emit LIGHT
18:10
We infrared light (heat) and reflect visible light
L =4piR^2sigmaT^4
Smallest unit of light called a photon has specific wavelength and specific energy
Wavelength distance from peak to peak, called gamma
Light of different colors corresponds to photons of different wavelength
All light travels at the speed of light, regardless of its wavelength
In a vacuum, that speed is 3 x 108 meters/second
Use the letter c to represent the speed of light in equations
Frequency the number of peaks that go by a point per second
f=c/
Light actually behaves as both a particle and a wave at the same time called the wave-particle
duality of light
Energy of a photon E is:
Energy= E =h c/= h f
H = plancks constant
Units in joules (J)
Long wavelength photons have small energies shorter wavelength photons have more energy and
X-rays and Gamma rays have the most energy
White light is really a mixture of all colors (wavelengths) of visible light
Matter can:
emit light -- the element of a light bulb
absorb light -- a black cloth reflect
scatter light a white cloth
Planck curve describes how a body emits light according to its temperature
Cold bodies emit light at infrared or radio wavelengths, warmer bodies emit more light at all
wavelengths
Wiens Displacement Law describes the wavelength of maximum emission of the Planck Curve
as a function of temperature.
max =
b/T
max is the wavelength of the peak and b = 2.9 x 10-3 meters-K
Emission = T4
= 5.67 x 10-8 watts/m2/K4
Watts/m2 = Joules/sec/m2
Stephen-Boltzman Law
Luminosity = surface area x T4
L = 4 R^2 T4 for spherical bodies, like planets
Watts = joules/sec
Apparent brightness = b = L/ (4 d2)
Matter can absorb light, however no type of material uniform absorbs light of all wavelengths so
the interaction typically is a combination of reflection, absorption, and transmission
In many situations, the absorption spectrum is the complement of the reflection spectrum
We see the light that is reflected so the color of the wavelengths of the reflected light is the color
that we assign to the object
Transmission, which is the lack of absorption, occurs when the matter does not interact with light
at a particular wavelength. In general, any material is only transparent over a range of
wavelengths.
There are three broad types of spectra:
continuous spectra
Generally thermal emission from a solid body. It is characterized by emission over a wide range
of wavelength without detailed structure.
absorption line spectra
Absorption features arise when a continuous spectrum is seen through material that absorbs light
at discrete wavelengths.
The simplest example is a source seen through a cloud of gas.
emission line spectra
Emission spectra arise when you view a gas without a continuous spectrum in the background.
Spectral lines arise because the energy levels of atoms are quantized that means that the atom
can only have discrete energy levels like the steps of a stairs.
An atom can change its energy level by emitting or absorbing a photon (think of light as a
particle).
Since the energy difference between any two levels is very specific, the photon has a specific
energy wavelength!
If the atom absorbs a photon from a continuous spectrum, an absorption line is create. If it emits
a photon without a background source... it creates an emission line spectrum.
What is an atom doing when it changes energy level?
One of the electrons in the cloud surrounding the nucleus is receiving or giving up energy
Because spectral lines are well-understood and unique signatures of elements, they can be used
to study things like:
the abundance of elements in stars and nebulae the temperature of astronomical objects
And, perhaps surprisingly, spectral lines can be used to measure the velocities of motion of
astronomical objects.
The Doppler Shift is a change in the wavelength of light that occurs when the light is emitted
from a body that is moving toward or away from an observer.
The doppler shift also occurs for sound
When an object is moving toward you, the wave is bunched-up shifted to shorter
wavelengths... and we call that Blue-shifted. The light appears bluer than expected.
When an object is moving away from you, the wave is stretched-out shifted to longer
wavelength... we call that Red-shifted. The light appear redder than expected.
