29th June = 1st of Ramadan 1435
Let’s Get United And Start
Ramadan On The Same Day
Follow The Visibility Curve!
(M. Javed Naseem)
إِنَّ رَبَّكُمُ
ٱللَّهُ ٱلَّذِى خَلَقَ ٱلسَمَاوَاتِ وَٱلأَرْضَ فِى سِتَّةِ أَيَّامٍ
ثُمَّ ٱسْتَوَىٰ
عَلَى ٱلْعَرْشِ يُغْشِى ٱلْلَّيْلَ ٱلنَّهَارَ يَطْلُبُهُ حَثِيثاً
وَٱلشَّمْسَ
وَٱلْقَمَرَ وَٱلنُّجُومَ مُسَخَّرَاتٍ بِأَمْرِهِ أَلاَ لَهُ ٱلْخَلْقُ
وَٱلأَمْرُ تَبَارَكَ
ٱللَّهُ رَبُّ ٱلْعَالَمِينَ
“Your Guardian-Lord is Allah, Who created the
“Your Guardian-Lord is Allah, Who created the
heavens and the earth in six days, and is
firmly
established on the throne (of authority).
He draws
the night as a veil over the day, each
seeking the
other in rapid succession. He created the
sun,
the moon, and the stars, (all) governed by
laws
under His command. Is it not His to create
and
to govern? Blessed be Allah, the Cherisher
and Sustainer of the worlds!”
(al-Quran
7:54)
Allah tells us in the Holy Quran that He created us as One
Ummah (‘Ummat-an Wahida’) or one nation. The Faith of Islam binds us together
regardless of color, race or ethnic background. All believers of One God are
one nation, therefore, they should be united as one big community. We are
commanded to hold unto the Rope of Allah all together and be not divided. So,
there is no room of sectarianism in Islam. Sectarianism violates and disobeys the
command of Allah. Now, anybody who disobeys Allah and His commands, can he/she
still claim to be a true Muslim?
People in America
and Europe get confused (it is hard for them to understand) that in one city (New York , London , Birmingham , Paris or Copenhagen , etc.)
different groups of Muslims (Arabs, Indo-Pakistanis, Egyptians and Africans)
start Ramadan on different dates and celebrate Eid festivals on different days.
It gets more ridiculous in countries like Pakistan ,
India , Canada where people from the same
ethnic group observe Ramadan on different dates. Even two neighboring Muslim
countries observe Ramadan and Eid on different dates. Non-Muslims laugh at them
and ask: Have you ever seen Christians celebrating Christmas on a date other
than 25th December?
Muslims sheepishly try to justify by saying that Islamic
festivals and occasions are governed by the lunar (moon) calendar and not by
the Gregorian (sun) one. But that does not justify two (sometimes three) Eid
festivals in one city. Most Muslims don’t know that the lunar (moon) calendar
is as correct and specific as the Gregorian one. They ‘read’ the Quran but they
don’t “study” the Quran. The Quran guides you on all aspects of your Deen. To
avoid confusion about the lunar calendar, it is important that we acquire some basic
knowledge/education.
ٱلشَّمْسُ
وَٱلْقَمَرُ بِحُسْبَانٍ
“The sun and the moon follow courses
“The sun and the moon follow courses
(exactly) computed.”
(al-Quran 55:5)
يَسْأَلُونَكَ عَنِ
ٱلأَهِلَّةِ قُلْ هِىَ مَوَاقِيتُ لِلنَّاسِ وَٱلْحَجِّ
“They ask you concerning the new moons. Say:
“They ask you concerning the new moons. Say:
They are but signs to mark fixed periods
of time
in (the affairs of) men, and for pilgrimage.”
(al-Quran 2:189)
هُوَ ٱلَّذِى جَعَلَ
ٱلشَّمْسَ ضِيَآءً وَٱلْقَمَرَ نُوراً وَقَدَّرَهُ مَنَازِلَ
لِتَعْلَمُواْ
عَدَدَ ٱلسِّنِينَ وَٱلْحِسَابَ مَا خَلَقَ ٱللَّهُ ذٰلِكَ
إِلاَّ بِٱلْحَقِّ
يُفَصِّلُ ٱلآيَاتِ لِقَوْمٍ يَعْلَمُونَ
“It is He Who made the sun to be a shining glory
“It is He Who made the sun to be a shining glory
and the moon to be a light (of beauty),
and
measured out stages for her; that you
might know
the number of years and the count (of
time).
