IB PHYSICS ASTROPHYSICS Section E

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IB PHYSICS ASTROPHYSICSSection E
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The Universe(A good video to watch)
http//www.youtube.com/watch?vtnhken4_-A0
http//www.youtube.com/watch?vAUF38eHqdxs
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Solar system

• Solar system has 8 planets (earlier 9 planets
  including Pluto)
• Planets move around in elliptical orbits
• The elliptical orbits are characterized by their
  eccentricities
• Ellipse with e close to 1 are more flatter
• Near circular orbits have e close to 0
• Inner planets are planets closest to Sun
  Mercury, Venus, Earth and Mars
• Outer planet are Jupiter, Saturn, Uranus,
  Neptune

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Eccentricity of an elliptical orbit

• Eccentricity is the ratio between the distance
  between the two foci of the ellipse and the
  length of the major axis of the ellipse (e0 is
  perfect circle and e1 is straight line)

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Status of Pluto

• Pluto first discovered in 1930 by Clyde W.
  Tombaugh
• A full-fledged planet is an object that orbits
  the sun and is large enough to have become round
  due to the force of its own gravity. In addition,
  a planet has to dominate the neighborhood around
  its orbit.
• Pluto has been demoted to be a Dwarf planet
  (2006) because it does not dominate its
  neighborhood. Charon, its large moon, is only
  about half the size of Pluto, while all the true
  planets are far larger than their moons.

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Solar system(Sidereal period is the Time
required for a celestial body in the solar system
to complete one revolution with respect to the
fixed stars)
Aspects Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto
Mean Distance from the Sun (AU) 0.3871 0.7233 1 1.524 5.203 9.539 19.19 30.06 39.48
Orbital period (years) 0.24 0.62 1 1.88 11.86 29.46 84.01 164.79 248.54
Mean Orbital Velocity (km/sec) 47.89 35.04 29.79 24.14 13.06 9.64 6.81 5.43 4.74
Orbital  Eccentricity 0.206 0.007 0.017 0.093 0.048 0.056 0.046 0.010 0.248
Body rotation period (hours) 1408 5832 23.93 24.62 9.92 10.66 17.24 16.11 153.3
Number of observed satellites 0 0 1 2 gt28 30 24 8 1
 
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Asteroid belt

• Asteroid Belt is the region between the inner
  planets and outer plants where thousands of
  asteroids are found orbiting around the Sun
• Asteroids are chunks of rock and metal that
  orbit around the Sun
• The largest known asteroid is CERES

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Beyond solar system Other stars

• Other stars There billions and billions of
  stars other than our sun in the universe -
  Nearest star system is Alpha Centauri which
  consists of 3 stars - Proxima Centauri at 4.22
  light years and Alpha Centauri A, B (binary
  stars) at 4.35 light years
• Stars are of different types Giants, Super
  Giants, Red Giants, Neutron Star, White Dwarfs,
  Main Sequence Stars, Black Holes - all names
  based on their different stages of evolution

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Beyond solar system Stellar clusters

• Stellar clusters are groups of stars that are
  gravitationally bound
• Two types of stellar clusters
• Globular cluster tight groups of hundreds of
  thousands of very old stars
• Open cluster - contain less than a few hundred
  members, and are often very young - may
  eventually become disrupted over time and no
  longer gravitational bound move in same
  direction in space referred to as stellar
  association or moving group

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Beyond solar system - Galaxies

• We belong to the Milky Way galaxy spiral
  galaxy 100,000 light years wide 16,000 light
  years thick at the centre has three distinct
  spiral arms - Sun is positioned in one of these
  arms about two-thirds of the way from the
  galactic center, at a distance of about 30,000
  light-years
• The Andromeda Galaxy, M31, is the nearest major
  galaxy to our own Milky Way. It is about 3
  million light years away

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Clusters

• Group of galaxies form a cluster
• Milky Way belongs to The Local Group cluster
  that consists of over 30 galaxies
• Local Group is held together by the gravitational
  attraction between its members, and does not
  expand with the expanding universe
• Its two largest galaxies are the Milky Way and
  the Andromeda galaxy - most of the others are
  small and faint.

