* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download The Scales of Things
Hubble Space Telescope wikipedia , lookup
Rare Earth hypothesis wikipedia , lookup
Fine-tuned Universe wikipedia , lookup
Cassiopeia (constellation) wikipedia , lookup
Dark energy wikipedia , lookup
Geocentric model wikipedia , lookup
Outer space wikipedia , lookup
History of supernova observation wikipedia , lookup
Cygnus (constellation) wikipedia , lookup
Perseus (constellation) wikipedia , lookup
Non-standard cosmology wikipedia , lookup
Extraterrestrial life wikipedia , lookup
History of astronomy wikipedia , lookup
Theoretical astronomy wikipedia , lookup
Aquarius (constellation) wikipedia , lookup
Flatness problem wikipedia , lookup
International Ultraviolet Explorer wikipedia , lookup
Stellar kinematics wikipedia , lookup
Star formation wikipedia , lookup
Lambda-CDM model wikipedia , lookup
Physical cosmology wikipedia , lookup
Dialogue Concerning the Two Chief World Systems wikipedia , lookup
Corvus (constellation) wikipedia , lookup
Chronology of the universe wikipedia , lookup
H II region wikipedia , lookup
Structure formation wikipedia , lookup
Expansion of the universe wikipedia , lookup
Future of an expanding universe wikipedia , lookup
Hubble Deep Field wikipedia , lookup
Timeline of astronomy wikipedia , lookup
Observational astronomy wikipedia , lookup
The Cosmic Distance Scale Laura A. Whitlock / Sonoma State U Rohnert Park, CA Outline A quick review of notation and units An examination of Distance • • • • Measuring inside our solar system Measuring to “nearby” stars Measuring distant objects Measuring the Universe Remember: Big or small, numbers are given meaning in our Universe! Quick Review of Scientific Notation Powers of Ten Scientific Notation • 10n means 10 x 10 x 10 x 10 … [n times] • 10-n means 1/(10 x 10 x 10 ….) [n times] There are 1010 – 1011 stars in our Galaxy, and a similar number of galaxies in the Universe And remember... To Multiply & Divide 10a •10b = 10 a + b 10a ÷10b = 10 a - b How Many Grains of Sand? If Earth were made of sand, would it contain more or less than a googol (10100) grains of sand? Draw a 1 cm segment. Mark pencil points along the segment to get an estimate of the number of tightly packed grains of sand in 1 linear cm. Calculate the number of grains of sand in 1 cubic km. (Remember: 100 cm = 1 m , 1000 m = 1 km) Earth’s radius is about 6400 km. Use the equation for the volume of a sphere {V = (4/3)pr3} to calculate the number of grains in a sandy Earth. A Quick Tour from the Unimaginably Tiny to the Incomprehensibly Big QuickTime™ and a Intel Indeo® Video R3.2 decompressor are needed to see this picture. …an oldie, but a goodie! Units for Time and Distance Kilometer (km) = .621 miles Light-year (lt-yr) = The distance light travels in one year in a vacuum. 1 lt-yr = 9.5 x 1012 km Parsec = 3.3 light-years (Mpc = 1,000 pc) arc-second = (1 degree/3600) Radar (the replacement method for Kepler’s Law, P2 ~ a3) Parallax Cepheid Period/Luminosity Relationship Supernovae Redshift and Hubble’s Law Radar Measurements • Beam travels at speed of light, c • Measure the time it takes beam to leave Earth, bounce off planet (or whatever), and return to Earth. This represents the time for the beam, traveling at c, to cover twice the distance between Earth and the target object. 2d = c t d = ct/2 d But... Radar techniques are only feasible for objects inside our solar system. The Nearest Stars Distance to Alpha or Proxima Centauri is ~4 x 1013 km (~4.2 light-years) Distance between Alpha and Proxima Centauri is ~23 AU The Solar Neighborhood Some stars are within about 2 x 1014 km (~ 20 light-years) Distances to Nearby Stars Parallax : determined by the change of position of a nearby star with respect to the distant stars, as seen from the Earth at two different times separated by 6 months. Parallax Gold standard for astronomical distances. It is based on measuring two angles and the included side of a triangle The parallax of a star is one-half the angle parallax angle Approximation! D = Earth-Sun distance parallax Astronomers usually say the Earth-Sun distance is 1 astronomical unit, where 1 au = 1.5x1013 cm, and measure small angles in arc-seconds. Arc-seconds are often denoted by , just Historical Note The first stellar parallax (of the star 61 Cygni) was measured by Friedrich Wilhelm Bessel (1784-1846) in 1838. Bessel is also known for the Bessel functions in mathematical physics. Parallax QuickTime™ and a decompressor are needed to see this picture. Parallax to Proxima Centauri is only 0.76 So... Only the nearest stars to us have a measurable parallax. Cepheids Cepheid variable stars are pulsating stars, named after the brightest member of the class, Delta Cephei. Cepheids are brightest when they are hottest, close to the minimum size. Since all Cepheids are about the same temperature, the size of a Cepheid determines its luminosity. Thus there is a period-brightness relationship for Cepheids. Since it is easy to measure the period of a variable star and they can be very bright, Cepheids are wonderful for determining distances to galaxies! Cepheid Variables Henrietta Leavitt studied variable stars that were all at the same distance (in the LMC or SMC) and found that their pulsation periods were related to their brightnesses L =K P1.3 Polaris (the North Star) is not constant, it is a Cepheid variable! Distances to Cepheids Distance to closest Cepheid (Delta Cephei) in our Galaxy can be found using parallax measurements. This determines K in the period-luminosity relation (L = KP1. 