ASTRO 101

ASTRO 101

Principles of Astronomy

Instructor: Jerome A. Orosz (rhymes with “boris”)Contact:• Telephone: 594-7118

• E-mail: [email protected]

• WWW: http://mintaka.sdsu.edu/faculty/orosz/web/

• Office: Physics 241, hours T TH 3:30-5:00

Text:

“Discovering the Essential Universe, Fifth Edition”

by Neil F. Comins

Course WWW Pagehttp://mintaka.sdsu.edu/faculty/orosz/web/ast101_fall2012.html

Note the underline: … ast101_fall2012.html …

Also check out Nick Strobel’s Astronomy Notes:

http://www.astronomynotes.com/

Homework/Announcements

• Homework due Tuesday, November 13: Question 4, Chapter 8 (Describe the three main layers of the Sun’s interior.)

• Chapter 9 homework due November 20: Question 13 (Draw an H-R Diagram …)

Next:

How Does the Sun Work?

How Does the Sun Work?• Some useful numbers:

The mass of the Sun is 2x1030 kg. The luminosity of the Sun is 4x1026 Watts.

The first question to ask is: What is the energy source inside the Sun?

Energy Sources• A definition:

Efficiency = energy released/(fuel mass x [speed of light]2)

• Chemical energy (e.g. burning wood, combining hydrogen and oxygen to make water, etc.). Efficiency = 1.5 x 10-10

Solar lifetime = 30 to 30,000 years, depending on the reaction. Too short!



• Gravitational settling (falling material compresses stuff below, releasing heat). Efficiency = 1 x 10-6

Solar lifetime = 30 million years. Too short, although this point was not obvious in the late 1800s.



• Nuclear reactions: fusion of light elements (as in a hydrogen bomb). Efficiency = 0.007 Solar lifetime = billions of years.

Ways to Transport Energy

Ways to Transport Energy

• Conduction: direct contact

• Radiation: via photons

• Convection: via mass motions

The Phases of Matter

Phases of Matter

• Matter has three “phases”1. Solid. Constant volume and constant shape.

2. Liquid. Constant volume but variable shape.

3. Gas. Variable volume and variable shape.

The Gas Phase

• In a gas, the atoms and/or molecules are widely separated and are moving at high velocities:– Relatively heavy molecules such as CO2 move

relatively slowly.

– Relatively light molecules like H2 move relatively quickly.

– The average velocities of the gas particles depend on the temperature of the gas.

Heating a Gas

• The velocity of a gas particle depends on the mass of the particle and its temperature.

Image from Nick Strobel (http://www.astronomynotes.com)

Ideal Gas• For a fixed volume, a hotter gas exerts a higher

pressure:

Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

The 4 “Forces” in Nature

The 4 “Forces” of Nature• There are 4 “fundamental forces” in nature:

1. Gravity: relative strength = 1, range = infinite.

2. Electromagnetic: rel. str. = 1036, range = infinite.

3. “Weak” nuclear: rel. str. = 1025, range = 10-10 meter.

4. “Strong” nuclear: rel. str. = 1038, range = 10-15 meter.

• Gravity is an attractive force between all matter in the Universe. The more mass something has, the larger the net gravitational force is.






• The electromagnetic force can be repulsive (+,+ or -,-) or attractive (+,-). Normal chemical reactions are governed by this force.






• The weak force governs certain radioactive decay reactions.

• The strong force holds atomic nuclei together.

The Strong Force.

n p

p n

• Here is a helium nucleus. The protons are held together by the strongforce.

p = proton, positive chargen = neutron, no charge






• Gravity is the most important force over large scales since positive and negative charges tend to cancel.

How to get energy from atoms

• Fission: break apart the nucleus of a heavy element like uranium.

• Fusion: combine the nuclei of a light element like hydrogen.

More Nuclear Fusion• Each atomic nucleus has a

“binding energy” associated with it. The curve is increasing as you go up to iron from small nuclei, and decreasing as you go down from large nuclei.

• The tendency of Nature is to increase binding energy, much like the tendency of water to flow downhill.

Image from Vik Dhillon (http://www.shef.ac.uk/physics/people/vdhillon/teaching/phy213/phy213_fusion1.html)

More Nuclear Fusion• Fusion of elements

lighter than iron can release energy (leads to higher BE’s).

• Fission of elements heaver than iron can release energy (leads to higher BE’s).

Nuclear Fusion• Summary: 4 hydrogen nuclei (which are

protons) combine to form 1 helium nucleus (which has two protons and two neutrons).

• Why does this produce energy? Before: the mass of 4 protons is 4 proton masses. After: the mass of 2 protons and 2 neutrons is 3.97

proton masses. Einstein: E = mc2. The missing mass went into

energy! 4H ---> 1He + energy



• Extremely high temperatures and densities are needed!

