Astronomical Distances Blendon Middle School April 13, 2010 Dr. Uwe Trittmann Otterbein College.
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Transcript of Astronomical Distances Blendon Middle School April 13, 2010 Dr. Uwe Trittmann Otterbein College.
Astronomical Distances
Blendon Middle SchoolApril 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)
Together they give the location of an object in three-dimensional space
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
Angles and Size
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
The Universe is structured on different length scales
THE UNIVERSE
clustersand
superclusters
voids
galaxieslike the
Milky Way
quasars
Starsnebulaemolecular cloudsstar clusters
Solar System
black holespulsars
Sun
planets
moonscometsmeteorsasteroidsdust
terrestrialjovian
Big ----------------------------- small
Powers of Ten – From Man to Universe -
100 meters =1 meter
The Human Scale
Street Size
103 meters =1000 m= 1 km
Harbour
City Size
104 meters = 10,000 m=10 km
Chicago
Planet Size: thousands of km
• 1000 km = 1,000,000 m = 1 million meters
Star Size: 1,000,000,000 m =1 billion meters
• The Sun (a typical star): diameter 1.4 million km.
Solar System Scale
Venus, Earth, Mars
Orbits 1011 meters =100,000,000,000m=100,000,000 km= about 1 A.U. (Astronomical Unit)
Farther out: Nebulae – Where stars are born...
… and die !
• How big ARE these?• They APPEAR tiny!
Black Holes – Dead Stars
• How big is a black hole?
Galaxies
• How big is a galaxy?
• Are all galaxies the same size?
Clusters of Galaxies
• What is the distance between galaxies?
The Universe
• How big is the Universe?• Does this question make sense?• If yes, can we answer it while living IN the universe?
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
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
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
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
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…
Our Stellar Neighborhood
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
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
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!
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)
Distance Determination Method
• Understand how bright an object is (L)is (L)• Observe how bright an object appears (B)appears (B)
• Calculate how far the object is away:
B L / d2
So
L/B d2 or d √L/B
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 yellow Sun, Centauri
K 4,000 K orange Arcturus
M 3,000 K red Betelgeuse
The hotter the bluer!
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
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
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
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!
Galaxies are close together – compared to their size
The Local Group The Virgo Cluster
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!
Spectral Lines – Fingerprints of the Elements
• Can use this to identify elements on distant objects!
• Different elements yield different emission spectra
Origin of Spectral Lines: Emission
Heated Gas emits light at specific frequencies “the positive fingerprints of the elements”
Origin of Spectral Lines: Absorption
Cool gas absorbs light at specific frequencies
“the negative fingerprints of the elements”
Use Spectra to measure the Size 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
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!
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/H0 or about 14 billion years
Velocity = H0 Distance
Distance = Velocity /H0
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 universeSupernovae are further away than expected for any decelerating (“standard”) universe
Supernova Data
redshift
magnitude
• Solid line is best fit to data
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!
Additional Material
Powers of Ten – From Man to Universe -
100 meters =1 meter
The Human Scale
Powers of Ten – From Man to Universe -
101 meters =10 meters
Lawn andBlanket
Powers of Ten – From Man to Universe -
102 meters =100 meters
Highway andBoats
Powers of Ten – From Man to Universe -
103 meters
=1000 m
Harbour
Powers of Ten – From Man to Universe -
104 meters =10 km
Chicago Lakeshore
Powers of Ten – From Man to Universe -
105 meters =100 km
Chicago & L. Michigan
Powers of Ten – From Man to Universe -
106 meters =1000 km
Lake Michigan
Powers of Ten – From Man to Universe -
107 meters
=10000 km
The Earth
Powers of Ten – From Man to Universe -
108 meters =100000 km
Earth inSpace
Powers of Ten – From Man to Universe -
109 meters
=1000000km
Moon Orbit
