celestial coordinate systems
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Basics of Celestial Navigation -
stars
• Coordinate systems
– Observer based – azimuth and altitude
– Earth based – latitude and longitude
– Celestial – declination and right ascension (or
sidereal hour angle)
• elationshi! among three – star !illars
• "otions of the stars in the s#y
• "a$or star grou!ings
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Comments on coordinate systems
• %ll three are basically &ays of describing locations on as!here – inherently t&o dimensional – e'uires t&o !arameters (eg latitude and longitude)
• eality – three dimensionality
– eight of observer – Oblateness of earth* mountains – +tars at different distances (!aralla,)
• hat you see in the s#y de!ends on – .ate of year
– /ime – 0atitude – 0ongitude – hich is ho& &e can use the stars to navigate11
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Altitude-Azimuth coordinate system
Based on what an observer sees in the sky.
Zenith = point directly above the observer (90o
!adir = point directly below the observer (-90o " can#t be seen
$orizon = plane (0o
Altitude = an%le above the horizon to an ob&ect (star' sun' etc
(ran%e = 0o to 90o
Azimuth = an%le rom
true north (clockwise
to the perpendicular arc
rom star to horizon
(ran%e = 0o to )*0o
Note: lines of azimuth
converge at zenith
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+he arc in the sky rom azimuth o 0o to ,0o
is called the local meridian
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oint o view o the observer
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/atitude
/atitude – an%le rom the euator (0o north (positive or
south (ne%ative to a point on the earth " (ran%e = 90o
= northpole to " 90o = south pole. , minute o latitude is always =
, nautical mile (,.,1, statute miles
Note: It’s more
common to express
Latitude as 26 oS or
42o N
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/on%itude
/on%itude = an%le rom the prime meridian (=0o
parallelto the euator to a point on earth (ran%e = -,0o to 0 to
2,0o 3ast o 4 = positive' 5est o 4 is ne%ative.
6istance between lines o lon%itude depend on latitude77
Note: sometimes positive longitude
is expressed as
West !ut this is
inconsistent "ithmath conventions#
$void confusion:
4%oW or 4%o &
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8omments on lon%itude
/ocation o prime meridian is arbitrary = reenwichobservatory in :;
1 minute of longitude = 1 nautical mile * cosine(latitude)
/ines o lon%itude conver%e at the north and south poles
+o ind lon%itude typically reuires a clock' althou%h there
is a techniue' called the lunar method that relies on the act
that the moon moves < o a de%ree per hour.
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8elestial coordinates - some deinitions
!orth celestial pole = point in sky directly above north pole
on earth (i.e. zenith o north poleouth celestial pole = zenith o south pole on earth
8elestial euator " circle
surroundin% euator on earth
3cliptic " path ollowed
by the sun throu%h the
sky over the course o
the year a%ainst a>i?ed@ back%round o
stars
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6eclination " an%le rom celestial euator (=0o' positive
%oin% north (north celestial pole = 2 90o' ne%ative %oin%
south (south celestial pole = - 90o
i%ht ascension (A " an%le rom celestial >prime meridian@ "
euivalent o celestial lon%itude
A " typically e?pressed
as a time %oin% east " 0 to
C hours is )*0o
>rime meridian@ " pointwhere sun is located at
the vernal euino? (sprin%
(called vernal euinoctial
colure
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6eclination and >star pillars@
6eclination >maps@ onto latitude "
At some point a star o a %iven
declination will pass over the zenith
at a point on the earth at its correspondin% latitude.
+his happens once every
C hours
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Alternative to i%ht Ascension
idereal $our An%le ($A - same as A' e?cept measured
in de%rees' %oin% rom 0 to )*0o
" conversion is strai%htorward
Note: '$ is("as useful
for navigation "ith cloc)s
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As with lon%itude' the actual an%ular width between
lines o $A shrinks with hi%her declination as
8osine(declination
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Dohn $uth#s alternative to $A' A
:se same convention as or terrestrial lon%itude' with
positive and ne%ative an%les. rime meridian correspondsto 0o or $A
ame as $A or 0o to ,0o and ()*0o " $A or values
o $A rom ,0o to )*0o
5hyE 3asy to remember'
and allows you to associate
star coordinates with points
on earth. 4akes it easier tovisualize and memorize.
Also " declination and latitude
%o to%ether.
