Physics Notes: Evolution of Cosmology from Ancient to Modern - Prof. Bahram Mashhoon, Study notes of Physics

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Wed 8/26/09
-The Magic Universe  ~100,000 yrs ago
-The Mythic Universe  ~10,000 yrs ago
-The Anthropocentric Universe  ~Several thousand yrs ago
-According to Aristotle, the place [earth] we live on is different from those places out there in the night sky  It also seemed everything out there revolved around us  4 elements for earth o Earth o Fire o Air o Water o Each of the elements tends to go up or down  Sun/moon o Made of ether (etheric element) o 5th essence  Quintessence o Have circular motion  not up or down  represented by a snake eating it’s own tail
-Aristotle’s Universe  spatially finite o if it were infinite it wouldn’t work because it would compete with god because he is infinite  steady state  the circular motions are perfect because they have no beginning or end

-Claudius Ptolemy  2nd century AD  Worked at museum of Alexandria (Egypt)  Astronomer & Mathematician  Geocentric System (earth at center) o He realized this was wrong but he needed to agree with religion or else  So someone came up with the idea of using circles rotating on circles  Eccentrics  Epicycles  Equants
-Fourier Analysis
o Take the largest side  Semi-major axis of orbit  P = period for full orbit  (P^2) = (fixed number)(R^3)  (t^2) = [(4(pi^2))/(gm)](R^3)
-Earth orbiting seasons  summer is at the furthest but we’re tilted closer so it’s warmer o ecliptic tilt of 23 degrees  sept 21 is the autumnal equinox o start of fall  dec 21 is the winter solstice o start of winter  mar21 is spring/vernal equinox o start of spring  june21 is summer solstice o start of summer  middle of fall is oct31  middle of winter is groundhog dog Mon 8/31/09
-continuing the orbit discussion
- Galileo Galilei 1564 (birth of Shakespeare) – 1642 (birth of Newton)  Opposed physicist Aristotle  Supported Copernicus  Did experiments  Improved telescope  1610 – wrote The Starry Messenger o says moon isn’t ether, but a rock or something  mountains on the moon o Saw satellites around Jupiter o Numerous stars of the milky way  All their light made the ‘cloud’
- We live in a spiral arm galaxy Wed 9/2/09 Velocity – change in position / change in time Acceleration – change in velocity / change in time Impetus = momentum (amount of motion) = mv Momentum = mass*velocity - Galileo  Acceleration of gravity does not depend on weight of object  “Impetus is conserved for a fleeting moving body.”  Intertia
I. The laws of physics apply everywhere
II. Earth is not the center of the Universe
- The Cosmological Principle: On the largest scales, all places are alike. On average, every place in the universe is just the same as any other place
- Rene Descartes (1596-1650)  French philosopher and mathematician  Came up with graph coordinates o Cartesian coordinates o A,b axis  “I think, therefore I am”  Mathematization of Phys. Sci o Or Mechanical Worldview o Or Clockwork Universe

Fri Sept. 4, 09
Renaissance – 14th, 15th, 16th centuries
- Descartes con’t  proposed there was an infinite god o he set down these laws  figure out the laws, figure out god Age of Reason  Came up with 0 degrees freezing 100 degrees boiling (for Celsius)  Human temperature 37 degrees
Fahrenheit  German physicist  32 freezing  212 boiling  98.6 human temperature
Kelvin  K = 273 + C o C = Celsius  Another branch of physics studying getting closer to absolute zero and what happens when near there  K = absolute scale o Can’t go negative
Hertzsprung - Russel (H-R diagram)  Diagram in book o Y – axis  Intrinsic luminosity  Starts 10^-2  Goes up to 10^4 o X – axis  Surface temperature (in K)  24k is ‘0’ point o sun is 1 luminosity  6k temp o mostly a negative sloping line  but all the other places have points, too.  Called this the ‘Main Sequence’  A star on the main sequence generates it’s energy by slowly converting hydrogen into helium  Upper right the main sequence are red giants  Don’t gain mass, just increase their physical size  Lower left the main sequence are white dwarfs 
MsubSUN = 2 x (10^33) gm
RsubSUN = 7 x (10^10) cm
LsubSUN = 4 x (10^33) ergs/sec = 4 x (10^22)megawatts
Star  Why don’t stars collapse due to gravity? o Core energy gives off heat/pressure counter acting gravity  Stars are globes of gas that radiate energy away into space. o Pressure of the gas balances attraction of gravity

