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ASTRONOMY 373

INTRODUCTION TO ASTRONOMY –

Stars, Galaxies, & Universe

Spring 2015

Sachiko Tsuruta

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Lec 1

I. INTRODUCTION FK (= Freedman, Geller & Kaufmann 10th Edition) Ch. 1)

II. INTRODUCTION TO CLASSICAL ASTRONOMY

II-1. Stellar Distance and Stellar Motion (Main Ref.: Lecture notes; FK Sec.17-1)

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II-1a. Stellar Distance

Stellar Parallax: = Apparentmotion of a star due to Earth’s annual motion = Angular size of semi-major axis of the orbit of Earth around Sun

Fig. II-1: Parallax

4 Fig. II-2: Stellar Parallax

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Units of Distance:

Use mks system: length=meter, mass =kgm, time=sec

Astronomical Unit (AU): Distance from the earth to the sun = semi-major axis of the orbit of Earth around Sun

1 AU = d(sun) = 1.5 x 1011 m

Parsec (PC): Distance at which 1 AU subtends Angle of 1 second

1 pc (parsec) = 206625 AU = 3.086 x 1016 m = 3.262 ly

Light Year (ly): Distance light travels in 1 year1 light year (ly) = 63240 AU = 9.46 x 1015 m

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DISTANCE

d (pc) = 1 / p(sec.) Eqn (1)

•Distances to the nearer stars can be determined by parallax, the apparent shift of a star against the background stars observed as the Earth moves along its orbit

*****************************************************EX 1: Alpha Centauri

•p = 0.76 sec

•d = 1 / p = 1 / 0.76 = 1.32 pc = 4.29 lys

See class notes for details

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EX 2: Barnard’s StarBarnard’s star has a parallax of 0.547 arcsec

See class notes for details

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9Fig. II-3: Stellar Velocity

II-1b Stellar Motion

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V

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Doppler shift: see class notes and FK Sec. 5-9, and Box 5-6

d

vr

vT

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• TRANSVERSE VELOCITY vT vT = 4.74 / p Eqn (2b)

• vT in km/s; in arc second/year; p in arc second

• SPACE VELOCITY v v2 = vr

2 + vT2 Eqn(2c)

Study Examples in FK Box 17-1 (Non-science majors optional)

•RADIAL VELOCITY vr vr / c = ( – 0) / 0 = / 0 Eqn(2a)

Non-relativistic (see FK 5-9)

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for

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II-2. Stellar Brightness, Magnitude, and Luminosity

(Main Ref.: Lecture notes; FK Sec.17-2, 17-3)

II-2a. Brightness and Luminosity (Main Ref.: Lecture notes; FK Sec.17-2, Box 17-2) Definitions: Luminosity: L = energy/sec = Power Output

(Watts = W) Brightness: b = Luminosity/surface area (W/m2) Area: A = 4 d2 Eqn (3) d = distance

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Inverse Square Law

b = L / A = L / (4 d2) 1/d2 Eqn (4)

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Fig. II-4a: The Inverse-Square Law

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EX 3: Candle at 10 m and 100 m Ans: At 10m 100 times brighter

See class notes for details

EX 4: Sun

L(sun) = 3.86 x 1026 W ; d(sun) = 1.5 x 1011 m; Use Eqn (4), and get

Ans: b(sun) = 1370 W/m2

See class notes for details

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From Eqn (4) L = 4 d2 b Eqn (5a)

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Divide Eqn(5a) for star by that for sun L / L(sun) = (d / d(sun))2 (b / b(sun)) Eqn (5b)

Do the same for Star *1 and Star *2

L1 / L2 = (d1 / d2 )2 (b1 / b2) Eqn (5c)

*2 d1

d2

21 Fig. II-4b: The

Inverse-Square Law (conti.)

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EX 5: Sirius A: d = 8.61 ly; L = 26.1 L(sun);

What is brightness b?Ans: 8.79 x 10-11 brightness of Sun (See class notes for details.)

*********************************EX 6: Star *1 and Star *2 (same brightness: b1 = b2 = b)

Star 1: L1 = 1 L(sun); Star 2: L2 = 9 L(sun)

How far is Star 2 compared with Star 1?Ans: 3 times further away.(See class notes for details.)

Study more examples in FK Box 17-2.