天文觀測 i coordinate, time & name. 古老的科學天文學是一門古老的科學 –...

天文觀測 I

Coordinate, Time &Name

古老的科學

• 天文學是一門古老的科學– 幾乎所有的古文明都對天文有其傳承。

• 古老的科學至今仍能存在，通常有下面的過程：– 定性 ( 半量化 ) 量化– 以星星亮度為例

• 亮的星，暗的星 ( 定性 )• 星等 ( 一等星、二等星…… )

– 較隨意的指定– 無小數部分

• 較嚴格定義星等– 每星等差 2.5 倍 (log scale)– 有小數部分

尊重傳統的科學

• 天文學的另一特色 : 尊重傳統– 如果傳統不太影響科學研究

• 以星等為例，它“不太方便”，但至今仍使用它– 數字小者亮，數字大者暗，與一般觀念相反– Log scale ( 源自於肉眼對光之反應 ) ，非線性 scale– 某些“新”的天文學已“更正”這個習慣，如 X-ray 天文學用

erg/s/cm2 來表示亮度。• 其它如距離等都有類似現象 ( 光年，秒差 ) ，弄到天

文學好像變得很複雜。– 要學會“行話”。– 不同波段的研究者有不同的“行話”。– 習慣就好。

星星的位置

• 古代 : 定性描述– 文字：星星的特性，出沒時間– 星圖，星區……

• 三垣、四象、廿八宿……

– 星座• 獵戶、蛇夫……• 辨認星座 ( 肉眼觀測第一課 )

• 依星座命名– 1603 年，貝葉 (Johannes Bayer) 使用星座中最亮叫，

次亮叫……– 不在星座 ( 連線 ) 上的呢 ?

天區

• 為統一星星屬於哪一個星座，國際天文聯合會(International Astronomical Union, IAU)1930 年宣布將全天空依星座位置劃分為 88 個天區。

• 星座雖是在古希臘就開始定義，但至今仍在天文中廣泛應用。– 如變星的命名– SU UMa, DQ Her, V1445 Aql– 其後面三個字母就是變星所在天區。

位置的定量—天球座標

• 上述方法仍未能精確描述星星的位置。• 引入類似地球經緯度或數學上球座標概念描述星星位

置。– 恆星位置原為一三度空間問題。– 但由於距離量測在天文中是一大問題，暫時不管。– 因此星星的位置變成一個二度空間的問題，需要二個述來描

述其位置。– 星星好似“嵌”在天球上，因此可用二個“角度”來描述其位置。– 這二個角度必須先有“參考位置 ( 方向 )”( 原點，零點 ) ，才可

定義。• 如球座標的零點為 z 軸

常用的天文座標系統

• 依不同零點之定義，天文上慣用於描述天體位置的座標有• 地平座標系• 赤道座標系• 黃道座標系• 銀河座標系

• 不同的座標系有不同的用途• 所有座標系角度的算法都與地球經緯度相類似

http://upload.wikimedia.org/wikipedia/commons/1/1c/Celestial.gif

地平座標系

• 一個完全以觀測者 ( 或天文台 ) 為觀點之座標系。– 不同的觀測者在不同的位置有不同的地平座標系統。– 同一個天體同一時間對不同地點的觀測者有不同的的

地平座標。– 由於地球在旋轉，天體的地平座標原則上隨時在變。– 地平座標有時也用在其它方面 ( 如航海 )

Horizon Coordinate (地平座標系 )

Earth

Zenith

N

E

S

W

Horizon Coordinate

• Two angles– Altitude, a– Azimuths, A

• X: location of star• B: projection of X on

horizontal plane• Angle from B to X :

altitude (a, 0º to 90º)• Angle between N to B :

azimuths (A, 0º to 360º)• Azimuth direction :

– N E S W

N

E

ZX

B

Great circle

Horizon Coordinate

地平座標系的應用

• 天體在地平座標隨時而變，它的應用為何 ?• 圓頂的連動

– 無論望遠鏡的 mount 為何形式，圓頂必跟著地平座標(Azimuths)而動

• Alt-Az形式的mount– 製作容易– 機械運動簡單– 容易平衡 (可載較重儀器 )– 可加儀器在 Nysmith foci– 大型望遠鏡大多採使依形式

Equatorial Coordinate ( 赤道座標系 )

• Also named Celestial Coordinate.

• The Earth is a pretty good gyroscope so its axis points a constant in inertial space (??).

• For an observer on ground, the stars look like rotating about an axis passing through the North Celestial Pole to South Celestial Pole.

• Declination (δ or DEC，赤緯 ): North Celestial Pole=+90º; equator= 0º ; South Celestial Pole= -90 º

• The other longitude-like coordinate called “right ascension” (α, RA, 赤經 ) whose zero point is defined as the location of the Sun on the vernal equinox (also called “first point of Aries”.

