Celestial Coordinate Systems

7/21/2019 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



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



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



+he arc in the sky rom azimuth o 0o to ,0o

is called the local meridian



oint o view o the observer



/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



/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 &



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.



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



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



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



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



As with lon%itude' the actual an%ular width between

lines o $A shrinks with hi%her declination as

8osine(declination





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.



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



.&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



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



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



4appin% o three coordinate systems onto each other



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



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.



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



aths o stars as seenrom the !. Arctic 8ircle

**o ! " ew stars rise and

set " most make complete

circles



@

isin%Hsettin% an%le is (90o " /atitude due

eastHwest " alon% celestial euator

An%les are smaller the urther !H one %oes



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.



!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



8ircumpolar stars " never set



;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



+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



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,



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



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



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,



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



+ime lapse ima%e o Frion

irius

Betel%euse

i%el

Arcturus



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,

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Celestial Coordinate Systems

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