1. 1 Trigonometric Parallaxes William van Altena Yale University Basic Astrometric Methods Yale University July 18-22, 2005

2. 2 The Geometry

3. 3 More Geometry

4. 4 Yes, the Earth moves around the Sun!

5. 5 Parallactic motion in Ecliptic Coords

6. 6 The Parallactic Ellipse

7. 7 Parallax in RA and Dec

8. 8 Parallax in RA and Dec (cont.)

9. 9 Observational Techniques

10. 10 Maximum Parallax Factor

11. 11 Ecliptic Latitude Dependence

12. 12 Determination of π & µ

13. 13 Typical analysis “pipeline”

14. 14 Typical analysis “pipeline” (cont.)

15. 15 Solving for a single π

16. 16 Errors and weights

17. 17 Errors and weights (cont.)

18. 18 Errors and weights (cont.)

19. 19 Reference stars

20. 20 Atmospheric Refraction

21. 21 Effective wavelength of each star

22. 22 Refraction versus star color

23. 23 Correction to Absolute π

24. 24 Systematic errors

25. 25 External error sources

26. 26 Deriving external errors

27. 27 Parallax Programs CatalogDate#stars  mas) Comments YPC19958112±15 masCat. of all π through 1995 USNO pgTo 1992~1000±2.5 masPhotographic parallaxes USNO ccdFrom ‘92~150±0.5 masCCD parallaxes Nstars & GBCurrent100?± 2 masSouthern π programs Hipparcos199710 5 ±1 masFirst modern survey HST FGS1995-2010?100?±0.5 masA few important stars SIM2016?10 3 ±4 µasCritical targets & exoplanets Gaia2016?10 9 ±10µas“Ultimate” modern survey

28. 28 References for Parallax Programs CatalogCommentsReferences YPCCat. of all π through 1995van Altena, Lee & Hoffleit 1995 USNO pgPhotographic parallaxesDahn, Harrington, et al USNO ccdCCD parallaxesMonet, Dahn, et al. AJ,103,638,1992 Nstars & GBSouthern π programsHenry, Jao, Ianna, Costa, Mendez, … HipparcosFirst modern surveyESO HST FGSA few important starsBenedict & HST FGS Team SIMCritical targets & Exo-planetsNASA/JPL Gaia“Ultimate” modern surveyESO