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Motions of and Distances to Stars: Chapter 17 and 19

The ancients thought the stars were motionless and fixed to the firmament, unimaginably far, far away…. Motions of and Distances to Stars: Chapter 17 and 19. How can you guess the distance to stars?. Review: Angles. sin = opposite hypotenuse. cos = adjacent

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Motions of and Distances to Stars: Chapter 17 and 19

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  1. The ancients thought the stars were motionless and fixed to the firmament, unimaginably far, far away… Motions of and Distances to Stars: Chapter 17 and 19 How can you guess the distance to stars?

  2. Review: Angles sin = opposite hypotenuse cos = adjacent hypotenuse  hypotenuse tan = opposite adjacent adjacent 1 radian=2x105 arcsec opposite Most triangles we will make use of in the Universe are skinny (i.e., <10 deg). Skinny triangle rule: If  is small, sin  =  (in radians), tan = , cos =1 (e.g.,  =0.1 radians=5.7 degrees = sin  to 0.1 %)and adjacent=hypotenuse =width distance distance width 

  3. Stars appear fixed to a large, very distant celestial sphere North Celestial Pole Earth's axis of rotation celestial equator (far, far away) zenith of B B zenith of A A Earth horizon of B horizon of A South Celestial Pole Positionon Sky From any point on Earth, you can see half of the celestial sphere at any given time (if you have a clear horizon). As Earth rotates, stars move across sky-circles centered on NCP, SCP Two angles fix location of a star on the sphere. We use right ascension for East-West and declination for North-South

  4. Eight Hour time-lapse exposure looking at North Celestial Pole

  5. q Ecliptic (not equator!) • Ecliptic=Plane of the Earth’s orbit (~ other planets + Moon too) • Tilted at 23 to celestial equator (seasons) Northern summer Northern winter Imaginary point where ecliptic and equator cross (and the Sun reaches on March 21, vernal equinox) is 0 RA point

  6. So a Star’s two angular coordinates should never change, unless… • Edmond Halley (1718) measured stars positions and compared to • Ptolemy (Almagest) 1800 years earlier, found changes in • some of brightest stars, a degree to a few degrees!!! • Compare two bright stars in Bootes to the other stars… Arcturus Eta bootes

  7. Question: When You Give Directions to an Alien, why should you leave out the constellations? the figure of the constellations changes with location the figure of the constellations change with time a constellation star may explode all of the above none of the above answer, d)

  8. If we continuously monitored Arcturus in Bootes Time step=100 years, from 0 AD to 10000 AD

  9. What the Heck? Why? Precession? Nutation? Coherent! Aberration? Also a pattern Parallax? No, position changes were along random directions, not periodic… Some North, some South, etc (even since Tyco’s time)

  10. The Brighter they are, the Faster they move Mayer, 1723-1762 Why did the brighter stars show larger movements? Halley reasoned: Brighter=Closer. So? So, closer means angular (i.e. apparent )motion is greater! These motions called “proper motions” by Johann Mayer in 1750’s, measured in ~80 stars. So, if the Sun is a star, why wouldn’t it move too? Perhaps it does! How could we tell? Wouldn’t the Sun’s movement create the appearance of a pattern of star movements, like person walking through forest?

  11. Announcements Turn in HW #2 Observing this week, tonight New HW #3

  12. Flying Through Space

  13. Flying Through Space

  14. The “Stellar Wake” Johann Mayer, 1760, suggested motion of Sun should appear as stars perpendicular to motion “move aside”, couldn’t see it. In 1783 Hershel looked again for this effect, found it, towards Hercules Circle for RA (24 hrs) Hershel’s paper, 1783, “…we find that Sirius, Castor, Procyon, Pollux, Regulus, Arcturus, and α Aquilae appear to have respectively the following proper motions in right ascension: -0”.63; - 0”.28; - 0”.80 Nevil Maskelyne, then Great Britains Astronomer Royal. - 0”.93; - 0”.41; - 1”.40; and + 0”.57. And two of them, Sirius and Arcturus, in declination, viz. 1”.20 and 2”.01, both southward. Let figure [17.2] represent an equatorial zone with the above mentioned stars referred to it, according to their respective right ascensions, having the solar system in the center. Assume the direction AB …and suppose the sun to move in that direction from S towards B. Then will that one motion answer that of all the stars together” Hershel: imagine sun (S) moves to C Stars physically at positions s will appear to move from a to b

  15. Some Stars Also Vary Their Brightness in Time! • Star Algol (A-ghoul; “the demon star”) (known since 1660’s) varies by a factor of 4 in brightness every 2 days 20 hours…how could stars vary in brightness? • Cepheid and  Aquilae also varied (J. Goodricke 1784)

  16. Question: What could cause a star’s brightness to vary? starspots + spinning Eclipse by companion star changing size all of the above none of the above answer, d)

  17. So Stars were not so immutable as the ancients believed.And were they infinitely far away?

  18. Sun with Hole in Screen C. Huygens ~1690-when fraction Sunlight= Sirius then: hole/whole=bSirius/bSun=dSun2/dSirius2 because brightness  1/d2 Couldn’t make hole small enough! But got 27,664 AU (700 million times fainter!) What assumed? Sirius J. Gregory ~1668-when Saturn as bright as Sirius, same fraction given by light which reflects from Saturn, reaches Earth. 83,190 AU. What assumed? Newton: 1,000,000 AU Unreliable! Parallax would be better… “The Holy Grail” of Astronomy, 17th-19th Century:The Distance to a Star Recall that the absence of parallax previously argued that the stars were far away. Copernicus, “of near infinite magnitude”

