The following notes were taken primarily from Physics for IB by Chris Hamper and Physics Course Companion by Tim Kirk

Topic E: Astrophysics

Are they real?

E.1.1Outline the general structure of the solar system.Students should know that the planets orbit the Sun in

ellipses and moons orbit planets. (Details of Kepler’s laws are not required.) Students should also know the names of the planets, their approximate comparative sizes and comparative distances from the Sun, the nature of comets, and the nature and position of the asteroid belt.

http://solarsystem.nasa.gov/planets

Tons of interesting stuff about our solar system

Aug. 2006 the International Astronomical Union declared the official definition of a planet:A “planet” is a celestial body that:

a) is in orbit around the Sunb) has sufficient mass for its self-gravity to overcome

rigid body forces so that is assumes a hydrostatic equilibrium (nearly round) shape

c) has cleared the neighborhood around its orbit.

8 Planets – name them….Elliptical orbits – to have a circular orbit an object must

have a very specific velocity. Any variations create and elliptical or hyperbolic shape

MoonsPeriod - 27.3 daysWhich planets have them????

Our Solar System

Phases of the moon

Asteroids belt between Mars and Jupitersize – dust to hundreds kilometeres.

CometsSimilar to asteroids but made up of loose particles of ice and

rock.Tail is blown off by solar winds and melted by radiation.Some orbit, others only pass the sun once

Planetoids???Pluto….

Our Solar System

Relative size video.

http://www.wimp.com/starsize/

E.1.3Define the light year.

Light year (ly) – the distance that a beam of light will travel in one year. How far is that? (3 x 108m/s = c)Used to measure distances outside of our solar system

Other important units.Astronomical unit (AU) – the average distance between the Sun

and Earth1AU = 1.5 x 1011mUsed to measure distances inside our solar system

Parsec (pc) – 1parsec = 3.26 lyDefined by making a triangle between the Earth, the Sun and a

distant object. If the angle at the distant object is 1 arcsec then it would be 1 parsec away. (more later)

Super easy

E.1.2Distinguish between a stellar cluster and a constellationE.1.4Compare the relative distances between stars within a

galaxy and between galaxies, in terms of order of magnitude.

Stars are not evenly distributed.Stellar cluster – small groups of stars that gravitationally

interact with one another. Physically close to each otherClosest star, besides the sun is Proxima Centauri - 4.25ly

Distribution of stars

Galaxy – a very large number of stars bound together by gravityTrillions of stars103 – 105 light years acrossEach star is approx. 1 ly apartAndromeda is about 2.5x106ly away

Galaxy cluster – small group of galaxies that gravitationally interact with one another There are about 20 other galaxies we are clustered with.

Supercluster – bigger than a cluster

Distribution of stars

Virgo Cluster

Andromeda

The simplest explanation is that if all the gas is made into stars before the gas has time to form a disk,

then you get an elliptical galaxy. if the gas has time to stabalize into a disk before it is all used up, then

you get a spiral galaxy.Or perhaps some of the elliptical galaxies are made from merging of

other types of galaxies.Observations of distant galaxies indicates that spiral galaxies were

more common in the past than they are today.So maybe yesterday's spirals are todays ellipticals.

This is an active research area. One problem is that if most of the mass in galaxies is unaccounted for, we have a hard time understanding the dynamics of galaxy formation.

How did galaxies get that way?

Constellations – groups of stars that are “linked” visually Ancient civilizations played “connect the dots” Located in the same general direction from EarthNot necessarily close to each other88 totalDifferent ones are visible at different times during the year.

E.1.5Describe the apparent motion of the stars/constellations

over a period of a night and over a period of a year, and explain these observations in terms of the rotation and revolution of the Earth.

This is the basic background for stellar parallax. Other observations, for example, seasons and the motion of planets, are not expected

Why do the stars move through the night sky?Because the rotation of the EarthIt also matters where you are located on Earth Ex. North Polehttp://www.yorku.ca/ns1745b/figs-ch1.html

This rotation takes 23h and 56min every time.The effect is that it seams that the stars position at 12:00

changes each night. This means that the Earth rotates 360º in 23h and 56min.