Wed Sept 23
- Red Giant – distended gloves of cool gas with extremely large surface areas.  Becomes a white dwarf: about the size of earth, extremely dense and hot, dying stars, 10% of nearby stars are WD (no more than 20LY away)
- variable stars
- 25% eclipsing binary systems (two stars rotating around themselves)
- 75% pulsating variables  expanding and contracting with a definite period
- Cepheid  first discovered in the constellation Cepheus  over 700 in our galaxy  period 3-50 days  brightness can change by factor of 5  yellow giants above main sequence
- Cepheid variable: distance indicators
-1912 Henrietta Leavitt  discovered there is a relation between period and luminosity for Cepheid o period-luminosity relation o
-figuring distance to stars  I – stellar parallax o Works up to 300LY  II – L = Lsub0 / [4pi(r^2)]  Harlow Shaply o Was here at mizzou for journalism o A really, REALLY bad sickness going around the school  They closed it and not to said to comeback till it’s over o Ended up switching because got some astronomy books and read them  Was terrible at math but got tutored and ended up teaching astronomy here before graduating o Got a b.s and masters science 1910  1914 PhD o 1919  the debate over whether all stars or all galaxies caused such a split the world get together to talk about  shapely was our rep.  he won everyone over to believe galaxies o 1921  shaply became director of Harvard college observatory 
Wed Sept 29
- universe is expanding like a balloon
- Edwin Hubble ~1930
- our galaxy consists of a disk and halo  halo is globular clusters (actually sphere around galaxy) o GLOBULAR cluster is just a bunch of stars together within 100 LY sphere (100k-1,000k objects) o Don’t know how many we have because they have weird orbital patterns  Come in towards bulge and go out  These cause the bulge  Can pickup/leave stars  100k LY across  10k LY across central bulge  we have 100-200 globular clusters o from side to side it’s 200k LY  from solar system to center is 10kiloparsecs o or 30k LY  Disk o Population I stars  Young  Possibly have planets  Rich in heavy elements  Rich in dust + gas  Halo o Population II stars  Old  8-14 billion years  possibly no planets (not expected)  poor in heavy elements  poor in gas + dust
- stars in galaxies can organize in 2 ways  globular clusters o exist in halo and bulge o spherical in shape o diameter of ~100 LY o ~10^5 pop.II stars  open clusters o exist in the disk, pop.I stars, ~100 or several hundred stars o Pleiades cluster  Both clusters are important for distance measurements o H-R diagram  Use apparent for y-axis o For different clusters can be compared. If H-R diagram is 4 times fainter, it is 2 times more distant
- gas clouds and dust  nebula: cloud  reflection nebula: reflect light from nearby stars.  Emission nebula: heated by nearby or embedded stars  Obscuration: small grains of matter, dust
- our solar system/galaxy  lines/walls are galaxies and clusters and spaces are voids o called cellular structure  or honeycomb o THIS IS HOW THE UNIVERSE IS ORGANIZED ON THE LARGEST SCALE
- Why are some galaxies what they are?  We don’t know 
In the observable universe we expect there to be 100,000,000,000 universes
V = (2piR)/T
V = sqrt(GM/R)  G is Newton’s constant of gravity
It would take our solar system 200million years to go around our galaxy
- when all the systems in our galaxy were graphed  called the rotation curve  below is the theory used kepler-newton-einstein o









 in reality the curve goes straight out (red) o this means the further out from the bulge the larger mass it seems to have  explain this with dark matter  blue is bulge

