Download Document

IB PHYSICS
ASTROPHYSICS
Section E
The Universe
(A good video to watch)
http://www.youtube.com/watch?v=tnhken4_-A0
http://www.youtube.com/watch?v=AUF38eHqdxs
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
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)
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.
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
Eccentrici
ty
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
>28
30
24
8
1
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
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
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
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 lightyears
 The Andromeda Galaxy, M31, is the
nearest major galaxy to our own Milky
Way. It is about 3 million light years away
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.
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
Map of Super-clusters
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?
What is our address?
Universe
Local (virgo) super-cluster
Local cluster
Milky way
Solar system
Inner planets
Earth
North
America
Wisconsin
Lincoln High School
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
The Celestial Sphere
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.
Different sets of constellations are visible in
northern and southern skies.
Apparent Motion of The Celestial
Sphere
Apparent Motion of The Celestial
Sphere (2)
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
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.
Seasonal Changes in the Sky
• The night-time constellations change
with the seasons.
• This is due to the Earth’s orbit around
the Sun.
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)
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

Source of stellar energy
P-P Chain
o

H1
 H1

H1
He3
109years

1 sec
H1
He4
106year
H1
H1
H1


H1
Gamma ray

o
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.
Hydrostatic equilibrium
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
Black body
A black body is a good
emitter of radiation as
well as a good absorber
of radiation
•
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 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)
Practice Problem
• The sun has an approximate blackbody spectrum with most of the energy
radiated at a wavelength of 0.5 μm.
Find the surface temperature of the
sun.
Practice Problem
• The sun (radius R=7.0x10^8m) radiates a
total power of 3.9x10^26W. Find its
surface temperature.
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
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.
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.
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.
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
Practice Problem
• A star has half the sun’s surface
temperature and 400 times its luminosity.
How many times bigger is it?
LIGHT SPECTRA
Stellar Spectra
Absorption Lines
and
Classifications
Spectral Classification of Stars
Spectral
Class
Effective
Temperature
(K)
Colour
H Balmer
Features
Other Features
Main Sequence Lifespan
O
28,000 - 50,000
Blue
weak
ionised He+ lines, strong
UV continuum
1 - 10 Myr
B
10,000 - 28,000
Bluewhite
medium
neutral He lines
11 - 400 Myr
A
7,500 - 10,000
White
strong
strong H lines, ionised
metal lines
400 Myr - 3 Gyr
F
6,000 - 7,500
Whiteyellow
medium
weak ionised Ca+
3 - 7 Gyr
G
4,900 - 6,000
Yellow
weak
ionised Ca+, metal lines
7 - 15 Gyr
K
3,500 - 4,900
Orange
very weak
Ca+, Fe, strong
molecules, CH, CN
17 Gyr
M
2,000 - 3,500
Red
very weak
molecular lines, eg TiO,
neutral metals
56 Gyr
L?
<2,000
Tentative new (2000) classification for very low
mass stars.
Spectral Classification of Stars
Spectral Class Summary
Mnemonics to
remember the
spectral
sequence:
Oh
Oh
Only
Be
Boy,
Bad
A
An
Astronomers
Fine
F
Forget
Girl/Guy
Grade
Generally
Kiss
Kills
Known
Me
Me
Mnemonics
Organizing the Family of Stars:
The Hertzsprung-Russell Diagram
We know:
Stars have different temperatures,
different luminosities, and different sizes.
Absolute mag.
or
Luminosity
To bring some order into that zoo of different
types of stars: organize them in a diagram of
Luminosity
versus
Temperature (or spectral type)
Hertzsprung-Russell Diagram
Spectral type: O
Temperature
B
A
F
G
K
M
Hertzsprung-Russell Diagram
Absolute magnitude
Betelgeuse
Rigel
Sirius B
Color index, or spectral class
Stars in the vicinity of the Sun
L  Mass3.5
90% of the stars are on the Main Sequence!
Specific segments of the main sequence are occupied
by stars of a specific mass
Majority of stars are here
H R Diagram
H R Diagram
H R Diagram
To learn more visit,
http://aspire.cosmic-ray.org/labs/star_life/starlife_main.html
Binary stars –
Visual binary stars
Visual binary star can be
distinguished as two stars using a
telescope
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
Binary stars –
Eclipsing binary stars
Eclipsing binary star shows a periodic
drop in the brightness of the light from
the ‘star’
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.
Astrological conversions
•
•
•
•
•
•
1AU = 1.496*10^11m
1ly = 9.46*10^15m
1ly = 63240 AU
1pc = 3.086*10^16m
1pc = 3.26 ly
1pc = 206265 AU
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)
The Small-Angle
Formula
 d
D
206265
D = linear size of object
θ = angular size of
object (in arcseconds)
d = distance to the
object
On November 28, 2000, Jupiter was 609
million kilometers from Earth and had an
angular diameter of 48.6″. Using the smallangle formula, determine Jupiter’s actual
diameter.
D = 48.6″ x 609,000,000 km / 206265 = 143,000
km
The Small-Angle
Formula
D
 d
206265
D = linear size of object
θ = angular size of
object (in arcsec)
d = distance to the
object
Problems
1. 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)
2. Find the distance (in meters) to Procyon, which has a
parallax of 0.285 arc sec.
(1.08x10^17m)
3. The distance of Epsilon Eridani is 10.8ly. What is its
parallax?
(0.3 arcsec)
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.
Apparent magnitude (m)
1. The ratio of the apparent brightness of star with m=1 to that of a star
with m=6 is
b(m  1)
 100
b(m  6)
2. The ratio of the apparent brightness of stars with apparent magnitude
values differing by 1 is
1
b

b
b
b
b
(
m

1
)
(
m

2
)
(
m

3
)
(
m

4
)
(
m

5
)





 100 5  2.512
 b(m  2) b(m  3) b(m  4) b(m  5) b(m  6)



3. In general, the ratio of apparent brightness of stars with apparent
magnitudes m1 and m2 is
 bm

 1  2.512(m2 m1) 
 bm2

Absolute magnitude (M)
1. 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
2. The relation between apparent magnitude and absolute magnitude is
d
M  m  5 log 
 10 
‘d’ is to be taken in pc.
3. The ratio of the luminosities of two stars is given by
L1
 2.512 ( M 2  M1 )
L2
Practice Problem
• Calculate the absolute magnitude of a star
whose distance is 25.0ly and whose
apparent magnitude is 3.45.
Practice Problem
• Calculate the distance to Sirius using the
data m=-1.43 and M=1.4
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?
Distance measurement –
Spectroscopic parallax method
(up to 10 Mpc)
1. Step1 – Observe the star’s
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 star’s apparent
brightness (b)
4. Step4 – Calculate the distance
using the formula
Distance measurement Cepheid variables method
(suitable up to 4Mpc using terrestrial telescopes and up to about 40 Mpc using
Hubble Space Telescope)
1. Cepheid Variables are those
whose absolute Magnitude (or
luminosity) varies periodically
2. The period of variation is related
to their absolute magnitude (or
luminosity)
3. 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
d
M  m  5 log 
 10 
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
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….
Olber’s paradox
Olber’s paradox
Olbers’ Paradox in another way
There will be a tree at every line of direction
if the forest is sufficiently large
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.
Correct Answer(s)
• The Universe is expanding
• The Universe is young
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.
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
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
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)
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)
Space-time curvature
• For open universe:
W< 1 and spacetime has a negative
curvature
• For closed
universe: W> 1 and
space-time has a
positive curvature
• For flat universe:
W 1 and spacetime no curvature

r
W


r o 