Images from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)



• Extremely high temperatures and densities are needed! The temperature is about 15,000,000K at the core of the Sun.

More Nuclear Fusion• Fusion of elements lighter than iron can release energy (leads to

higher BE’s).

• As you fuse heavier elements up to iron, higher and higher temperatures are needed since more and more electrical charge repulsion needs to be overcome.– Hydrogen nuclei have 1 proton each

– Helium nuclei have 2 protons each

– Carbon nuclei have 6 protons each

– …..

• The Sun is presently only fusing hydrogen since it is not hot enough to fuse helium.



• Why does this produce energy? Before: the mass of 4 protons is 4 proton masses. After: the mass of 2 protons and 2 neutrons is 3.97

proton masses. Einstein: E = mc2. The missing mass went into

energy! 4H ---> 1He + energy



• The details are a bit complex:


Nuclear Fusion• Summary: 4

hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons).

• The details are a bit complex:



• The details are a bit complex: In the Sun, 6 hydrogen nuclei are involved in a

sequence that produces two hydrogen nuclei and one helium nucleus. This is the proton-proton chain.



• The details are a bit complex: In the Sun, 6 hydrogen nuclei are involved in a

sequence that produces two hydrogen nuclei and one helium nucleus. This is the proton-proton chain.

In more massive stars, a carbon nucleus is involved as a catalyst. This is the CNO cycle.

Nuclear Fusion

• The CNO cycle (left) and pp chain (right) are outlined.



• Why doesn’t the Sun blow up like a bomb? There is a natural “thermostat” in the core.

Controlled Fusion in the Sun


• First, note that the rate of the p-p chain or CNO cycle is very sensitive to the temperature.


• First, note that the rate of the p-p chain or CNO cycle is very sensitive to the temperature. Rate ~ (temperature)4 for p-p chain.


• First, note that the rate of the p-p chain or CNO cycle is very sensitive to the temperature. Rate ~ (temperature)4 for p-p chain. Rate ~ (temperature)15 for the CNO cycle.


• First, note that the rate of the p-p chain or CNO cycle is very sensitive to the temperature. Rate ~ (temperature)4 for p-p chain. Rate ~ (temperature)15 for the CNO cycle. Small changes in the temperature lead to large

changes in the fusion rate.




• Suppose the fusion rate inside the Sun increased:




• Suppose the fusion rate inside the Sun increased: The increased energy heats the core and expands the

star. But the expansion cools the core, lowering the fusion rate. The lower rate allows the core to shrink back to where it was before.

Models of the Solar Interior

• The interior of the Sun is relatively simple because it is an ideal gas, described by three quantities:

1. Temperature

2. Pressure

3. Mass density


• The interior of the Sun is relatively simple because it is an ideal gas, described by three quantities:

1. Temperature

2. Pressure

3. Mass density

• The relationship between these three quantities is called the equation of state.

Ideal Gas• For a fixed volume, a hotter gas exerts a higher

pressure:


Hydrostatic Equilibrium• The Sun does not collapse on itself, nor does it

expand rapidly.


expand rapidly. Gravity and internal pressure balance:



expand rapidly. Gravity and internal pressure balance. This is true at all layers of the Sun.


Hydrostatic Equilibrium• The Sun (and other

stars) does not collapse on itself, nor does it expand rapidly. Gravity and internal pressure balance. This is true at all layers of the Sun.

• The temperature increases as you go deeper and deeper into the Sun!


• The pieces so far: Energy generation (nuclear fusion). Ideal gas law (relation between temperature,

pressure, and volume. Hydrostatic equilibrium (gravity balances pressure).



pressure, and volume. Hydrostatic equilibrium (gravity balances pressure). Continuity of mass (smooth distribution throughout

the star).




the star). Continuity of energy (amount entering the bottom of

a layer is equal to the amount leaving the top).




the star). Continuity of energy (amount entering the bottom of

a layer is equal to the amount leaving the top). Energy transport (how energy is moved from the

core to the surface).


• Solve these equations on a computer: Compute the temperature and density at any layer, at

any time. Compute the size and luminosity of the star as a

function of the initial mass. Etc…….

Solar Structure Models


• Here is the model of the structure of the Sun.


• The Sun is mostly hydrogen and helium.

Solar Structure Models• Here is the model

of the structure of the Sun.

• Next: Characterizing Stars

The Sun and the Stars

• The Sun is the nearest example of a star.

• Basic questions to ask:– What do stars look like on their surfaces? Look

at the Sun since it is so close.– How do stars work on their insides? Look at

both the Sun and the stars to get many examples.

– What will happen to the Sun? Look at other stars that are in other stages of development.

Stellar Properties

• The Sun and the stars are similar objects.