Powers of Ten – From Man to Universe -
1010 meters
Part of Earth’sOrbit aroundthe Sun
Powers of Ten – From Man to Universe -
1011 meters = ca. 1 A.U.(Astronomical Unit)
Earth’s Orbit
Powers of Ten – From Man to Universe -
1012 meters
Inner Planets’ Orbits
Powers of Ten – From Man to Universe -
1013 meters
Outer Planet’s
Orbits
Powers of Ten – From Man to Universe -
1014 meters
Solar System
in Space
Powers of Ten – From Man to Universe -
1015 meters
The Sun -
“a bright star”
Powers of Ten – From Man to Universe -
1016 meters = ca. 1 ly(light year)
The Sun -“just another star”
Powers of Ten – From Man to Universe -
1017 m
= ca. 10 ly
Distinct Stars
Powers of Ten – From Man to Universe -
1018 m =
100 ly
Sun in center;
Arcturus (α Tauri)
Powers of Ten – From Man to Universe -
1019 m =
1000 ly
A cloud of Stars- making up constellations
Powers of Ten – From Man to Universe -
1020 m = ca.10000 ly
Clouds - made out of Stars
Powers of Ten – From Man to Universe -
1021 m =100000 ly
The Milky Way
– Our Galaxy
Powers of Ten – From Man to Universe -
1022 m
=1,000,000 ly
The Milky Way
in Space
Powers of Ten – From Man to Universe -
1023 m
= 10 x 106 ly
The Local Group
of Galaxies
Powers of Ten – From Man to Universe -
1024 m = 108 ly
The Virgo Cluster
of Galaxies
(incl. the local Group)
Powers of Ten – From Man to Universe -
1025 m = 109 ly
The Universe:Many clusters of galaxies – and even more empty space
The “old” PlanetsMercury Venus Mars
JupiterSaturn
The “new” Planets Uranus (1781) Neptune (1846)
Pluto (1930)
(“dwarf planet” since 2006)
Kepler’s Third Law: Relating OrbitsThe square of a planet’s orbital period is proportional to the cube of its orbital semi-major axis:
P 2 a3 Jupiter: 53 / 122 = 125/144 ~ 1
a PPlanet Semi-Major Axis Orbital Period Eccentricity ____ P2/a3
Mercury 0.387 0.241 0.206 1.002Venus 0.723 0.615 0.007 1.001Earth 1.000 1.000 0.017 1.000Mars 1.524 1.881 0.093 1.000Jupiter 5.203 11.86 0.048 0.999Saturn 9.539 29.46 0.056 1.000Uranus 19.19 84.01 0.046 0.999Neptune 30.06 164.8 0.010 1.000Pluto 39.53 248.6 0.248 1.001
(A.U.) (Earth years)
The Problem with Kepler’s Third Law
• The square of a planet’s orbital period is proportional to the cube of its orbital semi-major axis:
P 2 a3
• But: everything is expressed in “Earth units”, i.e. one Earth year, and one Earth-Sun distance.
• Problem: How big are these units?
Practical Problem: Determine the Sun’s Diameter?
• Trickier than you might think• We know only how big it appears
– It appears as big as the Moon
• Need to measure how far it is away– Kepler’s laws don’t help (only relative
distances)
• Without knowing its size, we don’t know how much energy it can produce, so we can’t figure out how the Sun “works”
Solution: relate to distances on Earth or fundamental constants
• Use two observations of Venus transit in front of Sun – Captain Cook in the 1700s– Hard and not very precise (100,000 km)
• Modern way: bounce radio signal off of Venus (measure traveling time of light)– In the 1960s, very precise (few centimeters)
Insight
• Sun is 109 times bigger than Earth
• Up to the 1930s no mechanism was known to produce so much energy
• Know now that the Sun fuses hydrogen to helium
More Insight: Understanding Variable Stars yields another
Method
• Two useful types:– Cepheids– RR Lyrae
• Again, method uses insight to get absolute brightness, then concludes distance from apparent brightness
Cepheids • Named after δ Cephei
• Period-Luminosity Relations
• Used as “standard candles”
• “yard-sticks” for distance measurement
• Cepeids in Andromeda Galaxies established the “extragalacticity” of this “nebula”
Cepheids• Henrietta Leavitt (1908) discovers the
period-luminosity relationship for Cepheid variables
• Period thus tells us luminosity, which then tells us the distance
• Since Cepheids are brighter than RR Lyrae,they can be used to measure out to further distances
Properties of Cepheids
• Period of pulsation: a few days
• Luminosity: 200-20000 suns
• Radius: 10-100 solar radii
Properties of RR Lyrae Stars• Period of pulsation: less than a day
• Luminosity: 100 suns
• Radius: 5 solar radii
Distance Measurements with variable stars• Extends the cosmic
distance ladder out as far as we can see Cepheids – about 50 million ly
• In 1920 Hubble used this technique to measure the distance to Andromeda (about 2 million ly)
• Works best for periodic variables
Cepheids and RR Lyrae: Yard-Sticks
• Normal stars undergoing a phase of instability
• Cepheids are more massive and brighter than RR Lyrae
• Note: all RR Lyrae have the same luminosity
• Apparent brightness thus tells us the distance to them!– Recall: B L/d2
Insight: How does our Galaxy look like?