Equatorial Coordinate

Equatorial vs. Horizon Coordinate

Equatorial Coordinate

• α : hour minute second– 1 circle = 24 hours; 1 hour= 60 min; 1 min= 60 sec

• Why the RA uses such strange expression instead of the convenient degree?– In fact, you may imagine the celestial sphere is like a clock on

sky rotating with period of 1 sidereal day (~23 hrs 56 min). The RA value on the meridian is the local sidereal time.

• δ: degree (º) arcmin(`) arcsec(“)– Degree: -90º (South)-- 90º (North); 1 deg=60 arcmin;

1arcmin=60 arcsec

Precession of Equinox (歲差運動 )• Actually the rotational axis of the Earth is not fixed in the

inertial space.• Since the mass distribution of the Earth is not spherical

symmetry, due to the inclination between the plane of ecliptic and plane of equator (~23.5º), the Earth rotational axis precesses with period of 25800 years caused by the gravitational torque from the Moon and Sun.

• Thus the RA and DEC value of an astrophysical object is in fact change from time to time (change by tenths of arcsec per year).

• To correctly locate the source, the equatorial coordinate system renews every 50 year (called epoch).– J2000, B1950

• To express the location of a source, the epoch of coordinate system must be specified

Precession of Equinox

注意 epoch• 觀測時要注意使用的 epoch,否則目標可能完全不

在視野 (Field of View, FOV)內– 以鹿林一米望遠鏡為例 :P1300視野約 13 角分。– 若觀測 Cyg X-1 , 以 B1950 epoch當做 J2000 epoch 將

有 24.5 角分 (0.47 度 ) 之差。• 問題：歲差運動是連續的，也就是說就算我用

J2000 epoch也未必能將光軸 ( 影像中心 ) 指向目標。– 的確是，但現在用 J2000 epoch 應該是最接近的了，目

標應在視野之內，這時就要用尋星圖 (Finding Chart)比對，再將目標微調到視場中央。

– 我們應該用最接近的 epoch ，如在 2025 年後就應該用2050 epoch ，所以 2050 epoch 應在十年左右發佈。

Ecliptic Coordinate

• Ecliptic coordinate: base on the orbit of the Earth about the Sun. It is almost identical to the equatorial coordinate except the north pole is define as the ecliptic north pole.– Ecliptic longitude: λ (degree (0 to 360), arcmin, arcsec )

– Ecliptic latitude: β (degree (-90 to 90) ), arcmin, arcsec )

– The Sun: β=0, rotates 360º per year alone the ecliptic equator.

– Most of solar system objects lie on the low Ecliptic latitude

Ecliptic Coordinate

Galactic coordinate

• Galactic coordinate:– Equator: galactic plane

– Zero point: galactic center

– Galactic longitude: l (degree, 0 to 360)

– Galactic latitude: b (degree -90 to 90 )

– Galactic center at about (,)=(17h 45m 37.224s −28° 56 10.23″′ )• In southern hemisphere

• Observable but not very good in Taiwan

– Galactic north pole at about (,)=(12h 51m 26.282s +27° 07 42.01″′ )– Most of galactic objects locate around b=0

– Budge objects: small B and l either close to 0 or close to 360

Galactic Coordinate

Celestial north

Galactic Coordinate

Distribution of pulsars: concentrated on the galactic plane,especial near b=0º since they are galactic sources.

Galactic Coordinate

Distribution of γ-ray burst: not concentrated on the galactic plane. They are probably not the galactic source

Expressions of Source Location

h min sec

h min sec

Crab:

Equatorial coordinate:

RA=5 34 31.97 DEC=22 0 52.1 (J2000)

(J2000)=5 34 31.97 (J2000)=22 0 52.1

Ecliptic coordinate

=84 5 51.4 = -01 17 52.1

Galactic coordinate

184 33 27.2 b= -5 47 3.4 (rarely used)

184.5575 b= -5.7843 (often used)

l

l

Angular Separation• How to describe the separation of two sources : angle• How to calculate the angular separation of the two

sources?

1 1 2 2

1 1 1 1 1 1

2 2 2 2 2 2

1 2

Source 1: , ; Source 2: ,

Unit vector for source 1 and 2:

ˆ ˆ ˆ ˆcos cos cos sin sin

ˆ ˆ ˆ ˆcos cos cos sin sin

The angular separation

ˆ ˆcos

r x y z

r x y z

r r

Angular Separation

• However, the equation above is not sensitive to small angle since for small θ , which is a 2nd order approximation.

