1. IB PHYSICS ASTROPHYSICS Section E

2. The Universe (A good video to watch)

3. 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

4. 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 (e=0 is perfect circle and e=1 is straight line)

5. 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.

6. 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
1.88
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 2
>28 30 24 8

7. 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

8. 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

9. 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

10. 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

11. 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.

12. 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

13. Map of Super-clusters

14. 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?

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

16. 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

17. The Celestial Sphere

18. 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 Earth’s equator onto the c. s.
North celestial pole = projection of Earth’s north pole onto the c. s.

19. Different sets of constellations are visible in northern and southern skies.

20. Apparent Motion of The Celestial Sphere

21. Apparent Motion of The Celestial Sphere (2)

22. 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

24. 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.

25. Seasonal Changes in the Sky
The night-time constellations change with the seasons.
This is due to the Earth’s orbit around the Sun.

26. The Sun and Its Motions
Due to Earth’s 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)

28. 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

30. Source of stellar energy P-P Chain
109years H1 H1
He3 H1
1 sec
He4 H1
106year H1 H1 H1
Gamma ray H1

31. P-P Chain
The net result is
4H1 --> He4 + energy + 2 neutrinos
where the released energy is in the form of gamma rays and visible light.

32. Hydrostatic equilibrium

33. 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 earth’s surface.
**The luminosity from our sun is
3.9 x 10^26W

34. Black body
A black body is a good emitter of radiation as well as a good absorber of radiation

35. Black body radiation lmax T = constant (2.9 x 10-3 mK)
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 Wien’s 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 4πr^2) and s (sigma) is the known as the Stefan constant (5.67 x 10-8 Wm-2K-4)

36. 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.

37. Practice Problem
The sun (radius R=7.0x10^8m) radiates a total power of 3.9x10^26W. Find its surface temperature.

38. Practice Problem
The sun is 1.5 x 10^11m from Earth. Estimate how much energy falls on a surface area of 1m^2 in one year.
3.9 x 10^26/(4pi(1.5 x 10^11)^2)
Ans x seconds in one year
= 4.4 x 10^10J

39. 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.

40. 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.

41. Practice Problem
The wavelength maximum in the spectrum of Betelgeuse is 9.6x10^-7m. The luminosity of Betelgeuse is 10^4 times the luminosity of the sun. Estimate the surface temperature of Betelgeuse and also its radius in terms of the radius of the sun.

42. Practice Problem
The apparent brightness of a star is 6.4 x 10^-8 W/m^2. If its distance is 15ly, what is its luminosity?
1ly = 9.46 x 10^15m

43. Practice Problem
A star has half the sun’s surface temperature and 400 times its luminosity. How many times bigger is it?

44. LIGHT SPECTRA

46. Stellar Spectra Absorption Lines and Classifications

47. Spectral Classification of Stars
Spectral Class Summary

48. Spectral Classification of Stars
Spectral Class Summary Oh Be A
Fine
Girl/Guy
Kiss Me Oh
Only
Boy,
Bad An
Astronomers F
Forget
Grade
Generally
Kills
Known Me
Mnemonics
Mnemonics to remember the spectral sequence:

49. 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
versus
Temperature (or spectral type)
Absolute mag.
Hertzsprung-Russell Diagram
Luminosity or
Temperature
Spectral type: O B A F G K M

50. Hertzsprung-Russell Diagram
Betelgeuse
Rigel
Absolute magnitude
Sirius B
Color index, or spectral class

51. Figure 8.6: We could analyze automobiles by plotting their horsepower versus their weight and thus reveal relationships between various models. Most would lie somewhere along the main sequence of “normal” cars.

52. Stars in the vicinity of the Sun

53. 90% of the stars are on the Main Sequence!

54. Specific segments of the main sequence are occupied
by stars of a specific mass
Majority of stars are here

55. H R Diagram

56. H R Diagram

57. H R Diagram To learn more visit,

58. Binary stars – Visual binary stars
Visual binary star can be distinguished as two stars using a telescope

59. 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

60. Binary stars – Eclipsing binary stars
Eclipsing binary star shows a periodic drop in the brightness of the light from the ‘star’

61. 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.

62. Astrological conversions
1AU = 1.496*10^11m
1ly = 9.46*10^15m
1ly = AU
1pc = 3.086*10^16m
1pc = 3.26 ly
1pc = AU

63. Distance measurement Trigonometric parallax method
Distance is given by the expression, d=1/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)

64. The Small-Angle Formula
D = linear size of object
θ = angular size of object (in arcseconds)
d = distance to the object

65. 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 Jupiter’s actual diameter.
D = 48.6″ x 609,000,000 km / = 143,000 km
The Small-Angle Formula
D = linear size of object
θ = angular size of object (in arcsec)
d = distance to the object q × d = D
206265

66. 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 arc sec.
(1.08x10^17m)
3. The distance of Epsilon Eridani is 10.8ly. What is its parallax?
(0.3 arcsec)

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

68. Apparent magnitude (m)
The ratio of the apparent brightness of star with m=1 to that of a star with m=6 is
The ratio of the apparent brightness of stars with apparent magnitude values differing by 1 is
In general, the ratio of apparent brightness of stars with apparent magnitudes m1 and m2 is

69. 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

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

71. Practice Problem
Calculate the distance to Sirius using the data m=-1.43 and M=1.4

72. Practice Problem
A main sequence star emits most of its energy at a wavelength of 2.4x10^-7m. It’s apparent brightness is measured to be 4.3x10^-9 W/m^2. How far is the star?

73. Distance measurement – Spectroscopic parallax method (up to 10 Mpc)
Step1 – Observe the star’s spectrum (with instruments) and identify its spectral type
Step2 – Get the luminosity (L) of the star from the HR diagram
Step3 – Measure (with instruments) the star’s apparent brightness (b)
Step4 – Calculate the distance using the formula

74. 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

75. Newton’s model of Universe
Universe is infinite (in space and time)
It is uniform and static
Newton’s model leads to Olber’s paradox

76. Olber’s 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….

77. Olber’s paradox

78. Olber’s paradox

79. Olbers’ Paradox in another way
There will be a tree at every line of direction
if the forest is sufficiently large

80. 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.

81. Correct Answer(s)
The Universe is expanding
The Universe is young

82. 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.

83. 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

84. 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

85. 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)

86. 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)

87. Space-time curvature
For open universe: W < 1 and space-time has a negative curvature
For closed universe: W > 1 and space-time has a positive curvature
For flat universe:
W = 1 and space-time no curvature