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Astronomical Distances

Astronomical Distances. Blendon Middle School April 13, 2010 Dr. Uwe Trittmann Otterbein College. Astronomical Distances. Locations in the sky are easy to measure: 2 angles Distances from observer are hard (one length)

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Astronomical Distances

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  1. Astronomical Distances Blendon Middle School April 13, 2010 Dr. Uwe Trittmann Otterbein College

  2. Astronomical Distances • Locations in the sky are easy to measure: 2 angles • Distances from observer are hard (one length)  Together they give the location of an object in three-dimensional space

  3. The Trouble with Angles Angular size of an object cannot tell us its actual size – depends on how far away it is Sun and Moon have very nearly the same angular size (30' = ½) when viewed from Earth

  4. Angles and Size

  5. Without Distances … • We do not know the size of an object • This makes it hard to figure out the “inner workings” of an object • We can’t picture the structure of the solar system, galaxy, cosmos

  6. Stars nebulae molecular clouds star clusters Solar System black holes pulsars Sun planets moons comets meteors asteroids dust terrestrial jovian clusters and superclusters voids galaxies like the Milky Way quasars THE UNIVERSE The Universe is structured on different length scales Big  ----------------------------- small

  7. Powers of Ten – From Man to Universe - 100 meters =1 meter The Human Scale

  8. Street Size 103 meters =1000 m = 1 km Harbour

  9. City Size 104 meters = 10,000 m =10 km Chicago

  10. Planet Size: thousands of km • 1000 km = 1,000,000 m = 1 million meters

  11. Star Size: 1,000,000,000 m =1 billion meters • The Sun (a typical star): diameter 1.4 million km.

  12. Solar System Scale Venus, Earth, Mars Orbits 1011 meters =100,000,000,000m =100,000,000 km = about 1 A.U. (Astronomical Unit)

  13. Farther out: Nebulae – Where stars are born...

  14. … and die ! • How big ARE these? • They APPEAR tiny!

  15. Black Holes – Dead Stars • How big is a black hole?

  16. Galaxies • How big is a galaxy? • Are all galaxies the same size?

  17. Clusters of Galaxies • What is the distance between galaxies?

  18. The Universe • How big is the Universe? • Does this question make sense? • If yes, can we answer it while living IN the universe?

  19. Different lengths scales  Different length units • Human scale: meters (yards) • Human height: 1.8 m • Geographical scale: kilometers (miles) • Distance to Cincinnati: 100 mi • Solar system scale: Astronomical Unit • Distance Earth-Sun: 1 A.U. • Intragalactic scale: lightyears (parsecs) • Next star: 4 lightyears • Intergalactic scale: millions of lightyears (Megaparsecs) • Andromeda galaxy: 2.2 million lightyears = 0.67 Mpc • Cosmological Scale: billions of ly (Gigaparsecs) • Edge of observable universe: about 15 billion ly

  20. Different lengths scales  Different length measurements • Human scale: yardstick • Geographical scale: triangulation • Solar system scale: Radar ranging • Intragalactic scale: • Close stars: stellar parallax • Far: spectroscopic parallax • Intergalactic scale: • Close: Variable stars • Far: Tully-Fisher relation • Cosmological Scale: Hubble’s Law

  21. Astronomical Distance Measurements Fundamental technique uses triangulation: Objects appear to move with respect to background if looked at from different vantage points Try looking at you thumb with only your left, then right eye The more the thumb jumps, the closer it is! Measure “jump”, get distance See: Link, Link 2

  22. Distances to the Stars • Measurements ½ year apart! • Parallax can be used out to about 100 light years • The bigger the parallactic angle, the closer the star! • A star with a measured parallax of 1” is 1 parsec away • 1 pc is about 3.3 light years • The nearest star (Proxima Centauri) is about 1.3 pc or 4.3 lyr away • Solar system is less than 1/1000 lyr

  23. Insight • Some stars are close to us (4 ly), other are far away (1000 ly) • This means that some stars appear dim but are actually very bright • That means that stars have different sizes, temperatures, life expectancy…

  24. Our Stellar Neighborhood

  25. Scale Model • If the Sun = a golf ball, then • Earth = a grain of sand • The Earth orbits the Sun at a distance of one meter • Proxima Centauri lies 270 kilometers (170 miles) away • Barnard’s Star lies 370 kilometers (230 miles) away • Less than 100 stars lie within 1000 kilometers (600 miles) • The Universe is almost empty! • Hipparcos satellite measured distances to nearly 1 million stars in the range of 330 ly • almost all of the stars in our Galaxy are more distant

  26. Luminosity and Brightness • Luminosity L is the total power (energy per unit time) radiated by the star, actual brightness of star, cf. 100 W lightbulb • Apparent brightness B is how bright it appears from Earth • Determined by the amount of light per unit area reaching Earth • B L / d2 • Just by looking, we cannot tell if a star is close and dim or far away and bright

  27. Brightness: simplified • 100 W light bulb will look 9 times dimmer from 3m away than from 1m away. • A 25W light bulb will look four times dimmer than a 100W light bulb if at the same distance! • If they appear equally bright, we can conclude that the 100W lightbulb is twice as far away!