• Alternatively , for small angular separation, we use:

2cos 1 2

1̂r

2̂r

1 2ˆ ˆr r

1 2ˆ ˆr r

2

1 2ˆ ˆ 2r r

1 2ˆ ˆ 2r r

1 2

1 2

ˆ ˆtan

ˆ ˆ2

For small

tan2 2

which is 1st order approximation

r r

r r

Radian vs. degree

• The angle obtained above is in radian, which used mostly in math (calculus)

• The applied angle system is in degree (arcmin, arcsec)

6

1 circle = 2 rad = 360

1 rad=57.296 3437.7 ' 206265"

1" 1/ 206265 rad 4.85 10 rad

Solid Angle

• How do we describe an observed size of a extended source?

• How do we describe the FOV if FOV is not a rectangular?

• Solid angle:

2

2

2

ˆ ˆ

ˆ : unit vector of line-of-sight

ˆ : normal vector of area A

R: distance

The unit of solid angle is steradian (sr)

The whole sky:

44

r ndAd

Rr

n

R

R

RdA

n̂r̂

Solid Angle• However, we sometimes prefer use square degree ……

2

2

2 2

180square degree = sr

180: radius of a unit in degree

Whole sky

1804 41252.96 40000 square degrees

Extended source

(on image)(deg ) (deg )

(on image)source

source fovfov

AS S

A

Time

• Calendar date– 2002 Feb 3rd …..

• Year + date number– 2002, 1=2002 Jan 1st (no 2002, 0)

– 2002, 34=34th day of 2002=2002 Feb 3rd

– 2002, 34.3=2002 Feb 3rd 07:12:00

• UT=Universal time, count from 0h at midnight. Unit is mean solar day.

Julian Day

• Julian Day (JD) or Julian date number– Reference epoch: 4713 BC Jan 1st at Greenwich mean

noon.

• Julian date may be a real number instead of an integer

• Julian day is too long fro present application.

• Modified Julian Day = MJD = JD-2400000.5

• Truncated Julian Day = TJD = JD-2440000.5 = MJD-40000– Note: both references of MJD and TJD are at midnight

Julian Day

• Some Julian days– 1900 Jan 1st at UTC00:00:00 = JD2415020.5– 1990 Jan 1st at UTC00:00:00 = JD2447892.5– 1995 Oct 10th at UTC00:00:00 = JD2450000.5=MJD50000– 2000 Jan 1st at UTC00:00:00 = JD2451544.5– 2010 Jan 1st at UTC00:00:00=JD2455197.5– 2023Feb25th at UTC00:00:00.00

=JD2460000.5=MJD60000

Time System

• The time system we use everyday is basically form the motion of celestial bodies– Like the day is define by the motion of the Sun observed

on the Earth, in fact, spin of the Earth (plus orbital motion of the Erath).

• However , the Earth is not a good time keeper– In additional to short term fluctuations (~1 ms day to

day), there is long-term drift.• Because of tidal force form the Moon and the Sun, there

friction between Ocean and the other solid part of Earth’s surface. Since the angular velocity for the Moon orbiting the Earth is much smaller than the Earth’s spin angular velocity, the Earth rotation is slow down.

Time System• UT: Universal Time:

– a kind of ET motion of the Sun as observed on Greenwich meridian, longitude 0˚ (mean value).

– However, the Earth is not a good time keeper ( )

• TAI: International Atomic Time– Present standard and a good time keeper.

• Because TAI is standard but UT is more match human life, people define UTC to coordinate both system

• UTC=Coordinate Universal Time– Synchronized with TAI but add “leap second” to match UT.

– Leap second is integer

Sidereal Time (ST)

• UT is defined by the motion of the Sun observed on the Earth

• ST is defined by the motion of distant stars observed on the Earth.

• 1 year=365.2422 solar day. But the Earth rotates 366.2422 revolution about its own axis.

• 1 year=366.242 sidereal day

Sidereal Time (ST)

• We still define– 1 sidereal day= 24 sidereal hours

– = 24 X 60 sidereal minutes

– = 24 X 60 X 60 sidereal seconds

• A sidereal day (hour, minute, second) is slightly smaller than a solar day (hour, minute, second).– 1 sidereal day 23h 56m

– 1 sidereal day=86164.0905 seconds

– 1.002737909 sidereal day=1 solar day

Sidereal time an RA

• Since sidereal time is defined by the motion of distant star observed on the Earth– Sidereal time RA

• GST– Greenwich sidereal time: the sidereal time at Greenwich

– The RA value of celestial meridian at Greenwich– At vernal equinox GST=0h 0m 0s

– At autumnal equinox GST=12h 0m 0s

• GST and UT agree at autumnal equinox every year

Local Sidereal Time

• LST– Local sidereal time

– LST= the RA value of celestial meridian at observer’s location.