Which means 4min it will rotate 1º.Which means it only takes 360 DAYS for the constellations to

make one compete rotation.

The Sun doesn’t make the same path through sky every day.

For us, the summers are high in the sky, winters are low on the horizon.

This is because the axis of rotation for the Earth and the axis in which we orbit around the sun aren’t the same angle.

Sun rise

The Earth is not a perfect sphere. This means that depending on it’s location in it’s orbit, it

will feel more or less pull from the SunThis pulls on the Earths axis of rotation and makes it

wooble.This is technically called presession. This means that the “North Star” won’t always be the

north star.Period – 26,000 years

Precession

The word planet comes from the Greek word for wanderer.Planets will shift back and forth in the night sky relative to

the constellation background.Apparent east/west motion comes from the Earth’s orbit

around the sun.See Diagram on board

Apparent north/south motion come from the other planet’s orbital plane being at a different angle from ours.

Other plant’s movement

E.2: Stellar Radiation and Stellar Types

E.2.1State that fusion is the main energy source of starsStudents should know that the basic process is one in

which hydrogen is converted into helium. They do not need to know about the fusion of elements with higher proton numbers.

E.2.2Explain that, in a stable star (for example, our Sun), there

is an equilibrium between radiation pressure and gravitational pressure.

How does our sun work?Fusion of hydrogen into helium that provides the energy, for

our sunHappens on the inside of the sun (Yes, there are different

layers)Produces neutrinos that leave the sun and travel to Earth

“H” is Fuel

This is the same reaction discussed in Topic 7. Each complete chain reaction produces 26.7MeV.

The proton-proton chain

Remember you need 4 H to end up with one He

See simplified equation:

Gravity pulls inwardSo much the sun should collapse.

Nuclear explosions push outwardThese two have to balance out to be at pressure

equilibrium Ex. Balloon.

Rubber is like gravityAir is like the explosionsIf the temp changes the inside pressure will change and

won’t be stable

Star Stability

E.2.3Define the luminosity of a star.E.2.4Define apparent brightness and state how it is measured.

Light measurements give us information about the temperature, size and chemical composition of a star.

Luminosity(L) is the total amount of energy emitted by the star per second.

Unit is watt (same as power)

Depends on the temp.Ex. Two stars have same temp, the bigger one will give out

more energySun’s luminosity of 3.839 x 1026W

Luminosity

Some stars appear brighter than others.Brightness depends on:

How much energy is radiated (luminosity)How far away it is located

Apparent brightness is the amount of energy per second received per unit area.

Unit is W/m2

b = (L) / 4πd2

d is distant to the star

Apparent brightness(b)

E.2.5Apply the Stefan–Boltzmann law to compare the

luminosities of different stars.E.2.6State Wien’s (displacement) law and apply it to explain

the connection between the color and temperature of stars.

Black bodies absorbs all wavelengths of light and reflects none. It also is a perfect emitter of radiation.

If temp is increased the energy available is increased.Means the electrons can gain more energy and move into

higher energy levelsMeans more photons released, and their average energy is

greater.E = hf, Higher energy means higher frequency/shorter

wavelength

Black Body Radiation

Each peek represents the intensity(apparent brightness) of radiation at different wavelengths.

Total intensity is the area under the curve.

Power per unit area = σ T4

σ = 5.6 x 10-8 W/m2K4 (Stefan-Boltzmann constant)

Stefan-Boltzmann

If a star has a surface area A and temperature T then the total power emitted (luminosity), L is given by:

L = σAT4

Stefan-Boltzmann

At the temperature increases, the peak wavelength is shorterRelationship between peak wavelength and temp is Wien

displacement law:

λmax = (2.90 x 10-3km) / T

Stefan-Boltzmann

ExampleThe maximum in the black body spectrum of the light

emitted from the sun is at 480 nm. Given that the Sun’s radius is 7.0 x 108m, calculate the temperature of the sun, the power emitted per square meter, and the luminosity.