Nowise did Allah create this but in truth
and
righteousness. (Thus) does He explain His
Signs
in detail, for those who understand.”
(al-Quran 10:5)
Allah has created the universe with Truth and knowledge and
some of this knowledge was bestowed upon human beings too. We should study the
Quran where Allah has explained everything that we need to know to live on this
planet Earth. He tells us that the movements of all elements (entities) of the
constellation in the atmosphere are fixed and pre-programmed.
وَآيَةٌ لَّهُمُ
ٱلْلَّيْلُ نَسْلَخُ مِنْهُ ٱلنَّهَارَ فَإِذَا هُم مُّظْلِمُونَ
“And a Sign for them is the Night. We
“And a Sign for them is the Night. We
withdraw from it the
Day, and behold!
They are plunged in
darkness.”
(al-Quran
36:37)
وَٱلشَّمْسُ تَجْرِى
لِمُسْتَقَرٍّ لَّهَـا ذٰلِكَ تَقْدِيرُ ٱلْعَزِيزِ ٱلْعَلِيمِ
“And the sun runs his course for a period
“And the sun runs his course for a period
determined for it;
that is the decree of (Him),
the Exalted in Might,
the All-Knowing.”
(al-Quran 36:38)
وَٱلْقَمَرَ
قَدَّرْنَاهُ مَنَازِلَ حَتَّىٰ عَادَ كَٱلعُرْجُونِ ٱلْقَدِيمِ
“And the Moon - We have measured for her
“And the Moon - We have measured for her
mansions (to
traverse) till she returns like the
old (and withered) lower
part of a date-stalk.”
(al-Quran 36:39)
Everything is floating on its prescribed axis in its
measured orbit. They cannot deviate or collide with each other. Allah has
created a celestial system, which is perfect, and He regulates or controls it.
No discrepancies! If we follow the system carefully, we can prepare a faultless
calendar not only for the entire year, but even for 100 years. There cannot be
two Eids in one city any more.
لاَ ٱلشَّمْسُ
يَنبَغِى لَهَآ أَن تدْرِكَ ٱلقَمَرَ وَلاَ
ٱلْلَّيْلُ سَابِقُ
ٱلنَّهَارِ وَكُلٌّ فِى فَلَكٍ يَسْبَحُونَ
“It is not permitted to the Sun to catch up the Moon,
“It is not permitted to the Sun to catch up the Moon,
nor can the Night
outstrip the Day. Each (just) swims
along in (its own)
orbit (according to Law).”
(al-Quran 36:40)
********************************
Ramadan 1435 gives
you the best
opportunity to get
united as the new
crescent moon
would be visible in
many countries of Americas , Europe ,
Africa, Asia and Australia .
This could
be the first step
toward solidarity,
brotherhood and
coordination. Let’s
start Ramadan on
29th June 2014.
********************************
لَّهَـا ذٰلِكَ
تَقْدِيرُ ٱلْعَزِيزِ ٱلْعَلِيمِ
“That is the decree of (Him), the Exalted
in Might, the All-Knowing (Allah).”
(al-Quran 36:38)
فَالِقُ ٱلإِصْبَاحِ
وَجَعَلَ ٱلْلَّيْلَ سَكَناً وَٱلشَّمْسَ
وَٱلْقَمَرَ
حُسْبَاناً ذٰلِكَ تَقْدِيرُ ٱلْعَزِيزِ ٱلْعَلِيمِ
“He it is that cleaves the day-break (from the dark).
“He it is that cleaves the day-break (from the dark).
He makes the night for rest and tranquility,
and
the sun and moon for the reckoning (of
time).
Such is the judgment and ordering of
(Him),
the Exalted in Power, the Omniscient.”
(al-Quran 6:96)
وَسَخَّر لَكُمُ
ٱلشَّمْسَ وَٱلْقَمَرَ دَآئِبَيْنِ
وَسَخَّرَ لَكُمُ
ٱلْلَّيْلَ وَٱلنَّهَارَ
“And He has made subject to you the sun and the
“And He has made subject to you the sun and the
moon, both diligently pursuing their
courses; and the
night and the day has He (also) made
subject to you.”
