities. At the turn
of the 21st century, advanced
electronic
and
computer
systems had evolved enabling
navigators to obtain automated
celestial sight fixes. These rare
systems are regarded mainly as
potential backups to the more
reliable satellite positioning
systems, but could play a role
in future space travel.
For Heavenly Mathematics: Instruments for Celestial Navigation
Instruments for Celestial Navigation
Before there were Global Positioning System and
Radio-transmission, these are the equipment that kept sailors
from being lost in the open sea. We will take a look at them
and try to find our way into using them!
ASTROLABE: used to measured
the altitude of the sun or stars,
later replaced by the sextant.
To determine latitude with an
astrolabe, first a sailor would identify
the constellations visible in the sky
nearest the sun at daybreak. Then at
noon, when the sun is at its highest
point, the sailor would measure the
degree difference between the sun and
the horizon with the astrolabe's
movable needle. Then with the help of
a chart like Abraham Zacuto's Rules
for the Astrolabe published in 1473,
our sailor would use both the
constallations and the sun's height in
the sky to determine latitude.
SEXTANTS are instruments used by mariners to measure
the angular distance between two objects (like the sun and
the horizon).
They are more accurate than astrolabes by having a telescope,
mirrors, and a graduated arm. The mirrors allow seeing both objects
simultaneously. They also surpass the cross-staff and the quadrant by
being able to measure angles up to 120 degrees (the quadrant only
reads up to 60).
QUADRANTS used for measuring the angle between
the horizon and the sun (or other celestial body).
Invented in 1731, it had an arc that measured 1/8th of a circle
plus two mirrors that allowed the sun or another star and the
horizon to be viewed simultaneously. Quadrant can measure
angles up to 90 degrees, for example, from the horizon to an
object directly over head. This angle is used to determine
latitude. The quadrant is the precursor to the sextant.
29
For Heavenly Mathematics: Instruments for Celestial Navigation
COMPASS, do I need to explain further?
The astrolabe or sextant can help you find your latitude, but to
determine the direction of your future course, the compass is a
faithful friend. It was first used in marine navigation starting
in the 1400's.
CHRONOMETER solved the great problem of finding
longitude.
The first seaworthy chronometers were created by an 18th-Century
Englishman, John Harrison.
GLOBAL POSITIONING SYSTEM Watch allows you to
find the exact position you are by just pressing a button.
It comes with electronic compass, thermometer and barometer all in
one watch!
STELLARSCOPE is a compact, handheld, easy-to-use
educational guide to the stars and constellations.
View the night sky for any date and time in either the Northern or
Southern hemispheres by simply setting the time and date dials on
the scope, point the scope towards a light source, and you will see
the stars and constellations appearing in the sky on that night.
30
____________________________________________________For Heavenly Mathematics: Astro-Book Review
Astro-Book review
We have done a few review on Celestial Navigation related books.
How this will help when you are thinking of investing in one!
the complete on-board
Celestial Navigator
by George C. Bennett
The ancient skill of celestial navigation has reliably guided seafarers
for centuries and is still a source of pride and respect among mariners.
In this era of electronic navigation, it remains the perfect backup
system, enabling you to determine your position if the GPS
malfunctions or your boat loses electrical power.
Specifically designed for the novice or rusty celestial navigator, The
Complete On-Board Celestial Navigator replaces $300 worth of
guides and almanacs traditionally required by celestial navigators,
and includes a star finder; a five-year nautical almanac (2003 - 2007)
for determining precise star, sun, moon, or planet locations at the
time of sighting; and sight reduction tables for crunching the numbers
and producing a fix anywhere in the world.
"The only complete self-contained work available. When your
electronic navigation fails, 'steering by the stars' will guide you safely
to your destination."--Sydney Afloat (Australia)
Norie's nautical tables
by A. Glance
This famous set of mathematical tables has been modernised and this
1983 edition contains a fully revised list of Ports of the World and
their geographical positions. This book is so reliable that most Naval
Officers use them to do their Celestial Navigation. Definitely a musthave for everyone who wants to start on learning Celestial Navigation.
32
For Heavenly Mathematics: IT Section The Navigator Software
I T Section:
The Navigator Software
In this issue, we will introduce one of the software available in the market that can provide navigation helps
when we are out in the sea. We will explain the features of the Navigator.
Star Finder
The figure below shows the Navigator's star finder window. This is a polar chart of the visible sky in a given
time and position. You can point a star and see its data (Name, Altitude and Azimuth). Or you can point on
the spreadsheet and see the corresponding objects on the chart.
The center of the chart is the Zenith and the external circle is the horizon. The two blue concentric circles are
the 30° and 60° altitude. The best stars to observe are between these two circles (altitudes between 30° and
60°).
33
For Heavenly Mathematics: IT Section The Navigator Software
Line of Position
Calculating a Line of Position is easy. Input:
•
Date and GMT time of the observation. You can also input the local time and click GMT!. The
program will calculate the GMT time, adding the time zone and watch error. Click Now! to fill with
the current date and time.
•
Select the star observed.
•
Instrumental altitude of the star. For the Sun and Moon, use the altitude of the lower limb, as
shown.
•
•
Estimated position (Latitude and Longitude).
Index Error in minutes and Height of the eye in meters or feet.
Press Calculate. The LOP will show in the chart, as illustrated.
All input fields and buttons have
hints that explain what they are
and what units should be used.
Place the cursor over the field to
see the hint.
