ASTRONOMY 373 INTRODUCTION TO ASTRONOMY Stars Galaxies Universe

ASTRONOMY 373 INTRODUCTION TO ASTRONOMY – Stars, Galaxies, & Universe Spring 2015 Sachiko Tsuruta 1

Lec 1 I. INTRODUCTION FK (= Freedman, Geller & Kaufmann 10 th Edition) Ch. 1) II. INTRODUCTION TO CLASSICAL ASTRONOMY II-1. Stellar Distance and Stellar Motion (Main Ref. : Lecture notes; FK Sec. 17 -1) 2

II-1 a. Stellar Distance Stellar Parallax: = Apparent motion of a star due to Earth’s annual motion = Angular size of semimajor axis of the orbit of Earth around Sun Fig. II-1: Parallax 3

Fig. II-2: Stellar Parallax 4

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 year 1 light year (ly) = 63240 AU = 9. 46 x 1015 m 5

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 6

EX 2: Barnard’s Star Barnard’s star has a parallax of 0. 547 arcsec See class notes for details 7

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II-1 b Stellar Motion Fig. II-3: Stellar Velocity 9

V 10

vr Doppler shift: see class notes and FK Sec. 5 -9, and Box 5 -6 v. T d 11

• RADIAL VELOCITY vr vr / c = ( – 0) / 0 = / 0 Eqn(2 a) Non-relativistic (see FK 5 -9) • TRANSVERSE VELOCITY v. T = 4. 74 / p Eqn (2 b) • v. T in km/s; in arc second/year; p in arc second • SPACE VELOCITY v v 2 = vr 2 + v. T 2 Eqn(2 c) Study Examples in FK Box 17 -1 (Non-science majors 12 optional)

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II-2. Stellar Brightness, Magnitude, and Luminosity (Main Ref. : Lecture notes; FK Sec. 17 -2, 17 -3) II-2 a. 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/m 2) Area: A = 4 d 2 d = distance Eqn (3) 14

Inverse Square Law b = L / A = L / (4 d 2) 1/d 2 Eqn (4) ******************* Fig. II-4 a: The Inverse-Square Law 15

EX 3: Candle at 10 m and 100 m Ans: At 10 m 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/m 2 See class notes for details **************************** From Eqn (4) L = 4 d 2 b Eqn (5 a) 16

Divide Eqn(5 a) for star by that for sun L / L(sun) = (d / d(sun))2 (b / b(sun)) Eqn (5 b) Do the same for Star *1 and Star *2 L 1 / L 2 = (d 1 / d 2 )2 (b 1 / b 2) 2 *2 1 d 2 Eqn (5 c) Fig. II-4 b: The Inverse-Square Law (conti. ) 17

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: b 1 = b 2 = b) Star 1: L 1 = 1 L(sun); Star 2: L 2 = 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. 18