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Edwin Hubble’s next project.
• Having established in 1925 that galaxies were not in
the Milky Way, Hubble used the Mt Wilson telescope
to obtain spectra of galaxies.
• When he analyzed the spectra he found that, with
the exception of the galaxies in our local group, all
other galaxies where moving away from us. He
found this using the Doppler shift of absorption lines
in the galaxy spectra.
• Not only were all the galaxies found to be moving
away, the farther away a galaxy was, the faster it was
moving away.
• In order to establish the relation between distance
and recessional velocity, Hubble needed to
determine the distance to the galaxies. He did this
by assuming all the galaxies he observed were of
similar size, and figured out their relative distance
from their apparent size.
• He had already calculated the actual distance to
several nearby galaxies, so this allowed him to find
the true distance to the galaxies that were farther
away.
• Here is a plot from his 1929 publication.
Recessional velocity verses Distance.
Modern Day Hubble plots
What is the equation for a straight line?
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1. y = ax2
2. y = 1/x + b
3. y = mx + b
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• So a straight line has the equation of
• y = mx + b
• In the Hubble plot the y-axis is velocity (v) and
the x-axis is distance (d)
• So we can write the equation as
• v = md + b
• What are m and b?
What are m and b?
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1. The slope and yintercept
2. The slope and the
rise over run
3. The x-intercept and
the y-intercept
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Modern Day Hubble plots
The Hubble Constant – The slope of the line
• The Hubble constant is a very fundamental quantity,
which tells us the age of the universe.
• Today we see that the universe is expanding, and it is
growing larger every day. This means that the
distance between galaxies are growing in size.
• What would happen if we could run the clock in
reverse? Move backward in time.
• The galaxies would get closer together, with the most
distant galaxies moving toward us at the greatest
speed. The result is that all galaxies would arrive at
the same point, at the same time.
• The equation of a straight line for the Hubble plot
looks like this, with b = 0
•
v = Hod
velocity = Ho times distance
• What does our normal velocity equation say?
• v = d/t
velocity = distance divided by time
• Or
• v = (1/t)d compared to v = (Ho)d
• So Ho tells us the time it takes for all the galaxies in the
universe to collapse to the same point. This is the age of
the universe.
• Ho = 1/tage
• Or
• tage = 1/Ho
Notice: Ho has units of km/s/Mpc
Today the best value is Ho = 71 km/s/Mpc
• We can use this value to compute the age of the
universe. We first need consistent distance units.
• 1 Mpc = 3.1 x 1019 km
• So Ho = (71km/s/Mpc)(1 Mpc/3.1 x 1019 km)
• Ho = 2.3 x 10-18 (1/seconds)
• tage = 1/Ho = 1/2.3 x 10-18 (1/seconds)
• tage = 4.37 x 1017 seconds
• There are 3.14 x 107 seconds in a year. So dividing
we get:
• tage = 13.7 x 109 years
• tage = 13.7 billion years
• The age of 13.7 billion years is consistent with
the age of the oldest known stars, which are
found to be between 12 and 14 billion years
old.
• Note that star age is based off of stellar
physics and has nothing to do, whatsoever
with the calculation of the age of the universe
using the Hubble constant.
Modern Day Hubble plots
• For our local portion of the universe the
Hubble relation is linear.
• That doesn’t have to be the case for the entire
universe.
• Space-time for the universe can appear very
flat over small distances but actually be very
curved over extremely large distances.
• Let’s think carefully about different possible
Hubble plots.
Here is Case #1
velocity
distance
What would this Hubble plot tell you?
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1. The universe is
contracting
2. The universe is
expanding
3. The universe is
static
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Universe is static, not expanding or contracting
velocity
#1
#2
distance
The rate of expansion is the slope of the line.
What would a linear slope, all the way back to the
greatest distances tell us.
velocity
today
Early
universe
distance
13.7 Glyrs
What would a linear relation back to the Big
Bang tell us about the universe
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1. The expansion rate
is zero
2. The expansion rate
is constant
3. The expansion rate
is increasing
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The universe (Space-time) is expanding, but the mass
in the universe is still going to be attracted from the
gravity of all the mass acting on each other.
Think carefully here. Which line would
represent a universe that has mass in it?
velocity
b
a
c
distance
13.7 Glyrs
Which universe has mass in it?
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1. a
2. b
3. c
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Think carefully here. Which line would
represent a universe that has mass in it?
velocity
b
a
c
distance
13.7 Glyrs
For a universe with mass only effected by gravity
we expect a curve like “a”
• “a” shows a universe that was expanding
quickly and has slowed as time goes by due to
the presence of gravity from massive objects.
• The more mass that was present in the early
universe, the more deceleration we expect.
And the curve “a” becomes steeper.
• Something like this.
We know that there is mass in the universe, so if
gravity is the only thing affecting the expansion…
Low density
velocity
High
density
Nothing should be
found below the
solid black line
distance
13.7 Glyrs
• The straight line represents a mass-less
universe with no gravity. In other words, the
expansion began and now the universe is
coasting. Growing in size but at a constant
rate.
• When the data falls below the sloping straight
line it means that the universe was moving
more slowly in the past and the expansion is
speeding up.
• How can this be?
What is required for the expansion to speed up
as time goes by?
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1. Dark matter
2. A universal repulsive
force
3. Less than zero
matter in the
universe
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• Gravity is only attractive. It can only work to help
slow the expansion of the universe.
• If the expansion is speeding up, then there has to
be a repulsive force that is acting to force the
expansion to grow more rapidly
• Gravity can’t do this.
• This repulsive force has been named “Dark
Energy”
• It fits into Einstein’s equations just like his old
cosmological constant. But this isn’t keeping the
universe static. It is forcing it to grow more
rapidly.
Using relativity we can model what will happen
in the future as well.
Past
Future
Today
Today
Our location in
the Universe
A distant galaxy or
quasar
Quiz 11
• Explain why we see many high luminosity
quasars at extremely large distances but none
in our local area of the universe.
• Consider these points.
• What is a quasar? Where does the luminosity
come from? When is the quasar? What is
happening at this time?