1. BASIC PROPERTIES of STARS - 2 Distances to the stars Stellar motions Stellar motions Sections 3.1 & 3.2, poorly Sections 3.1 & 3.2, poorly covered in the text covered in the text

2. DISTANCES to the STARS l Wide variety techniques to measure distances. l With increasing distance, each technique relies on measurements of nearer objects. l An error at one step translates through all subsequent steps. l “Nearby” objects  “Most distant” is a sequence of decreasing accuracy.

3. Astronomical Distance Pyramid

4. Distances inside Solar System Laser distance to Moon, radar distance to Venus. Radar timing to Venus gives accurate distance to Sun. Accuracy of a few cm (10 -8 % for Moon).

5. Some Laser Ranging Facts US Apollo manned missions to Moon left arrays of mirrors on Moon (late ‘60s - ‘70s) Like highway signposts Aiming to hit one of these like hitting dime With rifle from distance ~1 km Echo signal weak - only 1 in 10 18 photons sent is detected

6. Distances inside Solar System: Distance to the Sun Distances inside Solar System: Distance to the Sun Time radar returns (T distant + T nearest ) x c / 4 = E-S distance 1 Astronomical Unit (AU) = 1.49597870 x 10 8 km accuracy of about 100 1 Astronomical Unit (AU) = 1.49597870 x 10 8 km accuracy of about 100 m Orbit of Earth Orbit of Venus Closest approach of E and V Most distant E and V Sun

7. FlashcardsFlashcards Venus is about 105,000,000 km from the Sun. (1) What is approximate time to get the return signal from Venus when it is at its closest to Earth? C = 3 x 10 5 km/s (A 150; B 200; C 300; D 400 seconds) (2) What is the approximate time to get a return signal from Venus when Venus is at its most distant position? (A 850; B 1700; C 2550; D 3400 seconds) If (1) is 300 seconds and (2) is 1700 seconds, what is 1 AU in km?

8. Stellar Aberration & AU Stellar Aberration & AU Because of Earth’s motion, light from stars appears to come from a direction different from that if Earth were stationary. v<<c  displacement small tan  = v/c,  is the angle between direction motion and star Measure maximum  (20.5”) get v = 29.8 km/s Get AU = (29.8x3.2x10 7 )/2  = 1.5 x 10 8 km First measured in 1725 by Bradley

9. PARALLAX §3.1

10. PARALLAXPARALLAX With a Sun-centered Solar System and a moving Earth, objects outside the Solar System can potentially exhibit parallax. Whether we can measure it will depend on their distance. Tycho Brahe looked for parallax of the stars in the 1570’s as proof of the Copernican Theory. Did not see it - concluded that Earth did not move. Measurement accuracy 1’ whereas the parallax of nearest star < 1”.

11. STELLAR PARALLAX

12. STELLAR PARALLAX §3.1 Only direct way of getting distances to stars Smaller the parallax, farther is star Over year star, describes ellipse on sky (special cases: circle at pole, line if in ecliptic) - semi major axis is parallax (  ) Unit of distance is parsec (pc) defined so that at 1 pc star subtends angle 1” on E-S baseline From small angle formula: 1” = 1 AU / 1 pc  1/206265 = 1AU / 1parsec  1 pc = 206265 AU = 3 x 10 13 km D = 1/ ,  in “, D in pc; nearest star:  = 0.762”, 1.31 pc (limit 100 pc)

13. STELLAR PARALLAX Distance measurements possible with various baselines

14. Parallax and position Position of star Position of star determines the determines the parallax effect

15. Bessel Measures Stellar Parallax 1838! 61 Cygni Parallax 0.314” Manhattan taxi as viewed from Mexico City Mexico City

16. STELLAR PARALLAX §3.1 Only direct way of getting distances to stars Smaller the parallax, farther is star Over year star, describes ellipse on sky (special cases: circle at pole, line if in ecliptic) - semi major axis is parallax (  ) Unit of distance is parsec (pc) defined so that at 1 pc star subtends angle 1” on E-S baseline From small angle formula: 1” = 1 AU / 1 pc  1/206265 = 1AU / 1parsec  1 pc = 206265 AU = 3 x 10 13 km D = 1/ ,  in “, D in pc; nearest star:  = 0.762”, 1.31 pc limit 2-300 pc

17. Aside: Stellar Motions p.16-17 l Before continuing with distances we must have a small diversion and discuss stellar motions. l Beyond apparent motion due to parallax, many stars exhibit motion in a constant direction - proper motion. l Velocity of a star can be divided into 2 components. V t is tangential velocity V r is the radial velocity

18. RADIAL VELOCITIES Data obtained with spectrograph  / o = v/c Velocities of stars in our Galaxy range up to +/- 300 km/sec. A few up to 600 km/s (escape velocity from Galaxy). Typical for stars in disk is 30 km/sec.

19. PROPER MOTIONS p.17 Measured over a period of years from direct images. Unit is “/year. Largest measured Barnard’s star 10.25”/year. Few 100 stars with PM > 1”/year. Note that PM will depend on distance.

20. Effect of proper motions

21. Parallax and position This shows how parallax and proper motion are distingushed. Parallax repeats Itself yearly while proper motion does not. Solve for both simultaneously.

22. Back to distances Star Clusters Back to distances Star Clusters Clusters are groups stars formed at same time in same region space - gravitationally bound. More later.

23. Moving Cluster Method Distance Determination §16.2 Moving Cluster Method Distance Determination §16.2 Taurus and the Hyades: Pleiades at top, Saturn to left, Aldebaran is not a member Taurus and the Hyades: Pleiades at top, Saturn to left, Aldebaran is not a member.

24. Moving Cluster Method Distance Determination Moving Cluster Method Distance Determination Raphael Santi’s “The School of Athens” 1511

25. Moving Cluster Method Distance Determination Moving Cluster Method Distance Determination

26. True space velocity = v Radial velocity = v rad Tangential velocity = v t v t = 4.74  r v rad = v cos  v t = v sin  v t /v rad = tan  Thus: r = v rad tan  / 4.74  Do this for every star in cluster average r values to get distance

27. Moving Cluster Method Distance Determination Moving Cluster Method Distance Determination By measuring PMs, radial velocities, and the best position of the convergent point of stars in the Hyades, we derive the distance to the cluster. d hyades = 47 +/- 4 pc (8% precision cf Venus) Limit of technique ~100 pc Hyades cluster is one of fundamental calibrators of stellar distances - do with parallax and moving cluster.

28. A Problem The proper motion of Aldebaran is  = 0.20 ” /year The parallax of Aldebaran is  = 0.048 ” A spectral line of iron at = 440.5 nm is displaced 0.079 nm towards the red. What are radial, tangential and total velocities?