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Super-clusters

• Groups of clusters and smaller galaxy groups
• Not bound by gravity
• Take part in expansion of universe
• Largest known structure of cosmos
• Our local cluster belongs to the local super
  cluster, also known as the virgo super-cluster

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Map of Super-clusters
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What is our address

• If you mail something you need to let the post
  office know exactly where it needs to go.
• So.
• What is our address in the universe?

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What is our address?
Universe
Local (virgo) super-cluster
Local cluster
Milky way
Solar system
Inner planets
Earth
North America
Wisconsin
Lincoln High School
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Beyond solar system - Nebula

• Nebula is a huge, diffuse cloud of gas and dust
  in intergalactic space. The gas in nebulae (the
  plural of nebula) is mostly hydrogen gas (H2).
• THEY ARE THE BIRTH PLACE OF STARS

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The Celestial Sphere
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The Celestial Sphere
Zenith Point on the celestial sphere directly
overhead Nadir Point on the c.s. directly
underneath (not visible!)
Celestial equator projection of Earths
equator onto the c. s. North celestial pole
projection of Earths north pole onto the c. s.
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• Different sets of constellations are visible in
  northern and southern skies.

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Apparent Motion of The Celestial Sphere
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Apparent Motion of The Celestial Sphere (2)
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Constellation

• A constellation is a group of stars that, when
  seen from Earth, form a pattern
• The stars in the sky are divided into 88
  constellations (12 based on zodiac signs)
• The brightest constellation is Crux (the Southern
  Cross)
• The constellation with the greatest number of
  visible stars in it is Centaurus (the Centaur -
  with 101 stars)
• The largest constellation is Hydra (The Water
  Snake) which extends over 3.158 of the sky.
• One of the most popular constellation is the
  Orion

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What we see
The stars of a constellation only appear to be
close to one another Usually, this is only a
projection effect. The stars of a constellation
may be located at very different distances from
us.
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Seasonal Changes in the Sky

• The night-time constellations change with the
  seasons.
• This is due to the Earths orbit around the Sun.

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The Sun and Its Motions
Due to Earths revolution around the sun, the sun
appears to move through the zodiacal
constellations. (Imagine you look at the sun in
the daytime. The constellation that would be in
its background is the zodiac sign for that month)
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CONSTELLATIONS THAT WE MAY SEE IN THE
NIGHT January ? Caelum, Dorado, Mensa, Orion,
Reticulum, Taurus February ? Auriga,
Camelopardalis, Canis Major, Columba, Gemini,
Lepus, Monoceros, Pictor March ? Cancer, Canis,
Minor, Carina, Lynx, Puppis, Pyxis, Vela, Volans
April ? Antlia, Chamaeleon, Crater, Hydra, Leo,
Leo Minor, Sextans, Ursa Major May ? Canes
Venatici, Centaurus, Coma Berenices, Corvus,
Crux, Musca, Virgo June ? Boötes, Circinus,
Libra, Lupus, Ursa Minor July ? Apus, Ara,
Corona Borealis, Draco, Hercules, Norma,
Ophiuchus, Scorpius, Serpens, Triangulum
Australe August ? Corona Austrina, Lyra,
Sagittarius, Scutum, Telescopium September ?
Aquila, Capricornus, Cygnus, Delphinus, Equuleus,
Indus, Microscopium, Pavo, Sagitta,
Vulpecula October ? Aquarius, Cepheus, Grus,
Lacerta, Octans, Pegasus, Piscis
Austrinus November ? Andromeda, Cassiopeia,
Phoenix, Pisces, Sculptor, Tucana December ?
Aries, Cetus, Eridanus, Fornax, Horologium,
Hydrus, Perseus, Triangulum
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Source of stellar energy P-P Chain

• 109years

H1
H1
He3
H1
1 sec
He4
H1
106year
H1
H1
H1
Gamma ray
H1
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P-P Chain

• The net result is
• 4H1 --gt He4 energy 2 neutrinos
• where the released energy is in the form of
  gamma rays and visible light.