Answers: 6000K, 7.3 x 107 W/m2, 4.5 x 1026W

E.2.7Explain how atomic spectra may be used to deduce chemical

and physical data for stars.Students must have a qualitative appreciation of the Doppler

effect as applied to light, including the terms red-shift and blue-shift.

E.2.8Describe the overall classification system of spectral classes.Students need to refer only to the principal spectra classes

(OBAFGKM).

Remember:Electrons only exist in certain energy levelsWhen excited only produce specific wavelengths.

(Emission Spectrum)When white light passes through same gas these

wavelengths are absorbed. (Absorption spectrum)

Stellar Spectra

Stars emit a continuous spectrum of EMPeak intensity depends on the temp.As this EM pass through the outer layer of the star, some

is absorbed.The absorption spectrum of a star tells us what elements

are present because of the missing lines.

Stellar Spectra

The absorption spectra also helps us to calculate the temperature of the gas.

Hot gasMost electrons are already in higher energy levelsMeaning they can’t make the biggest jumpSee “Energy Levels” diagramMeans the higher energy photons will not be absorbed.Means a weak absorption lineWhich can let us find the temp

Stellar Spectra

E.2.8Describe the overall classification system of spectral

classes.Students need to refer only to the principal spectra classes

(OBAFGKM).

The spectrum of a star is related to it’s temp and chemical composition.

Also the color. The peak points to it’s colorOh Be A Fine Girl Kiss Me

Spectral Classification of Stars

Class Temperatrue ColorO 30k - 60k BlueB 10k - 30k Blue-WhiteA 7.5k - 10k WhiteF 6k - 7.5k Yellow-WhiteG 5k - 6k YellowK 3.5k - 5k OrangeM 2k - 3k Red

As objects move, the wave lengths they produce is either pushed together or spread apart.

Called doppler effect.Applies to all waves including light from stars.Red shift – longer λ – star moving awayBlue shift – shorter λ – star moving closer

Doppler Shift

E.2.11 - Identify the general regions of star types on a Hertzsprung–Russell (HR) diagram.Main sequence, red giant, red supergiant, white dwarf

and Cepheid stars should be shown, with scales of luminosity and/or absolute magnitude, spectral class and/or surface temperature indicated. Students should be aware that the scale is not linear. Students should know that the mass of main sequence stars is dependent on position on the HR diagram.

E.2.9 - Describe the different types of star.Students need to refer only to single and binary

stars, Cepheids, red giants, red supergiants and white dwarfs. Knowledge of different types of Cepheids is not required.

E.2.10 - Discuss the characteristics of spectroscopic and eclipsing binary stars.

E.3.9 - State that the luminosity of a star may be estimated from its spectrum

E.3.10 - Explain how stellar distance may be determined using apparent brightness and luminosity

E.3.11 - State that the method of spectroscopic parallax is limited to measuring stellar distances less than about 10 Mpc.

E.3.12 - Solve problems involving stellar distances, apparent brightness and luminosity

Limited to 0.01 arc sec on Earth due to bending of light in atmosphere. – 100pc

Using satellite telescopes, limited to about 0.001 arc sec – 1000pc

Stellar Parallax

Measure the spectra of a star.Determine the strongest wavelength (see graph)Use Wien’s law to calculate temp λmax = (2.90 x 10-3) / T

Spectroscopic parallax

Assuming it’s in the main sequence, use HR diagram to find its luminosity.

Measure the apparent brightness.Using luminosity(L) and apparent brightness(b) we can

solve for distance(d)

b = L / (4πd2)

Spectroscopic parallax

The maximum wavelength of a distant star is measured to be 600nm and its apparent trightness is 1.0 x 10-12Wm-2. What is it’s distance from the Earth?

First Wien’s Law for temp:λmax = (2.90 x 10-3) / T

T = (2.90 x 10-3) / (600 x 10-9)T = 4800K

Example

Next use the HR diagram to determine it’s luminosity is about 1 L(special dot **ask**)

Remember 1L = 3.84 x 1026 W

Use apparent brightness formula to solve for distance

b = L / (4πd2)

Answer: 584ly

Example

Exercise 15 HamperThe spectrum of a main sequence star has a maximu

intensity at 400nm and an apparent brightness of 0.5 x 10-

12 Wm-2. Use Wien’s law to find the temp.Use the HR diagram to find the luminosityCalculate the distance from the star to the Earth.

