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


100 meters =1 meter

The Human Scale


101 meters =10 meters

Lawn andBlanket


102 meters =100 meters

Highway andBoats


103 meters

=1000 m

Harbour


104 meters =10 km

Chicago Lakeshore


105 meters =100 km

Chicago & L. Michigan


106 meters =1000 km

Lake Michigan


107 meters

=10000 km

The Earth


108 meters =100000 km

Earth inSpace


109 meters

=1000000km

Moon Orbit


1010 meters

Part of Earth’sOrbit aroundthe Sun


1011 meters = ca. 1 A.U.(Astronomical Unit)

Earth’s Orbit


1012 meters

Inner Planets’ Orbits


1013 meters

Outer Planet’s

Orbits


1014 meters

Solar System

in Space


1015 meters

The Sun -

“a bright star”


1016 meters = ca. 1 ly(light year)

The Sun -“just another star”


1017 m

= ca. 10 ly

Distinct Stars


1018 m =

100 ly

Sun in center;

Arcturus (α Tauri)


1019 m =

1000 ly

A cloud of Stars- making up constellations


1020 m = ca.10000 ly

Clouds - made out of Stars


1021 m =100000 ly

The Milky Way

– Our Galaxy


1022 m

=1,000,000 ly

The Milky Way

in Space


1023 m

= 10 x 106 ly

The Local Group

of Galaxies


1024 m = 108 ly

The Virgo Cluster

of Galaxies

(incl. the local Group)


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)

Documents

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