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Hydrostatic equilibrium
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Luminosity and Apparent Brightness
Luminosity is the total light energy emitted
per second. (Power) Apparent brightness is the
light received per unit area per second at the
earths surface. The luminosity from our sun
is 3.9 x 1026W
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Black body

• A black body is a good emitter of radiation as
  well as a good absorber of radiation

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Black body radiation

• The intensity of light emitted by a black body is
  distributed over a range of wavelength.
• The maximum intensity is radiated at a
  particular wavelength designated as lmax
• The value of lmax decreases with increasing
  temperature as per the Wiens Displacement given
  by
• lmax T constant (2.9 x 10-3 mK)
• The area under each curve gives the total energy
  radiated by the black body (luminosity) per
  second at that temperature and is governed by the
  Stefan-Boltzmann law, which is
• L sAT4
• where A is the surface area of the black body
  (for a sphere 4pr2) and s (sigma) is the known
  as the Stefan constant (5.67 x 10-8 Wm-2K-4)

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Practice Problem

• The sun has an approximate black-body spectrum
  with most of the energy radiated at a wavelength
  of 0.5 µm. Find the surface temperature of the
  sun.

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Practice Problem

• The sun (radius R7.0x108m) radiates a total
  power of 3.9x1026W. Find its surface
  temperature.

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Practice Problem

• The sun is 1.5 x 1011m from Earth. Estimate how
  much energy falls on a surface area of 1m2 in
  one year.
• 3.9 x 1026/(4pi(1.5 x 1011)2)
• Ans x seconds in one year
• 4.4 x 1010J

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Practice Problem 2

• The radius of star A is three times that of star
  B, and its temperature is double that of B. Find
  the ratio of the luminosity of A to that of B.

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Practice Problem 2 continued

• The stars in the first part have the same
  apparent brightness when viewed from Earth.
  Calculate the ratio of their distances.

• The radius of star A is three times that of star
  B, and its temperature is double that of B. Find
  the ratio of the luminosity of A to that of B.

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Practice Problem

• The wavelength maximum in the spectrum of
  Betelgeuse is 9.6x10-7m. The luminosity of
  Betelgeuse is 104 times the luminosity of the
  sun. Estimate the surface temperature of
  Betelgeuse and also its radius in terms of the
  radius of the sun.

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Practice Problem

• The apparent brightness of a star is 6.4 x 10-8
  W/m2. If its distance is 15ly, what is its
  luminosity?
• 1ly 9.46 x 1015m

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Practice Problem

• A star has half the suns surface temperature and
  400 times its luminosity. How many times bigger
  is it?

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LIGHT SPECTRA
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Stellar Spectra Absorption Lines and
Classifications
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Spectral Classification of Stars
Spectral Class Summary
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Spectral Classification of Stars
Spectral Class Summary
Oh Only
Boy, Bad
An Astronomers
F Forget
Grade Generally
Kills Known
Me Mnemonics
Oh
Be
A
Fine
Girl/Guy
Kiss
Me
Mnemonics to remember the spectral sequence
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Organizing the Family of Stars The
Hertzsprung-Russell Diagram
We know Stars have different temperatures,
different luminosities, and different sizes.
To bring some order into that zoo of different
types of stars organize them in a diagram of
Luminosity
Temperature (or spectral type)
versus
Absolute mag.
Hertzsprung-Russell Diagram
Luminosity
or
Temperature
Spectral type O B A F G K M
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Hertzsprung-Russell Diagram
Betelgeuse
Rigel
Absolute magnitude
Sirius B
Color index, or spectral class
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Stars in the vicinity of the Sun
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90 of the stars are on the Main Sequence!
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Specific segments of the main sequence are
occupied by stars of a specific mass
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H R Diagram
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H R Diagram
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H R Diagram
To learn more visit, http//aspire.cosmic-ray.org
/labs/star_life/starlife_main.html
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Binary stars Visual binary stars
Visual binary star can be distinguished as two
stars using a telescope
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Binary stars Spectroscopic binary stars
Spectroscopic binary is a system of two stars
orbiting around a common centre of mass. They are
identified by a the periodic shift or splitting
infrequency. The shift is caused because of
Doppler effect
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Binary stars Eclipsing binary stars
Eclipsing binary star shows a periodic drop in
the brightness of the light from the star
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Cepheid variable
Cepheids, also called Cepheid Variables, are
stars which brighten and dim periodically. The
time period of variation is proportional to the
Luminosity of the star.
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Astrological conversions