(al-Quran 14:33)
وَسَخَّرَ لَكُمُ
ٱللَّيْلَ وَٱلْنَّهَارَ وَٱلشَّمْسَ وَٱلْقَمَرَ وَٱلْنُّجُومُ
مُسَخَّرَاتٌ
بِأَمْرِهِ إِنَّ فِى ذٰلِكَ لَآيَاتٍ لِّقَوْمٍ يَعْقِلُونَ
“He has made subject to you the Night and the Day; the
“He has made subject to you the Night and the Day; the
sun and the moon; and the stars are in
subjection by His
Command: verily in this are Signs for men
who are wise.”
(al-Quran 16:12)
خَلَقَ ٱلسَّمَاوَاتِ
وَٱلأَرْضَ بِٱلْحَقِّ يُكَوِّرُ ٱللَّيْـلَ عَلَى ٱلنَّهَـارِ
وَيُكَوِّرُ
ٱلنَّـهَارَ عَلَى ٱللَّيْلِ وَسَخَّـرَ ٱلشَّمْسَ وَٱلْقَمَرَ
كُـلٌّ يَجْرِى
لأَجَـلٍ مُّسَـمًّى أَلاَ هُوَ ٱلْعَزِيزُ ٱلْغَفَّارُ
“He created the heavens and the earth in true
“He created the heavens and the earth in true
(proportions). He makes the Night overlap
the
Day, and the Day overlap the Night. He has
subjected the sun and the moon (to His
law).
Each one follows a course for a time
appointed.
Is not He the Exalted in Power - He
Who forgives again and again?”
(al-Quran 39:5)
وَعَدَ ٱللَّهُ
ٱلَّذِينَ آمَنُواْ وَعَمِلُواْ ٱلصَّالِحَاتِ
لَهُم مَّغْفِرَةٌ
وَأَجْرٌ عَظِيمٌ
“To those who believe and do deeds of righteousness
“To those who believe and do deeds of righteousness
has Allah promised
forgiveness and a great reward.”
(al-Quran 5:9)
Moon
Phases:
Here’s some basic information about
the lunar cycle and phases from astronomical point of view:
From any location on the Earth, the Moon appears to be a
circular disk which, at any specific time, is illuminated to some degree by
direct sunlight. Like the Earth, the Moon is a sphere which is always half illuminated
by the Sun, but as the Moon orbits the Earth we get to see more or less of the
illuminated half. During each lunar orbit (a lunar month), we see the Moon's
appearance change from not visibly illuminated through partially illuminated to
fully illuminated, then back through partially illuminated to not illuminated
again. Although this cycle is a continuous process, there are eight distinct,
traditionally recognized stages, called phases. The phases designate both the
degree to which the Moon is illuminated and the geometric appearance of the
illuminated part of the moon.
ٱللَّهُ ٱلَّذِى
رَفَعَ ٱلسَّمَاوَاتِ بِغَيْرِ عَمَدٍ تَرَوْنَهَا ثُمَّ ٱسْتَوَىٰ عَلَى
ٱلْعَرْشِ
وَسَخَّرَ ٱلشَّمْسَ
وَٱلْقَمَرَ كُلٌّ يَجْرِى لِـأَجَلٍ مُّسَمًّـى
يُدَبِّرُ ٱلأَمْرَ
يُفَصِّلُ ٱلآيَاتِ لَعَلَّكُمْ بِلِقَآءِ رَبِّكُمْ تُوقِنُونَ
“Allah is He Who raised the heavens without any
“Allah is He Who raised the heavens without any
pillars that, you can see, is firmly
established on
the throne (of authority). He has
subjected the sun
and the moon (to His Law)! Each one runs (its
course) for a term appointed. He does
regulate all
affairs, explaining the signs in detail,
that you may
believe with certainty in the meeting with
your Lord.”
(al-Quran 13:2)
These phases of the Moon, in the sequence of their
occurrence (starting from New Moon), are listed below.
New Moon - The Moon's un-illuminated side
is facing the Earth. The Moon is not visible (except during a solar eclipse).
Waxing Crescent - The Moon appears to be
partly but less than one-half illuminated by direct sunlight. The fraction of
the Moon's disk that is illuminated is increasing.
First Quarter - One-half of the Moon
appears to be illuminated by direct sunlight. The fraction of the Moon's disk
that is illuminated is increasing.