  19. Parallax and The Parsec Against backdrop of very distant stars, Nearby star will move by an angle 2p, in 6 months. Parallax angle=p “Skinny Triangle” rule, p[radians]=1AU/d so d=1AU/p If p=1”=1/(2x105) radians then d=2x105 AU. Called “parsec”= 3x1013 km=3.26 light years Parsec is most common unit for distance in astronomy because its based on how we measure distance

  20. Earth 1 A.U. B A C p Sun p p d d d d (pc) = 1 p (arc sec) 1 A.U. 1" star 1 parsec As distance increases, parallax decreases The distance for which a 1 A.U. baseline has a one arc second (1") parallax is called 1 parsec (pc) Note: 1" means 1 arc second 60" = 1 arc minute (1') 60' = 1 degree (1°) 360° = full circle (for example, horizon to zenith = 1/4 circle = 90°) (1 pc ≈3.26 ly)

  21. More on Parallax Parallax is also a common surveyor’s tool

  22. Human Eyes Meteor ranging in Earth’s atmosphere 2.3 inches several miles tens of feet tens of miles Optical Range Finder Distance to Moon Moon several feet 8000 miles Earth many feet 240,000 miles Surveyor’s transit Distance to Star Sun 186 million miles many feet Earth’s Orbit many feet to few miles trillions of miles Broadening the Baseline: Parallax Measurements Near to Far

  23. What is the distance of a star with a parallax of 0.05 arcseconds? • 5 parsecs • 10 parsecs • 20 parsecs • 50 parsecs • 100 parsecs

  24. If a star were four times as far away from us, how many times less light would we receive from it? • 1/2 • 1/4 • 1/8 • 1/16 • 1/64

  25. The Astronomical “Holy Grail”:Distance to Stars by Parallax Galileo wrote about the method of parallax but measurements were too imprecise and stars to far to get a reliable result. J. Bradley & Molyneux had tried 1720’s with  Draconis, but had discovered aberration and nutation instead! (And also had to account for refraction). All these effects bigger than parallax, and coherent, not individual. Concluded lack of parallax to ~1”,  Draconis > 1 parsec !! W. Hershel, ~1800, had tried using double stars (so that refraction, aberration, precession drop out), had discovered binaries instead! Many others tried, spurious claims, none successful by ~1830

  26. 1784-1846 “Space Race” to Measure First Parallax, 1830’s Normal view 1838: Friedrich Bessel, 61 Cygni target reference Bessel’s heliometer--split objective lens Creates a double image, sections moved Until a star coincides with another and Angular separation is read off Bessel measured a dozen times per Night for 15 months! Heliometer: adjust Until stars align • Read Bessel’s Letter: He chose 61 Cygni because • Big proper motion (6”/yr) means its likely to be close enough for detectable parallax • Its near the pole so it will be visible throughout the year • Double star (24” sep) so he can better align it , aligning its bisection to calibration stars (stars are 1”) • Had to contend with: 1st reference stars too faint, Halley’s comet kicks him off the telescope, • Turbulence in the atmosphere means he needs to re-observe a dozen times per night

  27. Dial the reference Star to the bisection pt What Bessel Saw Easier than Aligning stars 60” Main effects we see: proper motion, 5”/year looking for a tiny 6 month variation 10 times smaller, this is hard!!

  28. Let’s Cheat A little We correct for (differential) aberration (as Bessel would have), (Note that the distant stars will also have aberration but Not parallax) Then zoom in to a 1’ sized field…Hubble like resolution. See that ripple every 6 months? There it is!! Bessel observed 2.5 of these cycles before he made his claim that….

  29. Answer is… 0.31” +/- 0.02” !! That’s 1/75 of the double separation (that angle is a dime 5 km away!) Corresponded to 3 parsecs (modern value = 0.28547”) or 10 ly! Thomas Henderson, went down to Cape Town, Alpha Centauri, parallax=1” (had it in 1832-33 but for lack of confidence published in 1839) . Closest star! Could have been detected in 18th century If it was in the North. Friedrich Struve measured parallax of Vega the same year. to be ~1/8” Right on Bessel’s Heals…

  30. Modern: Barnard’s Star at2 parsecs

  31. Today the Gold standard: Hipparcos Satellite 1989-1993: Measured 120,000 stars to 1 milli- arcsec precision. That’s A distance of 1000 pc or 300 ly (actually 1/10th that distance to get a significant measurement) rough distance for 2.5 million stars in total Science of measuring Positions on the sky: Astrometry

  32. Tomorrow’s Gold Standard: Gaia Launch: Aug 2011 by ESA, mission through 2020 will measure parallax of 1 billion stars in the Milky Way (20  arcsec precision for brightest, 200  arcsec for faintest a distance of 50 Kpc to 5 Kpc ) Distance and angular position (3D) and 3D motion too. Will address origin and evolution (life history) of Milky Way.

  33. History of Stellar Parallax

  34. New Approach Using Hubble Space Telescope:Precision Astrometry with Spatial Scanning (PASS) Scanning, average many rows, error =0.01 pix /√N rows or 0.001 pix Imaging: error in position of star=0.01 pix scan parallax parallax

  35. First PASS Cepheid Star SY AUR @ 2.3 Kpc

  36. Two Advantages of Spatial Scans,Jitter Removal and Repetition

  37. Astrometric Precision Per Exposure

  38. And so the Stars were Put in their proper place … Insert Powers of Ten Movie Here.

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