Wednesday October 7, 2009
Dark Matter / kepler-netwon-einstein  6-10x the amount of actual/luminous matter  Has to do with the flat rotation curve of spiral galaxies (referencing graph)  Page 391 in textbook
- MACHOs  MAssiv Compact Halo Objects 
Now ch7 – The Big Bang Theory
- Edwin Hubble  discovered far away galaxies are moving away from us o blue shift is towards o red is away  Hubble Law o v = Hr o speed of recession of far away galaxies = H(the Hubble constant) times distance of galaxy away from us  Hubble Flow o Motion of galaxies according to Hubble  Everything moving away from all  Imagine a balloon o Also peculiar motion 
- believed big bang happened 14 billion years ago

Friday October 9, 2009
Cosmic Microwave Background Radiation (CMBR)  Radiation leftover from big bang  Discovered in 1965  Temperature ~3k (2.7k more accurate)  Wavelength ~1millimeter o Lowercase lambda means wavelength  In every cm^3 space there are ~400 photons of CMBR  we’re actually surprised we haven’t come across another form of life  there are ~10^23 planets out there
3 – review of physics Wednesday October 14, 2009
MIDTERM IS OCT. 28!!!  Covers the book through ch9  Each question is 10 pts o BE VERY SPECIFIC!
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 Homogeneous, isotropic, edgeless universe. - Classical  Newton: mechanical o Newtonian point particles  Exist in absolute space and time  Obey his laws o Electricity  Discovered through when flashes of light would appear when wool was rubbed
- magnetism?
- James Clark Maxwell: classical  electromagnetism  came to conclusion that light is electromagnetic radiation


Friday October 16, 2009
Newton:  Space time  Newtonian point particle (m)  To study something’s motion you look at what it’s made of (point particle)  Laws of motion
Maxwell ~150yrs ago  Put together laws of electricity and magnetism o Electromagnetism  Described by his eq.  Particles have an electrical charge o Charge is called q  >0 = positive  proton  <0 = negative  electron  =0 neutral  neutron o Mass = m o Ion is an electron that got kicked out o Isotopes are added neutrons o Electric charge (E) has an electric field (lines going out in all directions) which extend infinitely  If a charge is moving it produces a magnetic field (B)  These fields ore rings expanding in size infinitely  Wave-particle duality o Under certain circumstances you should look at an electron as a wave or particle
- atoms  in the nucleus, why are protons able to sit by each other? o There’s some other force
- light is made up of electromagnetic radiation  much stronger than gravity
- quantum nature:  weak nuclear force  strong nuclear force 
Chapter 9: space and time
- time:  the circling of the moon, earth, sun, around each other  physical time (a measure of motion) o atomic time  all hydrogen atoms are the same here on earth as they are in space and in galaxies  best way to measure time on earth  atomic clocks are refrigerator sized  RIDICULOUSLY ACCURATE o cosmological time o thermodynamic time  heat flows from the hot object to cold  never reverse  thermodynamic arrow  biological time (sleep/awake) o all humans have bio clocks o animals have bio clocks o biologists are trying to figure what/how is this regulated  we could make people younger/slow down aging  psychological time (EMOTION) o under times of stress, time feels long o under times of joy, time feels shorter o piaget did many studies on babies to try and figure out how babies develop a sense of time
-v=Hr  1/H ~age of the universe
- Ludwig Boltzmann  for an isolated system the heat always increases o entropy

Wednesday October 21, 2009
Chapter 9 – space and time  3dimensions of space = x,y,z,  1 dimensions of time o times is the 4thd
Relativity theory
H, minkowski – 1908  Put space and time together o Spacetime
-Space  I – dressed or undressed (no vacuum or vacuum) o Dressed: Aristotle, rene Descartes, ether (fifth element)  James clerk Maxwell o Ether is what makes EM waves travel  Undressed: atomists of the ancient times o Newton  II – absolute or relative  Scaling o ‘why do dogs have the size they do’ Galileo
- quantum fixes scales  Planck length, time, energy, mass 
- geometry + algebra 08/26/2009 1 - Describe Kepler's laws of planetary motion. 
I. A planet goes around the sun on an ellipse the sun at the focus of the ellipse  Used all the available info he had and realized this  Ellipse have two focus o Sun is one of them
II. The straight line joining the planet to the sun sweeps out equals in equal time  Further out from sun means slower but closer means faster so the areas stay the same
III. "The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit."  R = avg. radius of orbit o Ellipse doesn’t have same radius throughout  Take the largest side  Semi-major axis of orbit  P = period for full orbit  (P^2) = (fixed number)(R^3)  (t^2) = [(4(pi^2))/(gm)](R^3) o t = time

2 – What is the cosmological principle
On the largest scales, all places are alike. On average, every place in the universe is just the same as any other.

