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 flatterNear 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

ty0.206 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 light-years

The Andromeda Galaxy, M31, is the nearest major galaxy to our own Milky Way. It is about 3 million light years away

ClustersGroup of galaxies form a clusterMilky Way belongs to “The Local Group” cluster that consists of over 30 galaxiesLocal Group is held together by the gravitational attraction between its members, and does not expand with the expanding universeIts 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?

Lincoln High School

Universe

Local (virgo) super-cluster

Milky way

Solar system

Local cluster

Wisconsin

North America

Earth

Inner planets

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

Celestial equator = projection of Earth’s equator onto the c. s.

North celestial pole = projection of

Earth’s north pole onto the c. s.

Zenith = Point on the celestial sphere directly overhead

Nadir = Point on the c.s. directly underneath (not visible!)

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 patternThe 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 MotionsDue 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

109years 1 sec

He3

H1

He4

Gamma ray

106year

o

o

H1

H1

H1

H1

H1

H1

H1

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 lightreceived per unit area per second atthe 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 max

• The value of max decreases with

increasing temperature as per the Wien’s Displacement given by

max 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 = AT4

where A is the surface area of the black body (for a sphere 4πr^2) and (sigma) is the known as the Stefan constant (5.67 x 10-8 Wm-2K-4)

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.

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 Blue-white

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 White-yellow 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

Oh Only

Boy, Bad

An Astronomers

F Forget

Grade Generally

Kills Known

Me Mnemonics

Mnemonics to remember the spectral sequence:

Oh

Be

A

Fine

Girl/Guy

Kiss

Me

Spectral Class Summary

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)

Lum

inos

ity

Temperature

Spectral type: O B A F G K M

Hertzsprung-Russell Diagram

orA

bsol

ute

mag

.

Hertzsprung-Russell DiagramA

bsol

ute

mag

nitu

de

Color index, or spectral class

Betelgeuse

Rigel

Sirius B

Stars in the vicinity of the Sun

5.3MassL

90% of the stars are on the Main Sequence!

Specific segments of the main sequence are occupiedby 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 measurementTrigonometric 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 = linear size of object

θ = angular size of object (in arcseconds)

d = distance to the object206265

dD

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 / 206265 = 143,000 km

The Small-Angle Formula

D = linear size of object

θ = angular size of object (in arcsec)

d = distance to the object206265

dD

Problems1. 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

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

)(

2

1 12512.2 mm

mb

mb

512.2100

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)5(

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mbmb

mbmb

mbmb

mbmb

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100)6(

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mbmb

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’ is to be taken in pc.3. The ratio of the luminosities of two stars is given by

10

log5d

mM

)(

2

1 12512.2 MM

L

L

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

10

log5d

mM

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 () of universe is less than critical density ()

• Closed Universe - density of universe () more than critical density ()

• Flat universe - density of the universe () is equal to critical universe ()

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: < 1 and space-time has a negative curvature

• For closed universe: 1 and space-time has a positive curvature

• For flat universe:

1 and space-time no curvature

o