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

2. 2 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)

3. 3 II-1a. Stellar Distance Stellar Parallax : = Apparent motion 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. 4 Fig. II-2: Stellar Parallax

5. 5 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 10 11 m Parsec (PC): Distance at which 1 AU subtends Angle of 1 second 1 pc (parsec) = 206625 AU = 3.086 x 10 16 m = 3.262 ly Light Year (ly): Distance light travels in 1 year 1 light year (ly) = 63240 AU = 9.46 x 10 15 m

6. 6 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

7. 7 EX 2: Barnard’s Star Barnard’s star has a parallax of 0.547 arcsec See class notes for details

8. 8

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

10. 10 V

11. 11 Doppler shift: see class notes and FK Sec. 5-9, and Box 5-6 d vrvr vTvT

12. 12 TRANSVERSE VELOCITY v T v T = 4.74  / p Eqn (2b) v T in km/s;  in arc second/year; p in arc second SPACE VELOCITY v v 2 = v r 2 + v T 2 Eqn(2c) Study Examples in FK Box 17-1 (Non-science majors optional) RADIAL VELOCITY v r v r / c = ( – 0 ) / 0 =  / 0 Eqn(2a) Non-relativistic (see FK 5-9)

13. 13   for

14. 14 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/m 2 ) Area: A = 4  d 2 Eqn (3) d = distance

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

16. 16 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 10 26 W ; d (sun) = 1.5 x 10 11 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 (5a)

17. 17 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  L 1 / L 2 = (d 1 / d 2 ) 2 (b 1 / b 2 ) Eqn (5c) *2 d1d1 d2d2 22 11 Fig. II-4b: The Inverse-Square Law (conti.)

18. 18 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.