• In order to understand them, we want to try and measure as many properties about them as we can: Power output (luminosity) Temperature at the “surface” Radius Mass Chemical composition

Observing Other Stars

• Recall there is basically no hope of spatially resolving the disk of any star (apart from the Sun). The stars are very far away, so their angular size as seen from Earth is extremely small.

• The light we receive from a star comes from the entire hemisphere that is facing us. That is, we see the “disk-integrated” light.

Observing Other Stars• To get an understanding of how a star works,

the most useful thing to do is to measure the spectral energy distribution, which is a plot of the intensity of the photons vs. their wavelengths (or frequencies or energies).

• There are two ways to do this: “Broad band”, by taking images with a camera and a

colored filter. “High resolution”, by using special optics to

disperse the light and record it.

Broad Band Photometry

• There are several standard filters in use in astronomy.

• The filter lets only light within a certain wavelength region through (that is why they have those particular colors).

Color Photography

• The separate images are digitally processed to obtain the final color image.

Color Photography

Color Photography

Broad Band Photometry

• Broad band photometry has the advantage in that it is easy (just need a camera and some filters on the back of your telescope), and it is efficient (relatively few photons are lost in the optics).

• The disadvantage is that the spectral resolution is poor, so subtle differences in photon energies are impossible to detect.

High Resolution Spectroscopy

• To obtain a high resolution spectrum, light from a star is passed through a prism (or reflected off a grating), and focused and detected using some complicated optics.

High Resolution Spectroscopy

• Using a good high resolution spectrum, you can get a much better measurement of the spectral energy distribution.

• The disadvantage is that the efficiency is lower (more photons are lost in the complex optics). Also, it is difficult to measure more than one star at a time (in contrast to the direct imaging where several stars can be on the same image).

Stellar Properties

• The Sun and the stars are similar objects.

• In order to understand them, we want to try and measure as many properties about them as we can: Power output (luminosity) Temperature at the “surface” Radius Mass Chemical composition

The Distance

• How can you measure the distance to something? Direct methods, e.g. a tape measure. Not good

for things in the sky. Sonar or radar: send out a signal with a known

velocity and measure the time it takes for the reflected signal. Works for only relatively nearby objects (e.g. the Moon, certain asteroids).

The Distance

• How can you measure the distance to something? Direct methods, e.g. a tape measure. Not good

for things in the sky. Sonar or radar: send out a signal with a know

velocity and measure the time it takes for the reflected signal. Works for only relatively nearby objects (e.g. the Moon, certain asteroids).

Triangulation: the use of parallax.

The Parallax

• Parallax is basically the apparent shifting of nearby objects with respect to far away objects when the viewing angle is changes.

• Example: hold out your finger and view it with one eye closed, then the other eye closed. Your finger shifts with respect to the background.

The Parallax

• Example: hold out your finger and view it with one eye closed, then the other eye closed. Your finger shifts with respect to the background.

The Parallax

• A better example: place an object on the table in front of the room and look at its position against the back wall as you walk by. In most practical applications you will have to change your position to make use of parallax.

Triangulation

• Triangulation is based on trigonometry, and is often used by surveyors.


Triangulation


• The length B and the angle p can be measured, so the distance can be computed: d=B/tan(p)


Triangulation


• This technique can be applied to nearby stars.


Triangulation


• Here is another diagram showing the technique. This technique can be applied to other stars!


Triangulating the Stars

• The largest baseline one can obtain is the orbit of the Earth!

• When viewed at 6 month intervals, a relatively nearby star will appear to shift with respect to distant stars.









Triangulating the Stars• Here are two neat Java tools demonstrating parallax:

http://www.astro.ubc.ca/~scharein/a310/Sim.html#Oneover

http://spiff.rit.edu/classes/phys240/lectures/parallax/para1_jan.html



• The angle p for the nearest star is 0.77 arcseconds. One can currently measure angles as small as a few thousands of an arcsecond.



• For very tiny angles, use the approximation that tan(p)=p, when p is in radians.

• Then d=B/tan(p) becomes d=B/p.



• Then d=B/tan(p) becomes d=B/p.• B=1 “astronomical unit” (e.g. the Earth-Sun distance).

Define a unit of distance such that d=1/p, if the angle p is measured in arcseconds.



• Then d=B/tan(p) becomes d=B/p.• B=1 “astronomical unit” (e.g. the Earth-Sun distance).

Define a unit of distance such that d=1/p, if the angle p is measured in arcseconds.

• This unit is the parsec, which is 3.26 light years.

Distances and Brightness

• What do we do with the distance measurement?

Distances and Brightness

• What do we do with the distance measurement? We need the distance to compute the star’s luminosity.

• Note the distinction between how bright a star appears and how luminous it actually is.

• Let’s review how to quantify brightness…

Documents

ASTRO 101