3 – Describe the Copernican Revolution
transition from the finite geocentric universe to the infinite and centerless universe. Proposed by Nicolaus Copernicus initially as a helio- centric universe.

4 –Describe Newton’s laws of motion
I. - In the absence of force, a body either is at rest or moves in a straight line with constant speed.
II. - A body experiencing a force F experiences an acceleration a related to F by F = ma, where m is the mass of the body. Alternatively, force is proportional to the time derivative of momentum.
III. - Whenever a first body exerts a force F on a second body, the second body exerts a force −F on the first body. F and −F are equal in magnitude and opposite in direction

5 – Describe Newton’s law of gravitation
Every mass attracts every other mass by a force pointing along the line intersection both points in an inertial frame of reference. The force is directly proportional to the product of the two masses and inversely proportional to the square distance between the point masses.



4 – Explain Hubble’s tuning fork diagram
the e0 e4 7 s0<Sa/SBa, Sb/SBb, Sc/SBc, diagram explaining how a elliptical galaxy go to a spiral galaxy

5 – describe open clusters and contrast them with globular clusters  Globular o Exist in halo and bulge of spiral galaxy o Spherical o Diameter ~100LY o ~10^5 population 2 stars  Open o Exist in the disk o Population 1 stars o ~100 or several hundred stars  contrast o they both are important for distance measurements by comparing different clusters  on the H-R diagram if .4x fainter then 2x more distant
homework 4 08/26/2009
1 – Describe the rotation of spiral galaxies. What is the dark matter problem?
According to theory, the rotation of a spiral galaxy should be:






 v = velocity  r = radius from center  up until the line is the bulge, after is not the bulge with the slop being represented by 1/sqrt(r)
In reality, the further from the center, the velocity stays the same. This means the further out from the bulge, the more mass there is.








This is explained because dark matter effects the stars in a way that we do not understand.


2 – What are radio galaxies? What are AGNs?
Radio galaxies and their relatives, radio-loud quasars and blazars, are types of active galaxy that are very luminous at radio wavelengths (up to 1039 W between 10 MHz and 100 GHz). The radio emission is due to the synchrotron process. The observed structure in radio emission is determined by the interaction between twin jets and the external medium, modified by the effects of relativistic beaming. The host galaxies are almost exclusively large elliptical galaxies. Radio-loud active galaxies are interesting not only in themselves, but also because they can be detected at large distances, making them valuable tools for observational cosmology. Recently, much work has been done on the effects of these objects on the intergalactic medium, particularly in galaxy groups and clusters.
An active galactic nucleus (AGN) is a compact region at the centre of a galaxy which has a much higher than normal luminosity over some or all of the electromagnetic spectrum (in the radio, infrared, optical, ultra-violet, X- ray and/or gamma ray wavebands). A galaxy hosting an AGN is called an active galaxy. The radiation from AGN is believed to be a result of accretion of mass by the supermassive black hole at the centre of the host galaxy. AGN are the most luminous persistent sources of electromagnetic radiation in the universe, and as such can be used as a means of discovering distant objects; their evolution as a function of cosmic time also provides constraints on cosmological models.

3 – Describe the large-scale distribution of luminous matter in the universe.
Large-Scale Distribution of (Luminous) Matter (galaxies) in the universe  Great wall around us  Voids where there is nothing  Some Australians studied a very small slice of the great wall and found it to repeat periodically


four forces/interactions of nature
weak  strong
gravity
EM force
Weak nuclear
Strong nuclear

4 – What is the arrow of time?
Arrow of time is uni-directrional: time always increases. This is because of the thermodynamic time and the idea that the entropy of an isolated system always increases.

