pembinaan2posastro - dr m irfan hakim.ppt

7/25/2019 pembinaan2PosAstro - Dr M Irfan Hakim.ppt

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Positional Astronomy

Compiled from:http://star-www.st-and.ac.uk


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Introduction

How to describe the position of an object in thesky.

hich different coordinate systems are

appropriate in different situations.

How to transform between coordinate systems.

hat corrections ha!e to be applied.


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"otes

#bjects in the sky appear to be positioned onthe celestial sphere$ an indefinite distance away.

A sphere is a three-dimensional object$ but its

surface is two-dimensional. %pherical &eometry is carried out on the surface

of a sphere:

it resembles ordinary 'plane( &eometry$ but itin!ol!es new rules and relationships.


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)he terrestrial sphere


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Celestial na!i&ation used at sea 'and in the air(in!ol!es spherical tri&onometry$

so the results are in an&ular measure

'de&rees(. )hese must be con!erted to linear measure for

practical use.

e define the nautical mile as * arc-minutealon& a &reat circle on +arth,s surface.


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+ercise *

Alderney$ in the Channel Islands$ has lon&itude $latitude 01".

innipe&$ in Canada$ has lon&itude 23$ latitude 01".

How far apart are they$ in nautical miles$ alon& a parallel oflatitude4 '* 5 61 nautical miles(


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7istance alon& a parallel of latitude is 'difference inlon&itude( cos'latitude(

5 '23 - ( cos'01( 5 6*.16

8ut * 5 61 nautical miles.

%o the distance is 6*.16 61 5 9669 nautical miles.


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%ine rule


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Cosine rule


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"ote about ambi&uity

sin'( 5 1.0$

then may be 91 or *01.

#r$ if the cosine rule yields

cos'( 5 1.0$

then may be 61 or 911 '-61(.

In this case$ there is no ambiguityif is a sideof thetrian&le$ as it must be less than 180$

but there could still be uncertainty if an angleof the trian&lewas positi!e or ne&ati!e.


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+ercise

Alderney$ in the Channel Islands$ has lon&itude $latitude 01".

innipe&$ in Canada$ has lon&itude 23$ latitude 01".

How far apart are they$ in nautical miles$ alon& a &reat-circle arc4

If you set off from Alderney on a &reat-circle route to

innipe&$ in what direction 'towards what aimuth( would you head4


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;se the cosine rule:

cos A 5 cos P cos AP < sin P sin AP cos P

5 cos=1 < sin=1 cos 20

5 1.001>

%o A 5 06.0>

5 9920 nautical miles

')his is 3? shorter than the route alon& a parallel oflatitude(.


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;se the sine rule:

sin A / sin P 5 sin P / sin A

so sin 5 sin =1 sin 20 / sin 06.0> 5 1.33

so 5 01.* or *2.2 .

Common sense says 01.* 'or check usin& cosine rule to&et P(.


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Coordinate %ystems:the horiontal or Alt-A system


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Comparison with the terrestrialsystem

Terrestrial

+@uator

"orth Pole

%outh Pole

atitude

Co-latitude

parallel of latitude

meridian of lon&itude

Breenwich eridian

lon&itude

alt-az

Horion

Denith

"adir

Altitude

enith distance

parallel of altitude

!ertical circle

Principal Eertical

aimuth


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+ercise 9

From %t.Andrews$ at 6 pm on *22> February nd$ theoon appeared at altitude


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)he difference in aimuth is *=.

;se the cosine rule:

cos % 5 cos D cos D% < sin D sin D% cos D 5 1.2>

so % 5 *.9

)he oon is further east$ and hi&her up$ than %aturn.


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Coordinate systems: the firste@uatorial or GHA-dec.G system


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)he Hour An&le or HA 'H( of object is the an&ular distancebetween the meridian of and GtheG celestial meridian.

It is measured westwards in hours$ 1h-=h$ since the +arthrotates 961 in = hours.

)his system is still dependent on the time of obser!ation$but an object,s declination &enerally doesn,t chan&e rapidly$and its Hour An&le can be determined @uite simply$ &i!enthe time and the location.

A telescope can be built on an e@uatorial mountin&$ with itsais pointin& at the "CP.


