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Cosmology

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Suzanne Cheney

on 24 November 2013

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Transcript of Cosmology

5.5.1 Structure of
the universe

An Ageing Star
The temperature and pressure at the center of the star starts to increase as the star becomes old and more complex fusion occurs. The thin shell of helium around the center begins to fuse to form more complex elements such as beryllium, carbon and oxygen nuclei.

This increased power causes the outer hydrogen layer to fuse rapidly. The increased radiation pressure causes the outer shell to expand.

mass < 3 solar masses
Stars, like our sun, which have a solar mass less than 3 solar masses, expand to red giant. The core continues to collapse and in a process called helium flash the material surrounding the core is ejected away from the core. There is a point where the electron degeneracy pressure prevents the star from collapsing further.
mass > 3 solar masses
A more massive star will then become a super red giant, after it collapses in to a white dwarf it can collapse further. The pressure overcomes the Fermi pressure, and electrons combine with protons to form neutrons and neutrinos. The neutrinos escape, leaving only neutrons. This generates a shockwave which causes it to supernova.
Contents of the universe
Our universe is everything that exists. This includes everything you can see such as stars and galaxies but also things you cannot see like microwave radiation. Galaxies, like our own milky way are a collection of stars held together by a force gravity. One of the stars of the milky way is our Sun which is surrounded by our solar system, this includes planets, dwarf planets, moons and comets.
Olbers' Paradox
Olbers' paradox states that for a infinite, uniform and static universe, the night sky should be bright because of light received in all directions from stars.
This is obviously not the case...
This therefore shows that the universe can not be static, infinite and uniform at the same time so one or more of these assumptions is incorrect.
The most famous comet is Halley's comet and is visible from the earth every 76 years.
Our solar system
Birth of a star
Stars are formed when clouds of dust and gas left behind after a supernovae are pulled together by gravity. When they have a large enough mass they begin to collapse in on themselves.

The temperature increases as gravitational potential energy is converted into kinetic energy. When the temperature becomes high enough the hydrogen nuclei begin to fuse to form helium nuclei.

The star is now stable as the attractive gravitational forces are in equilibrium with the radiation pressure. The star can stay in this stable state for billions of years
Definitions
Astronomical unit (AU
) -
The average distance of the Earth from the sun. 1AU = 1.496x10^11m

Parsec (pc)
-
The distance that gives a parallax an angle of 1 arc second. 1pc is roughly equal to 3.1x10^16m.

Light-years (ly)
-
The distance traveled by light in one year. 1ly is roughly equal to 9.5x10^15m

Olbers' paradox
-
For an infinite, uniform and static universe, the night sky should be bright because of light received in all directions.

Cosmological principle -

A principle that states that the universe has the same large-scale structure when observed from any point in the universe.

Hubble constant
-
The ratio of the speed v of a receding galaxy to it's distance x from the observer: Ho= v/x

The Expanding Universe
Modern telecopes can use spectrometers to observe the spectra of light from individual stars and galaxies.
Vesto Slipher noticed that the pattern of lines were the same for our own galaxy (this indicated they were made of the same elements), but the entire spectrum had shifted. This was either towards the blue end of the spectrum or the red end.
This means the wavelengths of some of these galaxies are slightly increased or decreased, when the wavelength is increased it is called red shift.
In terms of the Doppler effect this shows that these galaxies were moving away from us as the waves have been stretched out (wavelength has increased) from out prospective.

Cosmic Microwave Background Radiation
The Hot Big Bang model predicts that electromagnetic radiation should of been produced, this must therefore still be observed today.
As the universe has expanded the wavelengths of the background radiation has been stretched and is now in the microwave region.
In the late 1980's the Cosmic Background Explorer (COBE) found a coninous spectrum that had a constant temperature of 3K.
The radiation is isotropic and homogenous, which confirms the cosmological principle.
There are tiny fluctuations in temperature due to tiny energy-density variations.
The radiation also shows the Doppler shift, this shows that the milky way is rushing towards an unknown mass.
Cosmological Principle
A principle that states that the universe has the same large-scale structure when observed from any point in the universe.
This leaves behind the bright central core known as a white dwarf. It will then eventually cool down into a black dwarf.
For larger masses
After the supernova, a neutron star will remain. The mass of this neutron star is so large and so dense that it will collapse further. The star then becomes a black hole. The gravity is so strong that not even light can escape it. They are thought to be at the center of most galaxies.
For lighter stars
After the supernova the core of the star is left, it is now entirely made up of neutrons, this is called a neutron star and has an extremely high density (roughly about 10^18 kgm^-1).
What happens next depends on it's mass...
Our sun
Calculating red shift
c - the speed of light
v - the velocity of the source in the direction of the observer
lambda - the wavelength emitted
delta lambda - the difference between the observed wavelength and the emitted wavelength
z =
Hubble's law
D = the distance in Mpc
Ho = Hubble's constant (lies between 50kms^-1Mpc^-1 to 100kms^-1Mpc^-1)
v = recessional velocity in kms^-1
The velocity measured from the Doppler's shift, of galaxies moving away from the Earth, is proportional to their distance from the Earth for galaxies up to a few hundred megaparsecs away. Hubble's constant (Ho) is used as the constant.
Converting Hubble's constant into SI units
Hubble's constant is 70kms^-1mpc^-1
We first know that 1pc is roughly equal to 3.1x10^16m
so therefore 1Mpc is roughly equal to 3.1x10^22m
To get it into meters we times it by 1000
70kms^-1mpc^-1 = 70x10^3m s^-1 / 23.1X10^22m
= 2.26x10^-18 s^-1

The big bang
Hubble's Law implies that the universe is expanding.
This was the first evidence of there being a very hot explosion from which space and time evoloved, the Big Bang.
The graph can be used to calulate the age of the universe, a steap gradient would mean Ho was large and therefore th universe is young.
age of universe = 1 / Hubble constant
age of universe = 1/2.26x10^-18 = 4.43x10^17 s
= 4.43x10^17 / 3.16x10^7
= 14x10^9 years
Doppler effect
The change in frequency and wavelength of a wave caused by the relative movement between source and detector.
This means that an object traveling towards you would have wavelengths that are slightly bunched up, where as an object moving away from you would have wavelengths which had been stretched. This is noticeable in police sirens.
5.5.1 (a) and (b)
5.5.1 (c)
5.5.1 (d)
5.5.1 (e)
5.5.1 (h) and (i)
If the universe was 'static' then the night sky would by constantly lit by stars and the surface of the earth would be as hot as the surface of a star.
Even though the distant stars are very dim there would be large numbers of them and this would cause the night sky to be light
The milky way
5.5.1 (j)
5.5.1 (m)
5.5.1 (o)
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