Measuring Distance to a Star

1. Measuring Distance to a Star Height of Flag Pole Stellar Parallax Spectroscopic Parallax

2. Measuring the Height of the Flag Pole

3. Do Now • How do you tell if something is closer or father away?

4. Distance to flag pole

6. Tangent • Angle from Rico’s eyes to top of flag pole= 45 degree

7. How do we calculate the distance to the stars?

8. Parallax • An object appears to shift position when the observer moves.

9. Stellar Parallax • The nearby stars will appear to move relative to the background stars • Use trig to find the distance • Tanθ= D/orbital radius http://abyss.uoregon.edu/~js/glossary/parallax.html

10. Animation • http://highered.mcgraw-hill.com/olcweb/cgi/pluginpop.cgi?it=swf::800::600::/sites/dl/free/007299181x/78778/Parallax_Nav.swf::Stellar%20Parallax%20Interactive

13. Now you try it: Calculate the distance to the star if • a) the angle is 47 degrees and the baseline radius is 15 AU. • b) the angle is 78 degrees and the radius is 16 AU. • What is the relation ship between the angle and the star distance? 

14. Cork Activity Lab

21. Calculating Error • Compare your measurements or calculations to the actual (accepted) value % Error = measure – accepted x 100 accepted • In this case, = measured – calculated X 100 measured

22. http://astro.unl.edu/naap/distance/parallax.html • Stars are very far away – yet some stars are closer than others. Do these closer stars exhibit parallax? The answer turns out to be yes, but the parallax is very small – far smaller than can be seen with the naked eye. The first successful measurements of a stellar parallax were made by Friedrich Bessel in 1838, for the star 61 Cygni.

23. Hipparcos and Gaia Satellites • Before Hipparcos, literally only a hundred or so parallactic angles were known to any accuracy • Hipparcos (1989 to 1993)- measured a parallactic angle of about 0.001 arcsecond.. giving the distances to several thousand stars to < 5% error. • Gaia (Global Astrometric Interferometer for Astrophysics) - increase the angular resolution of Hipparcos by a factor of over a 1000.

24. To find distance calculate the Distance Modulus • Distance Modulus is (m-M) • Where • m = apparent magnitude • M = absolute magnitude where D is the distance in parsecs Distance Modulus (m-M) Where m = apparent magnitude And M = absolute magnitude

25. Spectroscopic Parallax • Assumption- stars with the same spectral class and pressure class have the absolute magnitude

26. Spectroscopic parallax

27. What is a parsec?

28. http://astro.unl.edu/naap/distance/parallax.html

29. http://astro.unl.edu/naap/distance/parallax.html

30. Parsec • The basic unit for measuring astronomical distances. • One second of arc of parallax • 1 second of arc (1") = 1 / 3600 degrees • Equivalent to 3.26 light years

31. From the figure above, the distance between the Sun and the star is : d = r / tan P

32. If P is 1 second of arc: • d = 150,000,000 / tan 1" • = 30 million million km

33. For the star above, the parallax angle - P is half the distance moved by the star between photos. Therefore P = 0.5 / 2 = 0.25 seconds of arc. How to calculate the distance to a star

34. Distance in parsecs = 1 / P • Where p is in seconds of arc

35. For the star in the figure above: d = r / tan P We know that for very small angles, tan P = P. So d = 1 / P = 1 / 0.25 = 4 Therefore the star is four parsecs away.

36. m – M = 5 log (D/10) Where D is distance in parsecs