– LSTs are different for observers at different geographical longitude.

Coordinate conversions• Basically, coordinate conversion among equatorial,

eclipse and galactic coordinates are independent of time so that the transformation formula are fixed.– They can be derived by matrix method.

• Or from web resources …….

Coordinate conversions

• Conversion Horizon to (or from ) other coordinates is more complex

• For example, if you want to convert a star’s equatorial coordinate to horizon coordinate, you need to know– RA, DEC of the source (definitely)

– Location of your telescope (geographic longitude and latitude)

– Local Time • Not the time on your watch because it is the time of time zone

• Using LST is prefer because it is highly related to the source location.

Hour angle

• Hour angle: H=LST-

Coordinate conversions

• The observer is at geographical latitude • The conversion for altitude in horizontal

coordinate

• The conversion for azimuths in horizontal coordinate

– If

– If

sin sin sin cos cos cosa H

sin 0H 1 sin sin sin

coscos cos

aA

a

sin 0H 1 sin sin sin

2 coscos cos

aA

a

Names of Astrophysical Sources

Names of Astrophysical Sources

• Names of astrophysical objects are rather complicate. A source with more than 10 names is often seen.

• Basically name of a source may come from:– Traditional conversion– Source location (constellation, celestial coordinate …..)– Characteristic of source (supernova, GRB, pulsar ……)– Catalog/survey– Time of discovery– Etc.

Several ways to name an astrophysical object

• Common names– For example, Polaris, Sirius

• Bright star name: Greek letter + constellation name (by Johannes Bayer in 17th centrury)– For example, α Leo, β Cyg, γ Cas

– Sorted by their brightness in the constellation

– Usually in same constellation, α brighter than β, β brighter than γ ……

– However, there are only 24 Greek letters

– So then a,b,c,……,z, A,B,C……,Z


• Bright star name: Number + constellation name (by John Flansteed & Joseph LaLande in 18th centrury)– Sorted by its location of its constellation

– 1, 2, 3 …… from east to west

– Taking織女星 as example• Vega (common name)

• Lyrae (Greek letter + constellation name )

• 3 Lyrae (Number + constellation name)

• But there are more stars ……

Several ways to name an astrophysical object• Catalog + index number, for example

– HD 197433 GD: Henry Draper catalog

– SAO 113271 SAO: Smithsonian Astrophysical Observatory

– NGC 4151 NGC: New General Catalog

– M 31 Messier catalog

• Catalog + DEC + index number– For example, BD+75˚ 752 BD: Bonner Durchmusterung

• Number + Catalog + index number– For example, 3C273

• “3” the third version (third survey)

• C: Cambridge Radio catalog

Several ways to name an astrophysical object• X-ray sources

– Old name (bright X-ray sources): constellation + ”X-” + index number• For example, Sco X-1, Cyg X-3

– [number] + catalog + RA + DEC• Catalog: usually the name of observatory which found the source in X-ray

band

• RA: If with “J” in front of it, it mean using 2000 epoch, otherwise, 1950 epoch

• RA + DEC: not very precise

• For example: 4U 2127+119: “4”, the 4th version (4th survey), U: Uhuru (all-sky survey) catalog 2127, RA= 21h 27 min, +119: DEC=11.9˚

• SAX J1808.4-3658

– The sources near galactic center: “GX” + l +b• For example: GX 9+9, GX339-4


• Name of radio pulsars “PSR” + RA + DEC– PSR B0531+219 = PSR J0530+200 = Crab pulsar

• B=1950 epoch, J=2000 epoch

• Supernova “SN”+ year + ordering letters– For example: SN 1054 A

– Ordering letters: A,B,……Z, aa,ab,……,az,ba,bb,……

• Gamma-ray burst: “GRB” + date + [ordering letter]– For example, GRB990123, GRB010222


• Variable stars: IAU appointed a committee to determine the names of variable stars:– If a variable star has a proper of Greek name,

the star is referred by its original name.

– Otherwise, ordering letter + constellation or “V”+ ordering number + constellation.


• Ordering letter– R, S, T, U, V, W, X, Y, Z up to 9th

– And then two letters starting from RR

• RR, RS, ……,RZ

• SS, ST, ……,SZ

• TT,……

• ……

• ZZ

• Up to 54th


• And then– AA, AB, AC, ……,AZ

– BB, BC, ……,BZ

– ……

– QQ, QR,……,QZ

– No “J” because it is too easily confused with “I”

– Up to 334th

• More variable stars in a constellation is named “V”+ ordering number + constellation starting from V335– V335, V336,……

天文觀測 i coordinate, time & name. 古老的科學 天文學是一門古老的科學 –...

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天文觀測 i coordinate, time & name. 古老的科學天文學是一門古老的科學 –...