The Expanding Universe Wednesday, October 22 Next planetarium show: Thurs, Nov. 6.
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Transcript of The Expanding Universe Wednesday, October 22 Next planetarium show: Thurs, Nov. 6.
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The Expanding Universe
Wednesday, October 22 Next planetarium show: Thurs, Nov. 6
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All distant galaxies have redshifts. (They are moving away from us.)
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Equal numbers of redshifts and
blueshifts.
Typical radial velocity v = 20 km/second
Thinking locally: stars within 3 parsecs3 parsecs of the Sun.
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Almost all redshiftsredshifts rather than blueshifts.
Typical radial velocity v = 1000 km/second
Thinking more globally: galaxies within 30 million parsecs30 million parsecs of the Milky Way.
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Climbing the “cosmic distance ladder”.
Can’t use the same technique to find distance to everyevery astronomical object.
Use one technique within Solar System (1st “rung” of ladder); another for nearby
stars (2nd “rung”), etc...
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11stst rung rung of the distance ladder: distances within the Solar System.
Distances from Earth to nearby planets are found by radarradar.
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22ndnd rung: rung: distances to nearby stars within the Milky Way Galaxy.
Distances from Solar System to nearby stars are found by parallaxparallax.
← Proxima Centauri
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33rdrd rung: rung: distances to galaxies beyond our own.
Distances from Milky Way to nearby galaxies are found with standard candlesstandard candles.
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A “standard candle” is a light source of known luminosity.
2r4
Lf
π
f 4
Lr
Know luminosity (L): measure flux (f): compute distance (r).
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Climbing the distance ladder.
1) Measure flux of two standard candles: one near, one far.
2) Find distance to near standard candle from its parallax.
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3) Compute luminosity of near standard candle: L = 4 π r2 f.
4) Assume far standard candle has same luminosity as the near.
5) Compute the distance to the far standard candle:
f 4
Lr
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A good standard candle: Cepheid variable stars
Cepheid stars vary in brightness with a period that depends on their
average luminosity.
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Observe Cepheid.
Measure period.
Look up luminosity.
Measure flux.
Compute its distance!
f 4
Lr
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In 1929, Edwin HubbleEdwin Hubble looked at the relation between radial velocityradial velocity and
distance distance for galaxies.
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Hubble’s result: Radial velocity of a galaxy is linearly
proportional to its distance.
Hubble’s original data
1 Mpc = 1 million parsecs
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Hubble’s law Hubble’s law in mathematical form:in mathematical form:
dH v 0v = radial velocity of galaxy
d = distance to galaxy
H0 = the “Hubble constant” (same for all galaxies in all directions)
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What’s the numerical value of H0?
What’s the slope of this line? →
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H0 = 71 kilometers per second per
megaparsec (million parsecs)
H0 = 71 km / sec / Mpc
Or, more concisely…
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Why it’s usefuluseful to know the Hubble constant, H0:
Measure redshift of galaxy: z =(λ-λ0)/λ0
Compute radial velocity: v = c z
Compute distance: d = v / H0
Cheap, fast way to find distance!
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A “redshift map” of a slice through the universe.
Each tiny dot represents a
galaxy.
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Kilometers per second per megaparsec??
What bizarrebizarre units!
1 megaparsec = 3.1 × 1019 kilometers
sec/103.2km/Mpc10 3.1
km/sec/Mpc 71H 18
190
sec10 4.4
1H
170
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Why it’s intriguingintriguing to know H0:
Two galaxies are separated by a distance d.
They are moving apart from each other with speed v = H0 d.
d
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sec104.4H
1
dH
dt 17
00
How long has it been since the galaxies
were touching?
speed
distance timetravel
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PLEASE NOTE:PLEASE NOTE: This length of time (t = 1/H0) is independent ofindependent of the
distance between galaxies!!
If galaxies’ speed has been constant, then at a time 1/H0 in the past, they
were allall scrunched together.
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Hubble’s law (radial velocity is proportional to distance) led to
acceptance of the Big BangBig Bang model.
Big Bang model: universe started in an extremely dense state, but
became less dense as it expanded.
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Heart of the “Big Bang” concept:
At a finite time in the past (t ≈ 1/H0), the universe began in a very dense state.
1/H0, called the “HubbleHubble timetime”, is the approximate age of the
universe in the Big Bang Model.
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sec104.4H
1t 17
0
Since there are 3.2 × 107 seconds per year, the Hubble time is
1/H0 = 14 billion years
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Big Bang model “de-paradoxes” Olbers’ paradox.
If age of universe ≈ 1/H0, light from stars farther than a distance ≈ c/H0
has not had time to reach us.
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Hubble time:Hubble time: 1/H0 = 14 billion years.
Hubble distance:Hubble distance: c/H0 = 14 billion light-years
= 4300 megaparsecs.
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Friday’s Lecture:
Reading:
Chapter 6
Newton vs. Einstein