(measured)(lab) / (lab)= velocity / c
Light can interact with matter in 4 ways:
Emission
Transmission
Absorption
Reflection/scattering
THESUN
18:10
Sun is 300,000 times bigger (in mass) than the Earth
Luminosity: 3.8x10^26
Visible surface of the sun is called the photosphere
Emits light with the spectrum of 5800 K
Surface is not uniformly bright (not all at same temp)
Granules little cells of rising and falling blobs of gas they rise (get hotter) and fall (cool
down) like a boiling pot of water
Sunspots = regions of strong magnetic activity that causes it to be cooler and appear black
Number and location of sunspots is constantly changing
11-year sunspot cycle of activity
Quiet sun at minima, active sun at maxima
Not sure what causes the cycle
Solar flares and prominences releases of energy associated with sunspots and magnetic field
activity
Largest flares blow solar gas out into space at high speeds, which are called coronal mass
ejection events
Material travels out into space as a wind of material
Sun can throw off huge amounts of material, and its nothing compared to suns mass
If a coronal mass ejection is headed for earth, it could be serious
Solar wind material interacts with the Earths magnetic field disrupting communications and
creating danger for airplanes flying near poles
Above the photosphere is the thin gas of the chromosphere, which is 5000 to 20,000 K
THESUN
18:10
Above that is the corona where the temp is as much as 1 million degrees
The corona is very low density, very hot plasma that extends millions of kilometers from suns
surface
Convective zone extends from just below the surface in roughly 30% of the radius
Convection is strong in this region
Radiative zone extends from about .25 to .7 of the suns radius
No convection
Energy streams through as radiation
2-7 million kelvins
Core inner 25% of the suns radius
Most energy of the suns energy is generated in the core
Temp and density inside the sun are determined by hydrostatic equilibrium and the need to
transport the energy from the core out into space to keep the energy balance
Energy generated in the core equals energy given off at the surface, or else the overall star must
be getting warmer or colder
Hydrostatic equilibrium the balance of pressure against the force of gravity in a gas or fluid
Equilibrium requires higher densities and temps with increasing depth into the sun
Sun is powered by nuclear fusion nuclear reactions which convert 4 hydrogen into 1 helium
atom and release a huge amount of energy
THESUN
18:10
Protein-proton chain fundamental set of reactions in the sun
Converts mass to energy bc 4 H have more mass than 1 He
.7% of mass of H converted to energy
energy = mass x c^2 (E=mc^2)
Key requirements for fusion are high density and high temp nuclear reactions can only occur
at core of sun because the protons positive charge naturally repel. You need to ram them
together hard enough to overcome the repelling force.
Temperature = 15 million K
Density = 150 kg/cm^3
Energy = mass x c2
E = mc2
THESTARS
18:10
Magnitude an old system for measuring the apparent brightness of a star
Originated with the Greek Hipparchos and is still uses today
Stars divided into 6 groups brightest were magnitude 1 and faintest were magnitude 6
Each magnitude is different by a factor of 2.5 in apparent brightness, ie a 1st mag star is 2.5 times
brighter than a 2nd mag, and a 4th mag star is 2.5x2.5 times brighter than 6th mag
**smaller means brighter!!
Stars with bright apparent magnitude are not common (only 14 stars plus the sun)
How do we know distances to stars?
Two eyes give you depth perception
Parallax the apparent change in position of a nearby object when compared to the positions of
far away objects.
Stellar parallax uses the Earths orbit to give two different points of view, separated in time by
6 months
Parallax angle p is the half-angle that the nearby star appears to move on the sky relative to
distant stars
Distance (in parsec) = 1/p (arcseconds)
Parsec = unit of distance defined by the distance at which an object shows 1 arcsecond of
parallax = 3.26 light-years
Arcsecond is a measure of angle, 3600 arcseconds in a degree of angle
If we know the distance to an object and its apparent brightness, then its luminosity can be
calculated
Apparent brightness = L/(4d^2pi)
Luminosity is the intrinsic property of the star how much energy it gives off
Apparent mag, which is a way to write apparent brightness, depends on the luminosity and the
distance
THESTARS
18:10
Absolute magnitude = magnitude that a star or object would have if it was at a distance of 10
parsecs from the earth
Similar to luminosity
Color of a star is the measure of the relative amount of emission at two different wavelengths
spectral type -- to quantify the differences in color, really photosphere temperature, of stars
O, A, B, F, G, K, and M
Oh, Be A Fine Girl/Guy Kiss Me or Oh Boy, An F Grade Kills Me
There are sub-divisions Within the Spectral Types which are assigned numbers from 1 to 9
sun is a G5 star
The O-stars are the hottest and the M stars are the coolest so goes from blue to red
O stars are the most massive and M stars are the lowest mass
HR Diagram:
THESTARS
18:10
White Dwarfs, Main Sequence stars, Giants, and Supergiant represent different luminosities of
stars for the same colors (or spectral types).