3) Since the period of a Cepheid is related to its absolute brightness, if you observe its period and the apparent brightness, you can then derive its distance (to within about 10%) Absolute Brightness Apparent Brightness = 4 p distance2 If no Cepheids can be seen... Life Cycles of Stars QuickTime™ and a Microsoft Video Utility decompressor are needed to see this picture. Supernova… Going out with a Blast! Crab Nebula Observed by Chinese astronomers in 1054 AD Age determined by tracing back exploding filaments Crab pulsar emits 30 pulses per second at all wavelengths from radio to TeV QuickTime™ and a Microsoft Video Utility decompressor are needed to see this picture. Crab Nebula Radio/VLA Infrared/Keck Crab Nebula Optical/Palomar Optical/HST WFPC2 Crab Nebula and Pulsar X-ray/Chandra Distances to Supernovae Brightest SN in modern times, occurred at t0 Supernova 1987A in LMC Measure angular diameter of ring, q Measure times when top and bottom of ring light up, t2 and t1 Ring radius is given by R = c(t1-t0 + t2-t0)/2 Distance = R / q D = 47 kpc Distances to Supernovae Type Ia supernovae are “standard candles” Occur in a binary system in which a white dwarf star accretes beyond the 1.4 Mo limit and collapses and explodes Decay time of light curve is correlated to absolute luminosity Good to 20% as a distance measure But to really “measure the Universe”... Historical Note Edwin Hubble discovered that the Universe is expanding! What Hubble Found The Hubble constant Ho = 558 km s -1 Mpc -1 is the slope of these graphs Compared to modern measurements, Hubble’s results were off by a factor of ten! Hubble’s Law v = Ho * d Ho is called the Hubble constant. It is generally believed to be around 65 km/sec/Mpc… plus or minus about 10 km/sec/Mpc. Note: The further away you are, the faster you are moving! Implications of Hubble’s Law Distance = velocity/(Hubble constant) To get a rough idea of how far away a very distant object is from Earth, all we need to know is the object's velocity. The velocity is relatively easy for us to measure using the Doppler effect, or Doppler shift. Doppler Shift Wavelength is shorter when approaching Stationary waves Wavelength is longer when receding What It Looks Like Comparison of laboratory to blue-shifted object Comparison of laboratory to red-shifted object Doppler Shift / Redshift Redshift, z, is a non-relativistic approximation to the Doppler shift z = Dl l = l - lo lo = v c Hubble’s Law Revisited v = Ho d = cz where v = velocity from spectral line measurements d = distance to object Ho = Hubble constant in km s-1 Mpc -1 z is the redshift Space between the galaxies expands while galaxies stay the same size Example A certain absorption line that is found at 5000Å in the lab is found at 5050Å when analyzing the spectrum of a particular galaxy. We then conclude that this galaxy is moving with a velocity v = (50/5000) * c = 3000 km/sec away from us. Putting it altogether now, if the object is moving away from us at 3000 km/ sec, its distance from us (according to the Hubble’s Law) is d = v/Ho = 3000/65 = 46 Mpc or 1.4 x 108 light-years And so the Universe is... v = H0d and d =vt Solving for t, we find the age of the Universe is: t ~ 1/H0 If H0 = 65 km/s/Mpc, then the age of the Universe is ~ 16 x 109 yr or 16 billion years Books and Slides Mitton, Jacqueline and Mitton, Simon, Scholastic Encyclopedia of Space, Scholastic Inc., 1998. Fraknoi, Andrew, A Grand Tour of the Universe Slide Set, Astronomical Society of the Pacific. Videos Powers of Ten: $39.95 through the Astronomical Society of the Pacific Catalog. http://www.aspsky.org/catalog/vt110.html or write to: ATTN: Catalog, ASP, 390 Ashton Ave, San Francisco, CA 94112 Cosmic Voyage: $29.95 through the Astronomical Society of the Pacific Catalog. http://www.aspsky.org/catalog or write to: ATTN: Catalog, ASP, 390 Ashton Ave, San Francisco, CA 94112 Web Cosmic Distance Ladder – 3 labs http://www.astro.washington.edu/labs/Distance_Ladder.html Extragalactic Cosmic Distance Scale ttp://www.uq.edu.au/~phjross/ph227/galaxy/candles.htm Cosmic Distance Ladder I: Parallax http://209.52.189.2/article.cfm/astronomy/11999 Cosmic Distance Ladder II – Stars as Standard Candles http://209.52.189.2/article.cfm/astronomy/13217 More Web Seeing is Believing! – Determining the Distance to Venus http://www.amtsgym-sdbg.dk/as/venus/ven-dist.htm Stellar Parallax Lab http://einstein.uhh.hawaii.edu/spacegrant/lab2/lab2.html More Web Cosmic Distance Scale http://csep10.phys.utk.edu/astr162/lect/cosmology/cosmicd.html Cepheid Variables and the Cosmic Distance Scale Lab http://einstein.uhh.hawaii.edu/spacegrant/lab4/lab4.html Wrap Up…at long last! Presentation will appear at http://perry.sonoma.edu/nbsp/materials/distances.html