• 1AU 1.4961011m
• 1ly 9.461015m
• 1ly 63240 AU
• 1pc 3.0861016m
• 1pc 3.26 ly
• 1pc 206265 AU

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Distance measurementTrigonometric parallax method

• Distance is given by the expression, d1/p (p
  expressed in seconds of arc)
• Distance is measured in parsec abbreviated as
  pc
• 1 pc is the distance of a star that has a
  parallax angle of one arc second using a baseline
  of 1 astronomical unit.
• 1pc 206,265 astronomical units 3.08 x 1016m
• This method is suitable up to a distance of
  100pc (25pc for ground based measurements)

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On November 28, 2000, Jupiter was 609 million
kilometers from Earth and had an angular diameter
of 48.6?. Using the small-angle formula,
determine Jupiters actual diameter.

• D 48.6? x 609,000,000 km / 206265 143,000 km

q

d

D
206265
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Problems

• The distance to Sun and Moon are about 1.5 x 1011
  m and 3.8 x 108 m respectively. Both subtend an
  angle of about 0.5o from earth. Use this
  information to estimate their radii.
• (6.8 x 108 m, 1.7 x 106 m)
• Find the distance (in meters) to Procyon, which
  has a parallax of 0.285 arc sec.
• (1.08x1017m)
• 3. The distance of Epsilon Eridani is 10.8ly.
  What is its parallax?
• (0.3 arcsec)

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Apparent magnitude (m)

1. It is a measure of how bright a star appears as
   seen from the earth
2. The brightness is rated from a scale of 1 to 6
3. The classification scheme was proposed and used
   by Greek Astronomer about 2000 years ago
4. Stars numbered 1 are the brightest and those
   numbered 6 are very dim
5. Now stars have been discovered with magnitude
   values outside the range from 1 to 6.

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Apparent magnitude (m)

1. The ratio of the apparent brightness of star with
   m1 to that of a star with m6 is
2. The ratio of the apparent brightness of stars
   with apparent magnitude values differing by 1 is
3. In general, the ratio of apparent brightness of
   stars with apparent magnitudes m1 and m2 is

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Absolute magnitude (M)

• Absolute magnitude is the apparent magnitude of a
  star at a distance of 10 pc from Earth (or) it is
  a measure of how bright a star would appear if it
  were at a distance of 10 pc from Earth
• The relation between apparent magnitude and
  absolute magnitude is
• d is to be taken in pc.
• 3. The ratio of the luminosities of two stars is
  given by

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Practice Problem

• Calculate the absolute magnitude of a star whose
  distance is 25.0ly and whose apparent magnitude
  is 3.45.

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Practice Problem

• Calculate the distance to Sirius using the data
  m-1.43 and M1.4

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Practice Problem

• A main sequence star emits most of its energy at
  a wavelength of 2.4x10-7m. Its apparent
  brightness is measured to be 4.3x10-9 W/m2.
  How far is the star?