Waxing Gibbous - The Moon appears to be
more than one-half but not fully illuminated by direct sunlight. The fraction
of the Moon's disk that is illuminated is increasing.
Full Moon - The Moon's illuminated side
is facing the Earth. The Moon appears to be completely illuminated by direct
sunlight.
Waning Gibbous - The Moon appears to be
more than one-half but not fully illuminated by direct sunlight. The fraction
of the Moon's disk that is illuminated is decreasing.
Last Quarter - One-half of the Moon
appears to be illuminated by direct sunlight. The fraction of the Moon's disk
that is illuminated is decreasing.
Waning Crescent - The Moon appears to be
partly but less than one-half illuminated by direct sunlight. The fraction of
the Moon's disk that is illuminated is decreasing.
Following waning crescent is New Moon, beginning a
repetition of the complete phase cycle of 29.5 days average duration.
The time in days counted from the time of New Moon is called
the Moon's "age". Each complete cycle of phases is called a
"lunation".
Because the cycle of the phases is shorter than most
calendar (solar) months, the phase of the Moon at the very beginning of the
month usually repeats at the very end of the month. When there are two Full
Moons in a month (which occurs, on average, every 2.7 years), the second one is
called a "Blue Moon".
The first time that the thin waxing crescent Moon is visible
after New Moon (low in the evening sky just after sunset) marks the beginning
of a month in the Islamic Calendar.
وَهُوَ ٱلَّذِى
خَلَقَ ٱلْلَّيْلَ وَٱلنَّهَارَ وَٱلشَّمْسَ وَٱلْقَمَرَ
كُلٌّ فِى فَلَكٍ
يَسْبَحُونَ
“It is He Who created the Night and the Day,
“It is He Who created the Night and the Day,
and the sun and the moon; all (the
celestial
bodies) swim along, each in an orbit.”
(al-Quran
21:33)
تَبَارَكَ ٱلَّذِى
جَعَلَ فِى ٱلسَّمَآءِ بُرُوجاً
وَجَعَلَ فِيهَا
سِرَاجاً وَقَمَراً مُّنِيراً
“Blessed is He Who made constellations
“Blessed is He Who made constellations
in the skies, and placed therein a Lamp
and a Moon giving light.”
(al-Quran 25:61)
Although Full Moon occurs each month at a specific date and
time, the Moon's disk may appear to be full for several nights in a row if it
is clear. This is because the percentage of the Moon's disk that appears
illuminated changes very slowly around the time of Full Moon (also around New Moon,
but the Moon is not visible at all then). The Moon may appear 100% illuminated
only on the night closest to the time of exact Full Moon, but on the night
before and night after will appear 97-99% illuminated; most people would not
notice the difference. Even two days from Full Moon the Moon's disk is 93-97%
illuminated.
New Moon, First Quarter, Full Moon, and Last Quarter phases
are considered to be primary phases and their dates and times are published in
almanacs and on calendars.
وَلَقَدْ جَعَلْنَا
فِى ٱلسَّمَاءِ بُرُوجاً وَزَيَّنَّاهَا لِلنَّاظِرِينَ
“And verily in the heaven We have set
mansions of the stars (galaxies), and We
have beautified it for beholders.”
(al-Quran
15:16)
وَهُوَ ٱلَّذِى
جَعَلَ لَكُمُ ٱلنُّجُومَ لِتَهْتَدُواْ بِهَا فِى
ظُلُمَاتِ ٱلْبَرِّ
وَٱلْبَحْرِ قَدْ فَصَّلْنَا ٱلآيَاتِ لِقَوْمٍ يَعْلَمُونَ
“It is He Who makes the stars (as beacons) for
“It is He Who makes the stars (as beacons) for
you, that you may guide yourselves, with
their
help, through the dark spaces of land and
sea.
We detail Our signs for people who know.”
(al-Quran
6:97)
فَٱسْتَقِيمَا وَلاَ
تَتَّبِعَآنِِّّ سَبِيلَ ٱلَّذِينَ لاَ يَعْلَمُونَ
“… So stand straight, and follow not
“… So stand straight, and follow not
the path of those who know not."
(al-Quran
10:89)
The phases of the Moon are related to (actually, caused by)
the relative positions of the Moon and Sun in the sky. For example, New Moon
occurs when the Sun and Moon are quite close together in the sky. Full Moon
occurs when the Sun and Moon are at nearly opposite positions in the sky -
which is why a Full Moon rises about the time of sunset, and sets about the
time of sunrise, for most places on Earth.