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Ne& .elhi
Calcutta.&ar#a
23oE 45oE 53oE
3?ample
Aldeberan (+aurus = *9o3
i%el (Frion = Go3Betel%euse (Frion = 9o3
Aldeberan
Betel%euse
i%el
irius
rocyon Orion
4ethod " lie >on your back@
look at the stars and visualize
the locations on the %lobe
(otherwise' it#s a mirror ima%e
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.&ar#a
Ne& .elhi
Calcutta
23oE45oE53oE
Aldeberan
Betel%euse
i%el
Orion
3?ample
Aldeberan (+aurus = *9o3 - 6warka
i%el (Frion = Go3 " !ew 6elhiBetel%euse (Frion = 9o3 - 8alcutta
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8an associate star coordinates with latitude and
/on%itude o locations on earth
Note: don’t expect alignment with any star – this is just
a way to memorize coordinates
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6m!ortant 7oint
• "ariners had to8have to rely on tables forstar coordinates
• 9ou can memorize ma$or navigational star
coordinates and eliminate tables• el!s identify stars* too
• On a desert island* &ith only a &atch* can
identify latitude and longitude – along &ithyour memory1
• /ell that to the creators of :0ost;11
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4appin% o three coordinate systems onto each other
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o& stars move through the s#y
• +tars move in arcs that !arallel thecelestial e'uator – angle !er!endicular tocelestial e'uator is the declination
• +tar move across the s#y at <=o !er hour(> minutes !er degree)
• Each day star !ositions move <o &est
• +tars on the celestial e'uator rise and set&ith angles of (3?o – 0atitude)
• +ome stars are :circum!olar; – never set
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tar paths in the sky orm arcs in the sky
At the euator'
stars rise and set at
ri%ht an%les to the
$orizon.
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At Boston (C,o!' stars due
east will rise and set at an
an%le (90o "/atitude = C9o
with respect to the horizon(i.e. on celestial euator
tars always move in arcs
parallel to the celestial
euator
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aths o stars as seenrom the !. Arctic 8ircle
**o ! " ew stars rise and
set " most make complete
circles
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@
isin%Hsettin% an%le is (90o " /atitude due
eastHwest " alon% celestial euator
An%les are smaller the urther !H one %oes
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elation between Azimuth' /atitude and 6eclination o
risin% and settin% stars
)cos(
)sin()cos( L
d ' z =
5here ' z * rising azimuth
d * declination
L * Latitude
o " at euator' /=0' cos+L, * -' risin% azimuth is the
declination o the star " e?ploited by olynesians instar compasses (near the euator cos+L, close to ,
8an use this to ind latitude' i you#re willin% to do the
math' and ind the azimuth o a risin% star' knowin%
the star#s declination.
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!otes on azimuth " when )cos()sin( Ld >
+hen star is either circumpolar or below the horizon
3?ample " at latitude C1o
!' cos(/=0.G0G' the star8apella (declination = C*o &ust becomes circumpolar
+hen cos(z is &ust sli%htly %reater than ,.
/ar%est risin%Hsettin% an%les or z = 90HG0 de%rees
(alon% celestial euator
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8ircumpolar stars " never set
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;nowin% a star#s declination' can %et latitude
rom horizon %razin% stars.
$orizon (est
4in. star hei%ht
olar distance =
(90o " 6eclination
/atitude = (polar distance " minimum hei%ht
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+ome star grou!ings
• 6f you can locate stars and #no& the
declination you can find your latitude
• ith a &atch* and +% (or :stellar
longitude;)* you can find your longitude
(must #no& date)
• Clustering into constellations and their
stories hel! locate stars by name
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Bi% dipper
Arcturus
pica
>Arc to Arcturus' spike to pica@
$fter sunset:
Spring(summer
$rcturus +.ecl * -/o N,
and Spica +.ecl * --oS,
0alone1 in this part of
the s) +0longitude1 *-46 oW and -3/oW
respectivel,
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6eneb Ie%a
Altair
Antares
Scorpio
ummer trian%le and Antares
$ntares is onl
visi!le for a short
period +hours, in
mid summer#
.eclination * 26 oS
ood candidate for a
horizon grazing star in
the summer
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Altair
Ie%a
6eneb
Summer Triangle
Cygnus/
Northern
Cross
ummer trian%le' northern cross (8y%nus
5ega +.ecl * /o N, and .ene! +.ecl * 43o , straddle zenith
in 7oston +Latitude * 42o , $ltair is /o N
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6ubhe
chedar
Cassiopeia
Big dipper/Ursa major
olaris
Jindin% olaris rom the bi% dipper
Schedar +.ecl * 36
o
,and .u!he +.ecl * 62o ,
are circumpolar for 7oston
$lso can !e used as
the !asis for a 0cloc)1
+pro8ect,
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Aldeberan
Betel%euse
i%el
irius
rocyonOrion
8onstellation story about Frion
leiades
Winter constellations 9 eus’ daughters ;leiades +24N 3<&,
are guarded ! =aurus +$lde!eran * orange ee 9 -<N 6/&, from
>rion the hunter +7etelgeuse * <N ?/& 'igel ?S<?&, follo"ed
! hunting dogs @anis Ainor +;rocon * 3N --3&, and
@anis Aa8or +Sirius * -<S and -%-&,
Ainta)a 9 right star
in !elt is on the eBuator
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+ime lapse ima%e o Frion
irius
Betel%euse
i%el
Arcturus
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e%ulus
eo ollu?
!emini
rocyon
/ate winterHearly sprin% constellations
;ollux(;rocon line +--3&, forms good northCsouth arc
;ollux +2?N --3&, is readil recognized "ith t"in @astor
'egulus +-2N -32&,
mar)s start of sparsel populated
region of stars in N# hemisphere 9
l t i $ t +-42W,