  28. Same with stars… • Sirius (white) will look 9 times dimmer from 3 lightyears away than from 1 lightyear away. • Vega (also white) is as bright as Sirius, but appears to be 9 times dimmer. • Vega must be three times farther away • (Sirius 9 ly, Vega 27 ly)

  29. Distance Determination Method • Understand how bright an object is (L) • Observe how bright an object appears (B) • Calculate how far the object is away: B L / d2 So L/B d2 or d  √L/B

  30. Understand Star Brightness: Classify Stars by their Temperature (Color) Class Temperature Color Examples O 30,000 K blue B 20,000 K bluish Rigel A 10,000 K white Vega, Sirius F 8,000 K white Canopus G 6,000 K yellowSun,  Centauri K 4,000 K orange Arcturus M 3,000 K red Betelgeuse The hotter  the bluer!

  31. Color-Luminosity Correlation • Hertzprung-Russell Diagram is a plot of absolute brightness (vertical scale) against spectral type or temperature (horizontal scale) • Most stars (90%) lie in a band known as the Main Sequence

  32. Spectroscopic Parallax • From the color of a main sequence star we can determine its absolute brightness • Then, from the apparent brightness compared to absolute luminosity, we can determine the distance d  √L/B

  33. Insight • We now know how far away stars are, so we know how big they are, and we can understand how they work. • We understand how big our galaxy is (100,000 ly) and that some “nebulae” are galaxies like our own

  34. Sizes of Stars • Dwarfs • Comparable in size, or smaller than, the Sun • Giants • Up to 100 times the size of the Sun • Supergiants • Up to 1000 times the size of the Sun • Note: Temperature (Color) changes!

  35. Galaxies are close together – compared to their size The Local Group The Virgo Cluster

  36. Aside: What are stars made out of ? • 90% of the universe is Hydrogen • The rest is mostly Helium • How do we know? By identifying the fingerprints of the elements, aka the light they send out!

  37. Spectral Lines – Fingerprints of the Elements • Can use this to identify elements on distant objects! • Different elements yield different emission spectra

  38. Origin of Spectral Lines: Emission Heated Gas emits light at specific frequencies  “the positive fingerprints of the elements”

  39. Origin of Spectral Lines: Absorption Cool gas absorbs light at specific frequencies  “the negative fingerprints of the elements”

  40. Use Spectra to measure theSize of the Universe • Measure spectrum of galaxies and compare to laboratory measurement • lines are shifted towards red • This is the Doppler effect: Red-shifted objects are moving away from us

  41. Using Redshift: Hubble’s Law The final rung on the cosmic distance ladder Hubble’s observations (1920’s): Light from distant galaxies is red-shifted The more distant the galaxy, the greater the red-shift Interpretation: Galaxies are moving away from us More distant galaxies are moving faster The universe is expanding, carrying the galaxies with it!

  42. Hubble’s Law H0= (65 ± 15) km/sec/Mpc is Hubble’s constant Compare to distance = velocitytime Appears the universe “exploded” from a single point in the past – the Big Bang Age of the universe is 1/H0or about 14 billion years Velocity = H0Distance Distance = Velocity /H0

  43. The Latest Surprise • Type Ia Supernovae are • standard candles • Can calculate distance • from brightness • Can measure redshift • General relativity gives us distance as a • function of redshift for a given universe • Supernovae are further away than expected for any decelerating (“standard”) universe

  44. Supernova Data magnitude • Solid line is best fit to data redshift

  45. Expansion of the Universe • Old lore: • Either it grows forever • Or it comes to a standstill • Or it falls back and collapses (“Big crunch”) • In any case: Expansion slows down! Surprise of the year 1998 (Birthday of Dark Energy): All wrong! It accelerates!

  46. Additional Material

  47. Powers of Ten – From Man to Universe - 100 meters =1 meter The Human Scale

  48. Powers of Ten – From Man to Universe - 101 meters =10 meters Lawn and Blanket

  49. Powers of Ten – From Man to Universe - 102 meters =100 meters Highway and Boats

  50. Powers of Ten – From Man to Universe - 103 meters =1000 m Harbour

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