First and Last Quarters occur when the Sun and Moon are
about 90 degrees apart in the sky. In fact, the two "half Moon"
phases are called First Quarter and Last Quarter because they occur when the
Moon is, respectively, one- and three-quarters of the way around the sky (i.e.,
along its orbit) from New Moon.
The relationship of the Moon's phase to its angular distance
in the sky from the Sun allows us to establish very exact definitions of when
the primary phases occur, independent of how they appear. Technically, the
phases New Moon, First Quarter, Full Moon, and Last Quarter are defined to
occur when the excess of the apparent ecliptic (celestial) longitude of the
Moon over that of the Sun is 0, 90, 180, and 270 degrees, respectively. These
definitions are used when the dates and times of the phases are computed for
almanacs, calendars, etc. Because the difference between the ecliptic
longitudes of the Moon and Sun is a monotonically and rapidly increasing
quantity, the dates and times of the phases of the Moon computed this way are
instantaneous and well defined.
For practical purposes, phases of the Moon and the percent
of the Moon illuminated are independent of the location on the Earth from where
the Moon is observed. That is, all the phases occur at the same time regardless
of the observer's position.
Crescent Moon
Visibility:
Although the date and time of each New Moon can be
computed exactly, the visibility of the lunar crescent as a function of the
Moon's ‘age’ - the time counted from New Moon -depends upon many factors and
cannot be predicted with certainty. During the first two days after New Moon,
the young crescent Moon appears very low in the western sky after sunset, must
be viewed through bright twilight, and sets shortly after sunset.
The sighting of the lunar crescent within one day of New
Moon is usually difficult. The crescent at this time is quite thin, has a low
surface brightness, and can easily be lost in the twilight. Generally, the
lunar crescent will become visible to suitably-located, experienced observers
with good sky conditions about one day after New Moon. However, the time that
the crescent actually becomes visible varies quite a bit from one month to another.
Naked-eye sightings as early as 15.5 hours after New Moon have been reliably
reported while observers with telescopes have made reliable reports as early as
12.1 hours after New Moon. Because these observations are exceptional, crescent
sightings this early in the lunar month should not be expected as the norm.
Ignoring local conditions for the moment and visualizing the
problem from outside the Earth's atmosphere, the size and brightness of the
lunar crescent depend on only one astronomical quantity:
the elongation of the Moon from the Sun, which is the apparent
angular distance between their centers. For this reason, the elongation has
also been called the ‘arc of light’. If the value of the elongation at any
instant is known, the width of the crescent can be computed.
The elongation as a function of the Moon's age depends on
several factors.
The Visibility Curve:
I am writing and appealing to the Muslim Ummah to observe
Ramadan, all together on the same day, on the basis of the ‘Geographical Truth’
of the Visibility Curve.
The following two ‘visibility curve’ maps are shown by
courtesy of the website ‘moonsighting.com’. The first map shows, from
astronomical point of view, the first day of the new moon which is geographically
visible only in Latin American countries (Brazil ,
Argentina , Chile , Peru , etc.) on 27th of
June. Therefore, any country in Europe, Middle East, Africa or Asia cannot claim the start of Ramadan because moon was
not (and could not be) visible there. The visibility in these regions is bound
by geographical limits whereas the birth of New Crescent Moon is on the
celestial scene with no geographical limits.
The second map shows the same astronomical phenomena with
geographical visibility extended (the 2nd day of New Crescent Moon, 28th
of June) to Europe, Africa, Middle East and Asia .
Therefore, a Muslim country in these regions can claim the start of Ramadan
from the next morning, i.e., 29th of June, 2014. The moon would be
visible with the naked eye on the evening of 28th of June, whether
somebody cares to see it or not. There should absolutely be no dispute about
the start of Ramadan from the USA
to Australia including Saudi Arabia , Pakistan ,
India , Bangladesh , Indonesia , etc. from the 29th
of June. Now, this is an ‘educated’ approach based on the scientific (astronomical)
data – the basis of all lunar calendars.
A Brief Introduction to
the Islamic Calendar:
The Islamic calendar is based on lunar months, which begin
when the thin crescent Moon is actually sighted in the western sky after sunset
a day or so after New Moon. For Islamic calendar purposes, the sighting must be
made with the unaided eye.