Your Turn

E.3.13 - Outline the nature of a Cepheid variableStudents should know that a Cepheid variable is a star in

which the outer layers undergo a periodic expansion and contraction, which produces a periodic variation in its luminosity.

E.3.14 - State the relationship between period and absolute magnitude for Cepheid variables.

E.3.15 - Explain how Cepheid variables may be used as “standard candles”.It is sufficient for students to know that, if a Cepheid

variable is located in a particular galaxy, then the distance to the galaxy may be determined.

E.3.16 - Determine the distance to a Cepheid variable using the luminosity–period relationship 

Stars further than 10Mpc are to weak to determine their temp.

Cepheid variable is unstable.Expands and contracts on a regular period.Time vs Apparent brightness graph

Cepheid variable

There are many Cepheid variable close enough to the Earth for us to use the stellar parallax method to find their distance.

If we measure their apparent brightness (b) we can then calculate their luminosity (L)

b = (L) / (4πd2)

Cepheid variable

If the luminosity and period are plotted on a graph, we find that they are directly related.

Notice this is only evident on a logarithmic scale.

Cepheid variable

Using the graph below and knowing that the period of a Cephied variable is 10 days and its brightness is 1.0 x 10-10 Wm-2, calculate how far is it from the Earth?

Answer: 3.0 x 1019m or 3200 ly

Example

A Cepeid variable has period 20 days and brightness of 8.0 x 10-10Wm-2. Calculate a) its luminosity b) its distance from the Earth.

Practice

E.4.1 - Describe Newton’s model of the universe.Students should know that Newton assumed an infinite (in

space and time), uniform and static universe.E.4.2 - Explain Olbers’ paradox.Students should be able to show quantitatively, using the

inverse square law of luminosity, that Newton’s model of the universe leads to a sky that should never be dark.

Infinitely bigGravitational force on each star is the same, giving static

equilibriumStars don’t moveStars haven’t ever movedStars have always beenUniverse must be uniform, if not then there would be

movement of stars. (And we all know that’s true!! LOL!!)

Newton’s Model

Infinitely big, infinitely old, static and uniform

Newton’s Model

If universe is infinite, then must be infinite number of stars, then why is the sky dark?

Answer: the universe is not infinite. Also time is not infinite, meaning that som of the light just

hasn’t reached us yet.

See Minute Physics Vdeohttps://www.youtube.com/watch?v=gxJ4M7tyLRE

Olber’s Paradox

Light from distance galaxies is red-shifted. Remember that a shift in spectral lines can tell use if a star

is moving toward or away. Red-shifted implies that the galaxies are receding.

Galaxies that are the furthest away are shifted more than the close ones.

Implying that the expansion is accelerating.It’s like a big explosion.

The outer parts flew off the fastest.

Nail in coffin

What was there before the Big Bang?What is it expanding into?

Length and time are created to define objects and events. With out a universe, these questions can’t be answers.There was no “space” to exist in.Don’t know when because there was no time.

The Big Bang

Where was the big bang? Was there a center?https://www.youtube.com/watch?v=W4c-gX9MT1Q

Are we expanding with the universe?https://www.youtube.com/watch?v=th_9ZR2I0_w

The Big Bang

Time and space grew out of the Big Bang. It didn’t expand into a void because there was not void.Don’t think expanding, spreading into nothingness.Do think growing

This also helps to explain why everything is red-shifted.

Calculating red shift(∆λ / λ ) = (v / c)

∆λ = change in wavelengthλ = original wavelengthv = relative velocityc = speed of light

Watch Ring’s Video 10 Option E

Hubble’s Law

Just after big bang (before 300,000 yr) there were not atom.

No starsNo galaxiesNO ATOMS – temp was to hot, photons ionized atoms.

Development of the Universe

Starts to cool down to 4000K, after 300,000yr.