Download The Expanding Universe

The
Expanding
Universe
The Hubble Law
The Hubble constant Ho is one of the most important
numbers in cosmology because it may be used to
estimate the size and age of the universe
It indicates the rate at which the universe is expanding.
Although the Hubble "constant" is not really constant
because it changes with time (and therefore should
probably more properly be called the "Hubble
parameter").
Hubble Expansion Law
1929, Edwin Hubble announced that almost all galaxies
appeared to be moving away from us. This phenomenon was
observed as a redshift of a galaxy's spectrum. This
redshift appeared to have a larger displacement for faint,
presumably further, galaxies.
Hence, the farther a galaxy, the faster it is receding from
Earth. The Hubble constant is given by
H0 = v/d
•v is the galaxy's radial outward velocity,
•d is the galaxy's distance from earth
• H is the current value of the Hubble constant.
Units
Ho = 2.3 x 10-18 s-1 , this is SI units
Hubble Constant
The units of the Hubble constant are "kilometers per
second per megaparsec."
In other words, for each megaparsec of distance, the
velocity of a distant object appears to increase by
some value.
For example, if the Hubble constant was determined
to be 50 km/s/Mpc, a galaxy at 10 Mpc would have a
redshift corresponding to a radial velocity of 500
km/s.
1 parsec = 3.26 light years
Hubble Constant
H0 = 73.8±2.4 kilometers per second per megaparsec
Turn this into SI units
Ans = 2.4 x10-18 s-1
The important bits
obs  rest
obs
z  redshift 
1
z
rest
rest
obs  observed wavelength
act  actual wavelength
act  actual wavelength
v
z
c
v  dH 0
Red shift example
Light from a distant galaxy is measured as 460 nm. On
earth the same spectral line is measured as 430nm.
Calculate the redshift , z
observe  rest
z
rest
z
460  430
430
 0.070
Calculate the speed of the galaxy relative to earth
v
z
c
v
0.07 
3x108
 v  3x10 x 0.07
8
 v  2.1x10 m s
7
1
How far is the galaxy from earth ?
v  Ho d
v
d 
Ho
2.1x107
d 
2.3x10 18
 d  9.13x10 m
24
8
or 9.65x10 light years
Where does it come from ?
H0 x d
z
c
obs
z  redshift 
1
rest
c = speed of light
obs  rest
z
rest
d = distance to galaxy
v
z
c
v  dH 0
c  vsource
1
c
c v
z   source  1
c
c
vsource
z
c
z
Redshift
Age of the Universe
The inverse of the Hubble constant is time
Ho = 2.3 x 10-18 s-1
4.348 x 10 17 s ( keep the number in your calculator ! )
1.38 x 1010 years or 13.8 billion years
Fate of the universe
1. Closed universe: the universe will slow its expansion
and eventually begin to contract.
2. Open universe: the universe will continue to expand
forever.
Gravity will determine what happens
Dark matter is a proposal to explain why the galaxies
rotate faster than the amount of visible mass
dictates AND Dark Energy is a proposal to explain
why the universe is expanding at a greater rate than
the mass of all the galaxies predicts.
Doppler Effect
The Doppler effect is the change in frequency you
notice when a source of sound waves is moving relative
to you.
When the source moves towards you, more waves reach
you per second and the frequency heard is increased.
If the source moves away from you less waves reach
you each second and the frequency heard decreases.
Doppler Effect, moving source and
stationary observer
 v 

f 0  f s 
 v  vs 
fo = observed frequency
fs = frequency of source
v = speed of sound
vs = speed of source
v+vs when source
moving away from
observer ( frequency
decreases)
v- vs when source
moving towards
observer (observed
frequency increases )
Source moving towards stationary
observer
A train travels at 44.7 ms-1 towards a stationary
observer when the driver sounds the 415 Hz horn.
Calculate the frequency of the sound as perceived by
the observer. Vsound = 340ms-1.
Fsource=415Hz
Vsource = 44.7 m
s-1
Vsound = 340 ms-1
f obs
f obs
f obs
340
 fs
340  44.7
 340 
 415

 295.3 
 478Hz
Source moving away from stationary
observer
A trumpet player is marching at 0.85 ms-1 away from a
stationary spectator at a football match. Calculate the
frequency of sound the spectator hears if the note
produced is 784 Hz.
f obs
fs = 784 Hz
Vs = 0.85
ms-1
Vsound = 340 m s-1
f obs
f obs
vsound
 fs
vsound  vsource
 340 
 784

 340  0.85 
 782 Hz
The BIG BANG
http://www.lifeinuniverse.org
Early theories
The universe started with a sudden appearance of
energy which consequently became matter and is
now everything around us. There were two theories
regarding the universe
The Steady State Universe: where the universe had
always been and would always continue to be in
existence.
The Created Universe: where at some time in the
past the universe was created.
Evidence
Hubble’s work
If the universe is expanding it seems reasonable to
suggest that it was smaller in the past !
Evidence
• if the universe was initially very, very hot as
the Big Bang suggests, we should be able to
find some remnant of this heat.
• In 1965, Radioastronomers Arno Penzias and
Robert Wilson discovered a 2.725 degree
Kelvin, (-270.425 degree Celsius) Cosmic
Microwave Background radiation (CMB) which
pervades the observable universe. This is
thought to be the remnant which scientists
were looking for. Penzias and Wilson shared in
the 1978 Nobel Prize for Physics for their
discovery.
Evidence
the abundance of the "light elements" Hydrogen and
Helium found in the observable universe are as
predicted by the Big Bang model of origins. ( 75%
Hydrogen and 25% helium )
Evidence Obler’s paradox
Why isn't the night sky uniformly at least as bright as
the surface of the Sun? If the Universe has infinitely
many stars, then presumably it should be. ( Infinitely
old ) After all, if you move the Sun twice as far away
from us, we will intercept one quarter as many photons,
but the Sun's angular area against the sky background
will also have now dropped to a quarter of what it
was. So its real intensity remains constant. With
infinitely many stars, every element of the sky
background should have a star, and the entire heavens
should be at least as bright as an average star like the
Sun.
Obler’s Paradox
The Universe is young. Distant light hasn't even
reached us yet. The universe must have had a
beginning
The temperature of stellar
objects
The temperature of an object determines the
frequency of light it emits
‘cold objects ‘ glow red
As the temperature is increased they glow white hot
Stefan’s Law
P = σT4
Where stefans constant, σ,
= 5.67 x 10-8 Wm-2K-4.
What this means is that by
examining the spectrum of a
distant star, its temperature
can effectively be measured.
Some stars
The higher the
temperature the lower
the peak wavelength
Hotter objects emit
more radiation per unit
surface than cold ones.