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74 Cards in this Set

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F= delta T^4
flux = delta temperature ^4

(for blackbodies)
L= FA
luminosity = flux * area
L = 4piR^2
Luminosity = 4pi radius ^2

(for any sphere)
Newton's First Law of Motion
o A body continues in state of rest or uniform motion in a straight line unless made to change by forces acting on it
Newton's Second Law of Motion
o F=MA
o The amount of acceleration A that a force F can produce depends directly on the mass M of the object being accelerated
o Apply the same force to two objects, smaller mass gets the bigger acceleration- think about the basketball versus the tennis ball demonstration


o Force 2= Mass 2*Acceleration 2 (N2)
o Force 1 = mass 1 * acceleration 1 (N2)
Newton's Third Law of Motion
o When two bodies interact, they create equal and opposite forces on each other
Newton’s Laws of Gravity
• Every mass exerts a force of attraction on every other mass
• Force = [(gravitational constant)(mass1)(mass2)]/distance between them)
o F= (Gm1m2)/r^2
Kepler’s Third Law of Orbital Motion
• P^2 = [4Π^2/G(m1+m2)] a^3
• Newton’s Form of Kepler’s 3rd law
• This describes orbits of 2 bodies around their center of mass
o P= orbital period (time)
o A= semi-major axis of elliptical orbit (the radius if the orbit is circular) * note, this A is not acceleration
o M1, M2 = masses of the bodies
What is light?
• A form of energy that can travel through space without any medium to carry it
- a particle and a wave
Blackbody radiation
an idealized opaque body at a uniform temperature which reflects no light but emits light with a spectral distribution of wavelengths which are specified by Planck’s Law
o Not necessarily dense
o Not necessarily solid
o Blackbody is not a good name because it doesn’t have to look black. Same as thermal radiation. Stars are not perfect blackbodies but they resemble perfect blackbodies.
Temperature
 Related to the speed of Kinetic Energy of particles (atom, molecules, other) that make up a substance.
 Proportional to the average speed of the molecules squared.
 Absolute zero
• Particles have no motion
 Kelvin temperature scale- based on absolute zero
• = 0°Kelvin. = -273°C = -460°F
• TK = TC + 273°
• Water freezes at 32°F = 0°C = 273°K
What does

λ Max = (.0029 Kelvin * Meter)/ temperature

mean?
The wavelength (λ) at which the intensity of a blackbody spectrum peaks given by Wien’s Law
flux
energy per time per area
Emission line spectrum
Blackbody through a prism produces a continuous spectrum
• Cold background (colder than the transparent gas ) through transparent gas through a prism and you get bright lines, but no rainbow. Intensity versus wavelengths would have only sharp peaks at certain discrete wavelengths.
Absorption line spectrum
Hot blackbody (hotter than the gas) --> transparent gas--> through a prism -> a rainbow minus some lines. Gaps. Rainbow with dark lines. Will look like a continuous spectrum but it will have gaps at landa 1 and landa t.
spectral lines
if the lines of one element are much stronger/brighter/deeper than the others, there is more of that element
4 fundamental forces of nature
• gravity
o very weak but important on large scales
• electromagnetism
• strong nuclear force- binds nucleons (p, n)
• weak nuclear force- radioactive decay of nuclei.
What is a star?
• Big, hot, self-luminous ball of gas (plasma) held together by its own gravity
• Powered by nuclear fusion (at some point in its lifetime)
• Requires mass > 1/10 Mass of the sun
What is gas pressure?
o Occurs from collisions of gas particles. Those collisions produce a pressure which can resist other forces
o So what is actually happening? Electrostatic repulsion!! They don’t actually touch each other, they just kind of bouce away. Picture like magnets.
o As gas is squeezed, particles are pushed toward one another and they collide more rapidly with each other and rebound due to electrostatic repulsion thus resist compression
Ideal Gas Law
o P= (some constant) * density * temperature
o P= knT
• N= number of particles/volume
The core of the Sun is undergoing the same process of nuclear fusion that occurs when a hydrogen bomb explodes. Why does the Sun not explode?
• ANSWER: the huge energy release is contained by the pressure of the overlaying material.
o Imagine hydrogen bombs under a huge steal slab- it stays elevated because of all the bombing.
Proton-proton chain (3 step process) this produces most of the energy in the sun
• H1 + H1 → H2 +( e+, positron) + neutrino
• H1 + H2 → 3He + (gamma ray photon)
• He3 + He3 → 4 He + H1 + H1
Gravity as energy
• Gravity as a source (waterfalls on earth, black holes, quasars which feed black holes) Varies enormously from 0-30%!!!!!!
o On earth this is close to chemical, but the most extreme places in the universe like a black hole. This is the most important source of energy in the universe
Lifetime of a star
• Total lifetime = total energy supply
Rate at which energy is consumed