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Distance measurement Spectroscopic parallax
method(up to 10 Mpc)

1. Step1 Observe the stars spectrum (with
   instruments) and identify its spectral type
2. Step2 Get the luminosity (L) of the star from
   the HR diagram
3. Step3 Measure (with instruments) the stars
   apparent brightness (b)
4. Step4 Calculate the distance using the formula

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Distance measurement - Cepheid variables
method(suitable up to 4Mpc using terrestrial
telescopes and up to about 40 Mpc using Hubble
Space Telescope)

• Cepheid Variables are those whose absolute
  Magnitude (or luminosity) varies periodically
• The period of variation is related to their
  absolute magnitude (or luminosity)
• Distance measurement method
• Measure apparent magnitude of the star (m)
• Measure period (T)
• Use period-luminosity law to find M
• Use the equation below and find distance

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Newtons model of Universe

• Universe is infinite (in space and time)
• It is uniform and static
• Newtons model leads to Olbers paradox

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Olbers paradox

• If the universe extends infinitely, then
  eventually if we look out into the night sky, we
  should be able to see a star in any direction,
  even if the star is really far away.
• Since the universe was infinitely old, the light
  from stars at extremely far distances would have
  already reached us, even if they were 40 billion
  light years away.
• Then according to Steady State Theory we should
  be able to see a star anywhere in the night sky,
  and so the sky should have the same brightness
  everywhere. But as you all know, if you look at
  the sky at night, it's dark and speckled with
  bright points of light called stars! How can this
  be explained? Something seemed to be amiss.

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Olbers paradox
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Olbers paradox
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Olbers Paradox in another way
There will be a tree at every line of direction
if the forest is sufficiently large
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Possible Explanations

• There's too much dust to see the distant stars.
• The Universe has only a finite number of stars.
• The distribution of stars is not uniform.  So,
  for example, there could be an infinity of
  stars,but they hide behind one another so that
  only a finite angular area is subtended by them.
• The Universe is expanding, so distant stars are
  red-shifted into obscurity (Doppler effect).
• The Universe is young.  Distant light hasn't even
  reached us yet.

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Correct Answer(s)

• The Universe is expanding
• The Universe is young

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The Universe is young

• We live inside a spherical shell of "Observable
  Universe" which has radius equal to the lifetime
  of the Universe. 
• Objects more than about 13.7 thousand million
  years old (the latest figure) are too far away
  for their light ever to reach us.
• Redshift effect certainly contributes.  But the
  finite age of the Universe is the most important
  effect.

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Big Bang Model

• Light from galaxies show red shift
• This indicates that the universe is expanding
• Working backward, it is predicted that the
  universe should have started with a tiny volume
  of extremely dense matter
• Big Bang NOT AN EXPLOSION just an expansion
  of the Universe from an extremely tiny and dense
  state to what it is today
• Space and time started with Big Bang
• Before Big Bang, nothing existed !
• Universe does not expand into a VOID

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Cosmic Microwave Background (CMB)

• In 1964, Penzias and Wilson discover Cosmic
  Microwave Background (CMB) radiation
• CMB comes from outside our galaxy and is
  remarkably uniform
• The CMB corresponds to a temperature of 2.725K
  and a wavelength of a few cms (microwave region).
• CMB is considered as the remnant of the radiation
  from the Big Bang
• CMB supports the Big Bang theory that the
  universe must have started with extremely high
  temperature and high density and has cooled by
  expansion to what is it now

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Fate of the Universe

• The future of the universe depends on the density
  of universe
• Open universe - density (r) of universe is less
  than critical density (ro)
• Closed Universe - density of universe (r) more
  than critical density (ro)
• Flat universe - density of the universe (r) is
  equal to critical universe (ro)

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Dark Matter, MACHO and WIMP

• There does not appear to be enough visible matter
  to account for the mass that is required to
  gravitationally bind the universe together. There
  could be some matter which is not visible
• There could invisible matter such a Dark Matter,
  Massive Compact Halo Objects (MACHO) and Weakly
  Interactive Massive Particles (WIMP)

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Space-time curvature

• For open universe W lt 1 and space-time has a
  negative curvature
• For closed universe W gt 1 and space-time has a
  positive curvature
• For flat universe
• W 1 and space-time no curvature