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 Law1929, 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

rest

restobsz

1

rest

obsredshiftz

c

vz

0dHv

wavelengthactualact

wavelengthobservedobs

wavelengthactualact

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

rest

restobservez

070.0

430

430460

z

Calculate the speed of the galaxy relative to earth

c

vz 8103

07.0x

v 07.0103 8 xxv

17101.2 smxv

How far is the galaxy from earth ?

dHv ooH

vd

18

7

103.2

101.2

x

xd

mxd 241013.9

yearslightxor 81065.9

Where does it come from ?

c

dxHz 0 1

rest

obsredshiftz

rest

restobsz

d = distance to galaxy

c = speed of light

c

vz

c

vz

c

v

c

cz

c

vcz

source

source

source

1

1

0dHv

Redshift

Age of the UniverseThe 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

s

s vv

vff0

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.

Hzf

f

fsf

obs

obs

obs

478

3.295

340415

7.44340

340

Fsource=415Hz

Vsource = 44.7 m s-1

Vsound = 340 ms-1

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.

fs = 784 Hz

Vs = 0.85 ms-1

Vsound = 340 m s-1

Hzf

f

vv

vff

obs

obs

sourcesound

soundsobs

782

85.0340

340784

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 universeThe 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 LawP = 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.