(t is proportional to Mass ^-2.5)

bigger the star with hotter temperature, the faster it uses up its supply
Evolution of Stars
o Pre main sequence stars are above main sequence but bellow giants. Not hot enough to fuse hydrogen in its core, but finally when it can fuse hydrogen it moves to main sequence. When it uses all the hydrogen, it becomes a Giant or Supergiant (depending on mass) and evolves off the main sequence. Then when the outer layer of the star is blow off after “things happen” it shifts again and becomes a white dwarf.
Fusion in the evolution of a star
1. Main sequence- fusing hydrogen in the core

2. Red giant I- fusion of hydrogen in the shell; no fusion in the core.

3. Red Giant II- you still have hydrogen fusion in a shell, but there is Helium fusion in the core.

4. Planetary Nebula/White Dwarf Phase: eventually, the envelope or outer layers of the star are ejected into space to form planetary nebula an the core of the star becomes a white dwarf.
Fusion of high mass stars
• Once the core turns to iron, there is no more heat/energy generated to support the core of the star against the weight of the overlying material. → Thus, the core of the star collapses and the star explodes in a Type II Supernova. The outer layers of the star shoot off really fast, violent ejection (not a gentle release like planetary nebulae) into interstellar space, carrying with it the stuff the star made- elements made during evolution and during explosion
Parallax example
• We look at the positions of the earth and Jupiter, and their moons, at distances of 6 months, noticed that there was a time delay. There is a difference however, because the distance between earth and Jupiter varies.
o First line (Jupiter to Earth) y= Distance between Jupiter and 2(distance between earth and sun)
o Time delay of 16.6 minutes in the orbital transits of Jovian moons at roughly 6 month intervals. Delay is due to extra light travel time across inner solar system.
o Difference of distances y-x = 2xdistance between earth and sun = 16.6 light minutes
o Des = 8.3 light minutes
o Distance = CT = (300,000km//sec)(8.3min) (60 sec/min)
• Des = 150,000,000 Km = 1AU
Distance formula
distance = 1/p
• if distance is in parsecs
 parsecs- invented to make this equation simple= 206,265 AU, or 3.25 light years.
if angle is in arcseconds
arcsecond: 1” = (1/3600) of 1 degree (a dime 2 miles away)
Brightness
• Brightness – luminosity/Area
• Brightness – luminosity over/ 4Πd^3

Brightness is how luminous a star APPEARS TO BE WHEN LOOKING FROM EARTH, not how luminous it ACTUALLY is
Difference between flux, luminosity and brightness
• Brightness: energy per time per area (Jsec^.2, m-2
• Luminosity- energy per time
• Flux and brightness similar qualities, but the difference is that flux is measured a the surface of emitting object. Brightness is measured at some distance away from object.
Why did it take us so long to realize we were part of the milky way?
o The galaxy is really big
o We’re inside of it (like being in a forest and trying to see how big the forest is)
o Dust obscures visible light from stars in the disk of the galaxy, especially distant ones
What is dust & why does it matter?
• Small specks of solid matter (biggest ones up to millions and billions of molecules)
Absorb and scatter light,
Schematic of the galaxy
• Schematic of the galaxy (edge on view) of the milky way Disk, thickness = 5,000ly. 35,000ly wide. No harp cutoff. Half the stars would be within this range.. Disk has most of the dust. The bulge is right in the middle Nucleus w/black hole. There are also stay clusters, or globular clusters, in the halo or region about the dist. We are within the thick part, about 2/3rds of the way out.
o Why can we see things in the halo without dust? Not too much dust in the halo.
Star cluster
• little piece of a galaxy at helps us figure out how the galaxy formed
• gravitationally; group of stars which all formed at the same time, so they have the same age. We can use the HR diagram or this.
• globular clusters. In a globular cluster, there is a well defined cutoff.
What stellar properties can you estimate simply by looking at a star on a clear night?
brightness and surface temperature
The distance to the nearest star (other than the Sun) is
250,000 times greater than the distance to the Sun

4ly
A star with 10 times the mass of the Sun has a main sequence lifetime how many times shorter/longer than the sun?
About 300x shorter than the sun
What 2 forces are in balance in main sequence stars?
gravity and gas pressure
The energy source for stars is...
Nuclear fusion
What property of a star determines its evolution?
Mass
The 2nd most abundant element in the universe is
Helium
Much of the visible light in the Milky Way Galaxy is
obscured by dust
When we observe stars near the center of the Milky Way Galaxy, we detect light that was emitted from those stars about
25,000 years ago
The star Rigel in the constellation of Orion has a surface temperature which is about 3 times that of the Sun, and a diameter which is about 100 times greater than that of the Sun. Therefore its luminosity is
800,000 times greater than that of the sun
At 100 mph it takes about 10 days to
drive around the earth. How long
would it take to drive to the Sun?
100 years
If you started right now to count to
1 billion you would be finished by
your 90th birthday
Which of the following is a
non-scientific idea?
.