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Coordinate systems: the seconde@uatorial or GA-dec.G system


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)he i&ht Ascension or A 'J( of object is the an&lealon& the celestial e@uator measured eastwards from the!ernal e@uino to the meridian of .

ike HA$ A is measured in hours 1-=h$ but it &oes in

the opposite direction.

)he i&ht Ascension and declination of a star do notnormally chan&e o!er short periods of timeK

but the Hour An&le chan&es constantly with time.

Conse@uently we ha!e to find a way of definin& the time.


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terrestrial alt-az HA-dec. RA-dec.

equator horizon celestial equator celestial equator

North Pole zenith North CelestialPole

North CelestialPole

South Pole nadir South CelestialPole

South CelestialPole

latitude altitude declination declination

co-latitude zenith distance North PolarDistance

North PolarDistance

parallel of latitude parallel of altitude parallel ofdeclination

parallel ofdeclination


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terrestrial alt-az HA-dec. RA-dec.

meridian oflongitude

vertical circle meridian meridian

GreenwichMeridian

PrincipalVertical

celestialmeridian

vernalequino

longitude azimuth !our "ngle #ight"scension


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%idereal )ime


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ocal %idereal )ime '%)(

e define ocal %idereal )ime '%)( to be 1 hours

when the !ernal e@uino Aries symbol is on the obser!er,s localmeridian.

#ne hour later$

the local Hour An&le 'HA( of the e@uino is


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ocal %idereal )ime '%)(

suppose that %) 5 *h.

)his means that the !ernal e@uino has mo!ed *0 '*h(west of the meridian$

and now some other star is on the meridian. 8ut the i&ht Ascension of star is the an&ular distance

from the !ernal e@uino to 5 *h 5 %).

%o at any instant

Local Sidereal Time = #ight Ascension of $hicheerstars are on the meridian


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In &eneral$

Local Hour Angle of a star =

Local Sidereal Time - #A of the star


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7ifferent obser!ers$ to the east or west$ will ha!e different stars ontheir local meridians.

e need to choose one particular meridian to act as a reference%ointK we choose &reen$ich.

e define the Breenwich Hour An&le of as the Hour An&le of relati!e to the celestial meridian at Breenwich.

)hen we can define Breenwich %idereal )ime 'B%)( as theBreenwich Hour An&le of the !ernal e@uino.

)his &i!es the important relation

LST = &ST - longitude $est


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Local Hour Angle 'LHA( of a star =

LST - #A of the star

&reen$ich Hour Angle '&HA( of a star =

&ST - #A of the star

LST = &ST - longitude $est

LHA'star( = &HA'star( - longitude $est


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+ercises

At midni&ht on *22> February =th$ ocal %idereal)ime at %t.Andrews was >h=0m. %t.Andrews haslon&itude =>, .

*.hat was the ocal Hour An&le of 8etel&euse '.A.5 0h00m( at midni&ht4

.At what time was 8etel&euse on the meridian at%t.Andrews4

9.At what time was 8etel&euse on the meridian atBreenwich4


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*. A of 8etel&euse 5 0h 00m$

At midni&ht$ %) 5 >h =0m

ocal Hour An&le 5 %) - A

so the ocal Hour An&le of 8etel&euse was >h =0m - 0h 00m 5 h01m.

*. #n the meridian$ ocal Hour An&le 5 1$

so if 8etel&euse was on the meridian at %t.Andrews$

%) in %t.Andrews 5 A of 8etel&euse 5 0h 00m.'ecall that %) 5 A of stars on local meridian.(


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9. %t.Andrews is =>, west of Breenwich 5 1h **m 'di!ide by*0(.

%o 8etel&euse was on the Breenwich meridian

** minutes before it reached the %t.Andrews meridian.i.e. at 1h 02m.


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Balactic coordinates


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Luestion

)he "orth Balactic Pole is at i&htAscension *h=2m$ declination


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+cliptic coordinates

All the objects considered so far ha!e been Gfied starsG$ which keepalmost constant !alues of i&ht Ascension and declination.

8ut bodies within the %olar %ystem chan&e their celestial positions.

)he most important one to consider is the %un.

)he %un,s declination can be found by measurin& its altitude when it,s onthe meridian 'at midday(.

