Option E - Astrophysics - SL

Agenda:

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

Eccentricity of an elliptical orbit

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.

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

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

Beyond solar system – Other stars



_{Other stars – There millions and millions of stars other than sun in the}

universe - Nearest star system is Alpha Centauri consists of 3 stars -

Proxima Centauri at 4.22 light years and Alpha Centauri A, B (binary

stars) at 4.35 light years

Beyond solar system – Stellar clusters

 Stellar clusters are groups of stars that are gravitational 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

Beyond solar system - Galaxies



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

Super-clusters

 Groups of clusters and smaller galaxy groups

 Not bound by gravity

Take part in expansion of universe

Largest known structure of cosmos

So where are we?

My school Universe

Local (virgo) super-cluster

Milky way Solar system Local cluster

Texas

North America Earth

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).

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

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.

What we see…

The stars of a

constellation

only appear to

be close to one

another

Usually, this is

only a

projection

effect

.

Seasonal Changes in the Sky

•

The night-time constellations change

with the seasons.

•

This is due to the Earth’s orbit around

The Sun and Its Motions

Due to Earth’s revolution around the sun, the sun

appears to move through the zodiacal

constellations.

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

Source of stellar energy

P-P Chain

10

years

1 sec

He

H

He

Gamma ray

10

year

P-P Chain

•

_{The net result is}

4H

--> He

+ energy + 2 neutrinos

Luminosity and Apparent Brightness

* Luminosity is the total light energy emitted per second.

Black body

•

_{A black body is a}

good emitter of

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

l

•

The value of

l

decreases with

increasing temperature as per the

Wien’s Displacement given by

l

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 =

s

AT

Stellar Spectra

Absorption Lines

and

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_{UV continuum} + lines, strong 1 - 10 Myr

B 10,000 - 28,000 _white Blue- 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 _{molecules, CH, CN} Ca+, Fe, strong 17 Gyr

M 2,000 - 3,500 Red very weak molecular lines, eg TiO, _{neutral metals} 56 Gyr

Spectral Classification of Stars

O

h

O

nly

B

oy,

B

ad

A

n

A

stronomers

F

F

orget

G

rade

G

enerally

K

ills

K

nown

M

e

M

nemonics

Mnemonics to

remember the

spectral

sequence:

O

h

B

e

A

F

ine

G

irl/

G

uy

K

iss

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)}

L

um

in

os

ity

Temperature

Spectral type: O B A F G K M

Hertzsprung-Russell Diagram

A

bs

ol

ut

e

m

a

gn

itu

de

Color index, or spectral class

Betelgeuse

Rigel

Stars in the vicinity of the Sun

5 . 3

Mass

Specific segments of the main sequence are occupied

by stars of a specific mass

H R Diagram

To learn more visit,

Binary stars –

Visual binary stars

Binary stars –

Spectroscopic binary stars

Spectroscopic binary is a system of two stars orbiting around a

Binary stars –

Eclipsing binary stars

Cepheid variable

Distance measurement

Trigonometric parallax method

•

• _{Distance is measured in “parsec” abbreviated as “pc”}

• _{1 pc is the distance 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 10}16_m

• _{This method is suitable up to a distance of 100pc (25pc for ground based}

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

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 _2.512 m2 m1

m b m b                           512 . 2 100 ) 6 ( ) 5 ( ) 5 ( ) 4 ( ) 4 ( ) 3 ( ) 3 ( ) 2 ( ) 2 ( ) 1

( ₅1

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

log

5

d

m

M

1

₂

_.

₅₁₂

L

Distance measurement –

Spectroscopic parallax method

(

)

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)

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

Newton’s model of Universe

•

_{Universe is infinite (in space and time)}

•

_{It is uniform and static}

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

Olbers’ Paradox in another way

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}

Correct Answer(s)

•

The Universe is expanding

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}

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 !}

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

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 (

r

)

•

_{Closed Universe - density}

of universe (

r

) more than

critical density (

r

)

•

_{Flat universe - density of}

the universe (

r

) is equal

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