1. The earth orbits the sun
2. The sun orbits the earth
3. The shape of earth’s orbit
is an ellipse
4. The shape of earth’s orbit
is a rhombus
5. The universe is large
6. The universe is expanding
5. The universe is large
If you’re standing in a train moving
on level ground at a constant velocity
of 200mph and leap straight up where will you land?
You will land in the same place
An earth-sized extrasolar
planet
orbits 1 AU from a star of 4 solar
masses. What is the approx
period of the star’s wobble?
0.25 yr
If light is a wave, what is waving?
Electromagnetic feild
Lightning generates EM radiation at many
wavelengths. How much longer does a pulse of
radio energy take to travel to you than a pulse of
UV energy?
the same amount of time
A particle of interplanetary material is heated by friction
from 400 K to 4000 K as it falls into Earth’s atmosphere,
producing a meteor or a shooting star. If it behaves like a
perfect blackbody, how does its emitted radiation change
as it is heated?
Its flux is 10,000x greater, while its peak
wavelength is 10x shorter (IR->VIS)
Suppose Barack and Rush look at the
spectrum of the same gas cloud in a
laboratory. Barack sees emission lines and
Rush sees absorption lines. How can this be?
Rush sees the gas against a
hot background
Spectral lines provide
information on:
1. Which elements are
present
2. The relative amounts of
different elements
What property makes the Sun a
star, and the Earth not a star?
Mass
The core of the Sun is undergoing the same process of nuclear fusion that occurs when a hydrogen bomb explodes. Why does the Sun not explode?
The huge energy release is
contained by the pressure of
the overlying material
The Photosphere (visible surface)
of the Sun is like:
1. The surface of the earth
2. The surface of the ocean
3. An apparent surface
4. The surface of a trampoline
An apparent surface you would notice very little change as you go through it, as when you fly through a cloud
When 2 Hydrogen nuclei, each of
mass m, fuse to form Deuterium:
A small part of their mass
is converted to energy
Our Sun has a main sequence lifetime of 10^10 years. According to the mass-lifetime relation, a star with a mass of 10 Msun has a lifetime of:
3x10^7 years
Stars in the “red giant region”
of the HR diagram must be larger than the sun because they are:
more luminous than the sun and
have a cooler temperature
The word “sequence” implies that stars on the main sequence of the HR diagram can be put in some sort of order. Which of the following is not ordered as one goes along the main sequence?

1. Temperature
2. Luminosity
3. Mass
4. Age
Age
The story of any star's evolution is
the story of its constant battle to __

1. balance the effects of
gravity
2. fuse its entire supply of
hydrogen
3. maintain its core
temperature
4. maintain its high mass
5. lose 5 pounds
Balance the effects of gravity
Why does a Red Giant star
become so large?
Fusion occurs outside core so
not as much overlying weight
to keep star compressed
Why does fusion of heavier elements
occur in more massive stars?
Cores are hotter so they have
faster particles
Why can’t we use parallax to
measure very large distances?
The parallax angle becomes
too small to measure.
Why can’t we use Cepheid variable
stars to measure the distances to
the most distant galaxies?
Their brightness is too small
to be detected
Why can’t we use supernovae to
measure the distances to stars in
our Galaxy?
There haven’t been any in
our Galaxy recently.
If the distance to the center of the Milky Way were scaled to the size of this room, then on the same scale the solar system would be about the size of
A molecule of DNA
The distance to the Milky Way center is 10 pc, and the size of the solar system is 10-4 pc. If the distance to the Milky Way center were scaled to the size of this room, then on the same scale the solar system would be the size of
A molecule of DNA (10^-7m)
Why do the best IR images come
from telescopes in space?
Earth’s atmosphere is only partly
transparent to IR photons
Why do the best visible light images
come from telescopes in space?
Earth’s atmosphere
causes images to be
blurred
Star clusters are useful to
astronomers because the clusters...
contain stars of the same age
AM/FM
AM = 10^3 hz
FM = 10^ 6 hz