)he %un,s i&ht Ascension can be found by measurin& the ocal %idereal)ime of meridian transit.

e find that the %un,s A increases by approimately = minutes a day$

and its declination !aries between


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)he ecliptic 'or celestial( lon&itude of 'symbol M( is thean&ular distance alon& the ecliptic from the !ernal e@uinoto the &reat circle throu&h .

It is measured eastwards 'like .A.($ but in de&rees$ 1-

961. )he ecliptic 'or celestial( latitude of 'symbol N( is the

an&ular distance from the ecliptic to $ measured from -21at O, to


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+ercise

)he oons orbit is tilted at 0>, to theecliptic. ould it be possible to obser!ethe oon as a circumpolar oon4 hat is

the lowest latitude from which the oonmay ne!er set4


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)he maimum hei&ht of the ecliptic abo!e the e@uator is Q 5, abo!e this$ i.e. up to 9,. %o theoon,s maimum declination is 9,.

An object of declination R will be circumpolar at latitude 21-R$i.e. at latitude 6*>,.

%o if the oon is at its &reatest possible declination$ it appearscircumpolar from any latitude north of 6*>,".

)he relation between ecliptic and


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)he relation between ecliptic ande@uatorial coordinates

)he relation between ecliptic and


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)he relation between ecliptic ande@uatorial coordinates

)he %un,s motion and its effect on


47/54

)he %un s motion$ and its effect ontime-keepin&

t it th idi ' (


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oon transit the meridian 'appro.(

At "ew oon$ the oon lies in the same direction as the %un. )he oon then mo!eseastwards$ relati!e to the %un.

It mo!es 961 in 2.09 days$ or about *. each day$ relati!e to the %unK whichcorresponds to la&&in& behind the %un$ as it crosses the sky$ by about =>.> minutes oftime each day.

If you know the Ga&eG of the oon$ you can calculate how much later the oon will crossthe sky$ compared to the %un.

)he %un crosses the meridian at noon$ so you can calculate the time at which the oonwill cross the meridian.

)he result will not be !ery accurate$ since the oon,s motion is not uniform$ but shouldbe correct to within an hour.

hen will the oon rise and set4


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hen will the oon rise and set4

)he %un declination !aries between 9.=" and 9.=%. At the e@uinoes$ the %un rises 6 hours before noon$ and sets 6 hours after noon.

)he oon follows rou&hly the same path as the %un$ but it takes only a month totrace the path which the %un takes in a year.

)he %un mo!es about * a day '961 in 960.0 days(.

)he oon la&s behind the %un by about *. a day$ so you can work out the dateon which the %un will be at the point where the oon now is.

)his means you can estimate rou&hly how lon& the oon will be abo!e the horion.

Ha!in& already calculated the time at which it will cross the meridian$ you can nowestimate its risin& and settin& times.

"ot be !ery accurate. 8ut it should be sufficient to determine$ for eample$ whethera particular ni&ht,s obser!in& will be affected by moonli&ht.

efraction


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efraction

%unrise sunset twili&ht


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%unrise$ sunset$$ twili&ht

)he %un is at declination -*=. hat will be its hour an&leat sunrise 'the moment the top ed&e of the %un firstappears o!er the horion($ at a latitude of


52/54

)he oon was "ew on 7ecember 0th$ 111. At%t.Andrews$ on Sanuary *st 11*$ the %un crossed themeridian at *:*0.

*. At what time did the oon cross the meridian4

. Bi!en the data in @uestion '*($ estimate the times ofmoonrise and moonset at %t.Andrews on Sanuary *st11*T


53/54

%aat melakukan ekspedisi$ kamu satu-satunya yan& selamatnamun terdampar di pulau terpencil den&an dibekali sebuahsekstan$ kronometer$ seekor merpati pos$ dan sebuah bukuSpherical Astronomy. Selaskan ba&aimana menyelamatkandiri den&an meminta pertolon&an yan& palin& se&era dapatdilakukanT 'An&&ap kronometer dalam waktu B)$ sehin&&akamu tahu tan&&al.(


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efraction Beocentric or diurnal paralla

Annual paralla

Aberration Precession

pembinaan2posastro - dr m irfan hakim.ppt

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