Other Galaxies
• Edwin Hubble identified single stars in the Andromeda nebula (“turning” it into a galaxy)
• Measured the distance to Andromeda to be 1 million Ly (modern value: 2.2 mill. Ly)
• Conclusion: it is 20 times more distant than the milky way’s radius Extragalacticity!
Old theory (Milky Way is the universe) falsified!
The Tully-Fisher Relation• A relation between the rotation speed of a spiral galaxy
and its luminosity• The more mass a galaxy has the brighter it is the
faster it rotates the wider the spectral lines are• Measuring rotation speed allows us to estimate
luminosity; comparing to observed (apparent) brightness then tells us the distance
Electromagnetic Spectrum
Energy: low medium high
Electromagnetic Radiation: Quick Facts
• There are different types of EM radiation, visible light is just one of them
• EM waves can travel in vacuum, no medium needed• The speed of EM radiation “c” is the same for all
types and very high ( light travels to the moon in 1 sec.)
• The higher the frequency, the smaller the wavelength ( f = c)
• The higher the frequency, the higher the energy of EM radiation (E= h f, where h is a constant)
Visible Light• Color of light determined
by its wavelength
• White light is a mixture of all colors
• Can separate individual colors with a prism
Three Things Light Tells Us
• Temperature – from black body spectrum
• Chemical composition– from spectral lines
• Radial velocity– from Doppler shift
Temperature Scales
Fahrenheit Centigrade Kelvin
Absolute zero 459 ºF 273 ºC 0 K
Ice melts 32 ºF 0 ºC 273 K
Human body temperature
98.6 ºF 37 ºC 310 K
Water boils 212 ºF 100 ºC 373 K
Black Body Spectrum• Objects emit radiation of all frequencies,
but with different intensities
Higher Temp.
Lower Temp.Ipeak
Ipeak
Ipeak
fpeak<fpeak <fpeak
Cool, invisible galactic gas
(60 K, fpeak in low radio
frequencies)
Dim, young star
(600K, fpeak in infrared)
The Sun’s surface
(6000K, fpeak in visible)
Hot stars in Omega Centauri
(60,000K, fpeak in ultraviolet)
The higher the temperature of an object, the higher its Ipeak and fpeak
Activity: Black Body Radiation
• Pick up a worksheet• Form a group of 3-4 people• Work on the questions on the sheet• Fill out the sheet and put your name on top• Hold on to the sheet until we’ve talked about
the correct answers• Hand them in at the end of the lecture or during
the break• I’ll come around to help out !
Kirchhoff’s Laws: Bright lines
Heated Gas emits light at specific frequencies “the positive fingerprints of the elements”
Kirchhoff’s Laws: Dark Lines
Cool gas absorbs light at specific frequencies
“the negative fingerprints of the elements”
Kirchhoff’s Laws
1. A luminous solid or liquid (or a sufficiently dense gas) emits light of all wavelengths: the black body spectrum
2. Light of a low density hot gas consists of a series of discrete bright emission lines: the positive “fingerprints” of its chemical elements!
3. A cool, thin gas absorbs certain wavelengths from a continuous spectrum dark absorption ( “Fraunhofer”) lines in continuous spectrum: negative “fingerprints” of its chemical elements, precisely at the same wavelengths as emission lines.
Spectral Lines • Origin of discrete spectral lines: atomic structure of matter
• Atoms are made up of electrons and nuclei– Nuclei themselves are made up
of protons and neutrons
• Electrons orbit the nuclei, as planets orbit the sun
• Only certain orbits allowed Quantum jumps!
• The energy of the electron depends on orbit• When an electron jumps from one orbital to
another, it emits (emission line) or absorbs (absorption line) a photon of a certain energy
• The frequency of emitted or absorbed photon is related to its energy
E = h f
(h is called Planck’s constant, f is frequency)