34
For Heavenly Mathematics: IT Section The Navigator Software
Astronomical position
After you calculate two or more Lines of Position, you can calculate your astronomical position. The figure
bellow shows an astronomical position calculated with 2 LOPs. Note the blue chart, showing the LOPs
diagram. The astronomical position is indicated by the white circle. Use the cursor to zoom in and out. Auto
transport LOP feature makes calculating a running fix an easy task.
35
For Heavenly Mathematics: IT Section The Navigator Software
Chart Navigation
Navigator Chart Viewer can work with vector and raster charts. Vector charts can be produced with
ChartMaker program (also included in the registered version). There are a couple charts available in our
chart library. It can also import popular raster image formats, like GIF, JPG and BMP. None of the other
proprietary chart formats is supported at this time.
In the Navigator chart viewer you can:
- View multiple charts, integrated in a whole world vector chart background.
- Draw routes and calculate leg distances and courses
- Connect a GPS and save your track on-line
- Draw marks, with text.
- Calculate rhumb lines and lines of great circle and generate routes.
Chart viewer showing a raster chart zoom animation
36
____________________________________________________For Heavenly Mathematics: Astro-Net Review
Astro-net review
Trying to search the net for help? Do not know which are the reliable ones? Hear what we have to say!
www.celestialnavigation.net
This website although is simply designed but it is
filled with all the necessary knowledge you need
for Celestial Navigation. It provides a wide range
of subjects from history of navigation to Celestial
Navigation practice session.
Apart from these, there are numerous good links
to other website if you found this website
insufficient to satisfy your thirst for knowledge.
However, this website seems to be last updated on
2001. I hope the webmistress, as the author calls
herself; will be updating this website again!
aa.usno.navy.mil
U.S. Naval Observatory
Applications Department.
–
Astronomical
The name says it all. It provides a lot of
information on the sun and moon. This includes
providing azimuth, altitudes, moon rise and set
timing, sun rise and set timing, etc just by keying
in the longitude, latitude and timing that you are
in.
You may think that the loading of the page will
take you a long time since they can provide so
much information. But to your surprise they uses
the most simple and least needed memory to give
you all the data you need. Loading of results takes
you not more than a few seconds!
37
Crossword puzzle
Theme: Celestial Navigation
Across
Down
1. A publication describing the positions and
movements of celestial bodies.
4. A great circle passing through the two poles of
the celestial sphere and the zenith of a given
observer.
5. The angles in the Pole between the Meridian
of Greenwich and that of the considered position.
(Plural)
9. The point in the celestial sphere located in the
vertical, over the head of the navigator.
1. An old instrument used to measure the altitude
of the sun or stars
2. The angle that a star makes with the True
North
3. Norie’s Nautical _______s.
4. One of the important celestial body used for
Celestial Navigation at night.
6. The longitude of the Geographical Position is
known as _______wich Hour Angle
7. The 27th celestial body in the Nautical
Almanac.
8. Number of voyages Admiral Zheng He made.
_______________________________________________________For Heavenly Mathematics: Just for a Smile
Just for a smile
Cartoons
All these won’t happened if they know Celestial Navigation.
Cartoons courtesy of www.cartoonstocks.com
Jokes
When Mr. Leno of the Tonight Show went J-walking and asked pedestrians some science questions, he
discovered some amazing new facts about the universe:
Jay Leno: "Why does dew appear on plants in the morning when the Sun comes up?"
A waitress: "Is it because the Sun makes them perspire?"
Jay Leno: "Why does the Moon orbit the Earth?"
An auto mechanic: "To get to the other side?"
Jay Leno: What are magnets?"
A taxi driver: "Are they the things crawling over a week-old dead cat?"
Jay Leno: Which is more useful, the Sun or the Moon?"
A thirteen-year old: [Pause] "I think it's the Moon because the moon shines at night when you want the light,
whereas the Sun shines during the day when you don't need it."
Jokes courtesy of www.jupiterscientific.org
40
___________________________________________________________For Heavenly Mathematics: Promotion
PROMOTION!
Other free
gifts
Celestial gifts of the month
FREE Trip to watch POLARIS!
Sponsored by Spears Travel.
This is a rare chance for you to visit the North Pole and view the
Polaris. An experienced guided tour guide will be along with you.
This special tour will cost you more than S$5000, but one lucky
winner with the correct answer will walk away with this trip.
Question: Who invented Chronometer?
Email your answer along with your personal particulars to
[email protected]
Closing Date: 30th October 2005
350mm Telescope
Features:
•
•
•
Color: Grey
Size: 17" L x 4"
diameter
Has an 80mm objective
lens with a 350mm
focal length, and is
equipped with 2
Kellner eyepieces.
SMS <TEL><NAME><NRIC
No.><email> to 73888
E.g. TEL Celest 7912345G
[email protected]
th
Closing Date: 30 October
2005
One lucky winner will bring
this home!
***********************************************************
5 sets of Book vouchers worth
5 sets of Book vouchers
Want to subscribe to our
worth S$50 each will be
magazine?
given to find lucky winners.
2 years subscription for S$90. Save
Sponsored by Astrobooks.
more than S$15!
To subscribe: www.fhm.com/subs
Just tell us in less than 200
words on why you want to
have these book vouchers.
Answer to Crosswords Puzzle
Remember to include your
personal particulars and email
to [email protected]
Free 2 years subscription to
For Heavenly Mathematics
magazines.
Just send in the magazine
barcodes from the last 3
months and you will stand a
chance to win!
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41