5 – What are c, G, and h/t? What is their significance?  c = speed of light  G = Newton’s constant of gravitation  h = Planck’s constant = quantum of action o h/(2pi) = o h bar sqrt](h-bar*G)/(c^3)] ~10^-33cm  Planck length  nucleus is ~10^-13cm  currently exploring 10^-18cm using LHC  there is also Planck mass, time  use these given variables to find out Planck’s length, time, and mass 08/26/2009 1 - Describe the aberration of starlight 
At the instant of any observation of an object, the apparent position of the object is displaced from its true position by an amount which depends solely upon the transverse component of the velocity of the observer, with respect to the vector of the incoming beam of light (i.e., the line actually taken by the light on its path to the observer). The result is a tilting of the direction of the incoming light which is independent of the distance between object and observer.

In the case of an observer on Earth, the direction of a star's velocity varies during the year as Earth revolves around the Sun (or strictly speaking, the barycenter of the solar system), and this in turn causes the apparent position of the star to vary. This particular effect is known as annual aberration or stellar aberration, because it causes the apparent position of a star to vary periodically over the course of a year. The maximum amount of the aberrational displacement of a star is approximately 20 arcseconds in right ascension or declination. Although this is a relatively small value, it was well within the observational capability of the instruments available in the early eighteenth century.

Aberration should not be confused with stellar parallax, although it was an initially fruitless search for parallax that first led to its discovery.[1] Parallax is caused by a change in the position of the observer looking at a relatively nearby object, as measured against more distant objects, and is therefore dependent upon the distance between the observer and the object. [1]

2 – What is the significance of c for the theory of relativity


3 – What is the Loretz-Fitzgerald contraction?
H.a. Lorentz
Changed Galilean transformation to
Tprime = t – [(vx)/(c^2)]
Xprime = x – (vt)
Lorentz transformation/length contraction
L = Lprime sqrt(1-(v^2/c^2) 08/26/2009
1 – What is the escape velocity?


2 – What is the gravitational radius of an astronomical body of mass M?
r = (2GM) / (c^2)

3 – What is the black hole horizon?
It is the area surrounding a black hole that seperates the stationary exterior (outside world) from the dunamic interior of the black hole.

4 – What is naked singularity?


5 – Describe the differences between stellar and massive black holes
Stellar black holes are roughly 10 to 100 solar masses in sizem have an accretion disk surrounding them, and emit many x-rays in all diretions from the disk.
Massive black holes are ~10^6 to ~10^9 solar masses in size and also have an accretion disk. They also seem to have jets spouting from the center shooting out jets of x-ray. We don’t know how they form but one possible idea is two stellar black holes join together. It is also thought that they exist in the nuclei of all galaxies.
08/26/2009 1 – Is the universe accelerating? Until roughly 10 years ago, people thought the gravitational attraction of all matter in the universe would slow down the Hubble Recession of galaxies. Based on recent observations 10 years ago, it appears the galaxies should be accelerating. This could be due to some cosmic repulsive force that we call dark energy. The interpretation of these observations has been the cause of controversy. 2 – What is the cosmological constant Λ? It is a form of dark energy and it produces a repulsive force. Effective density = Λ / (4piG) 3 – What is the force due to dark energy? For the form of dark energy of the cosmological constant Λ (1/3)Λr Λ = cosmological constant r = distant galaxies 4 – What is the geometry of pace if the average density of the universe is given by [3(c^2)(H^2)] / (8piG) Flat, 3 dimensional Euclidean space 5 – What percentage of is believed to be due to:  luminous matter: ~5%  dark matter: ~25%  dark energy: ~70%  08/26/2009
1 – Explain the definition of red shift z in terms of the relation 1+z = λ0 / λ


2 – Explain the cosmological red shift z using the relation 1+z = R0 / R


3 – What is the significance of  z = 0  z = ∞

4 – Describe briefly the epoch of galaxy formation


5 – Describe briefly the decoupling era.