The names of the 12 months of the Islamic calendar, transliterated
into the Roman alphabet, and their formal tabular lengths are:
Name
|
Length
|
Notes
|
Muharram
|
30
|
Holy month
|
Safar
|
29
|
|
Rabi' I
|
30
|
|
Rabi' II
|
29
|
|
Jumada I
|
30
|
|
Jumada II
|
29
|
|
Rajab
|
30
|
Holy month
|
Sha’ban
|
29
|
|
Ramadan
|
30
|
Month of fasting
|
Shawwal
|
29
|
|
Dhul-Qaada
|
30
|
Holy month
|
Dhul-Hijjah
|
29
|
Holy month; in a leap year Dhul-Hijjah has 30 days.
|
Since 12 lunar months are, on average, 11 days shorter than
the (Gregorian) civil year, the Islamic year shifts earlier in each civil year
by about this amount. The count of years for the Islamic calendar begins with 1
Muharram 1 A .H.
(Anno Hegira), which corresponds to Friday, 16 July AD 622 (Julian calendar).
أَلَمْ تَرَ أَنَّ
ٱللَّهَ يُولِجُ ٱلْلَّيْلَ فِى ٱلنَّهَارِ وَيُولِجُ ٱلنَّهَارَ فِى ٱلْلَّيْلِ
وَسَخَّرَ ٱلشَّمْسَ
وَٱلْقَمَرَ كُلٌّ يَجْرِيۤ إِلَىٰ أَجَلٍ مُّسَمًّى
وَأَنَّ
ٱللَّهَ بِمَا تَعْمَلُونَ خَبِيرٌ
“See you not that Allah merges Night into Day
“See you not that Allah merges Night into Day
and he merges Day into Night; that He has
subjected the sun, and the moon (to his
Law),
each running its course for a term
appointed; and
that Allah is well-acquainted with all
that you do?”
(al-Quran 31:29)
يُولِجُ ٱلْلَّيْلَ
فِى ٱلنَّهَارِ وَيُولِجُ ٱلنَّهَارَ فِى ٱلْلَّيْلِ وَسَخَّرَ ٱلشَّمْسَ
وَٱلْقَمَرَ كُلٌّ
يَجْرِى لأَجَلٍ مُّسَمًّى ذٰلِكُمُ ٱللَّهُ رَبُّكُمْ لَهُ ٱلْمُلْكُ
وَٱلَّذِينَ
تَدْعُونَ مِن دُونِهِ مَا يَمْلِكُونَ مِن قِطْمِيرٍ
“He merges Night into Day, and he merges
“He merges Night into Day, and he merges
Day into Night, and he has subjected the
sun
and the moon (to his Law); each one runs
its
course for a term appointed. Such is Allah,
your Lord; to Him belongs all Dominion.”
(al-Quran 35:13)
Tabular Islamic Calendar:
A tabular Islamic calendar has been established
for some non-religious purposes in which the lengths of the months alternate
between 29 and 30 days. This calendar consists of a 30-year cycle in which 11
of the 30 years are leap years. In leap years, an extra day is added to the
last month, Dhul-Hijjah. Civil dates corresponding to important Islamic dates
in this tabular calendar are:
First day of Ramadan 1434: July 9, 2013
Islamic New Year 1435: November 5, 2013
First day of Ramadan 1435: June 29, 2014
Islamic New Year 1436: October 25, 2014
First day of Ramadan 1436: June 18, 2015
Islamic New Year 1437: October 15, 2015
First day of Ramadan 1437: June 7, 2016
Islamic New Year 1438: October 3, 2016
(Note: These dates are the astronomical ‘first
day’ of New Moon. The start of Ramadan (or any other month) should be
determined by the geographical visibility-curve map for that particular
region.)
The Islamic dates begin at sunset of
the previous evening and end at sunset on the date listed above.
These dates may or may not correspond to the evenings on which the crescent
Moon is first visible, and it is the visibility of the crescent Moon that
determines when the religious observance begins. The Moon's visibility at these
times varies with location; generally, the visibility increases to the west,
and locations in the tropics are favored over those in middle or high
latitudes.
(Courtesy: Astronomical Applications Dept. , U.S.
Navy)
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