To classify these, Astronomers created Luminosity Classes using Roman numerals to designate
them:
I : Supergiant
II : Bright Giant
III : Giant
IV : Sub-giant
V : Main Sequence
VI : Sub-dwarf stars
VII: White Dwarf
THESTARS
18:10
Example: K2 III is a K spectral type giant star and A0 V is an A spectral type main sequence star
The traditional spectral classes stop at M-class, but there are even colder, less massive objects,
which are commonly referred to as Brown Dwarfs
L Dwarfs cooler than M-stars. T = 1,300-2,000 K
metal hydrides in spectrum
T Dwarfs cooler than L-Dwarfs. T = 700-1,300 K
Methane in the spectrum
Brown Dwarfs are sub-stellar mass objects more massive than planets but less than stars.
M1 = mass of sun
M2 = mass of planet
a = semi-major axis (AU)
P = period of orbit (yrs)
Visual Binary Systems:
the two stars of the system can be seen separately from Earth and their orbits followed.
Eclipsing Binary Systems:
the orbits are viewed nearly edge-on so one star passes in front of the other. You can see the
eclipse in the light from the system and that gives you the period.
Spectroscopic Binary Systems:
the stars are too close together to see as different but you can see the doppler shift in their lines
from the orbits.
luminosity increases quickly with mass.
Since the amount of Hydrogen fuel goes up linearly with mass, this means bigger stars die
quicker!
Measurable quantities:
THESTARS
apparent brightness
distance
color/spectrum
spectral lines
Intrinsic properties:
luminosity
surface temperature
size
mass
composition (abundances of elements)
Composition:
Not all stars have the same composition!
Sun is most similar to stars around us
18:10
STELLARLIFETIMES
18:10
fusion reaction a reactions that fuses nuclei together to make bigger nuclei
In more massive stars where central temperature is higher, another set of reactions called the
CNO cycle can also convert 4 H into 1 He with the same energy yield
Carbon-Nitrogen-Oxygen cycle, none of the C, N, or O is used up the original C atom is
returned at end of cycle
At even higher temperatures and densities, it is possible to get 3 helium atoms to interact to form
1 carbon atom this reaction is called the triple alpha reaction
At extreme densities and temperatures nuclear reactions creates silicon, sulfur and even up to
Iron in stars.
Each step towards iron, you get less energy out. In going from carbon to iron, another 0.12% of
the mass turned into energy
Stop producing energy for atoms greater than iron
Elements react with other elements +/- 2 atomic numbers away
Roughly, the lifetime of a star depends on the amount of fuel and the rate that the fuel is being
used:
Lifetime ~ energy available / rate energy is used
If we just consider the energy released from conversion of H to He:
energy available = 0.7% x mass of star x c^2
The rate energy is used is the luminosity of the star.
Lifetime ~ 0.07% x M(star) c^2 / L(star)
Remember when we were talking about the masses of stars, we found the mass-luminosity
relationship which said
L(in solar luminosities) ~ M(star in solar masses)^3.5
SO:
Lifetime ~ 0.07% c^2 / M^2.5
Rather then doing the calculation we can use the lifetime of the Sun (10 billion years) that we
learned earlier and write the equation as:
STELLARLIFETIMES
Lifetime = 10 Byrs / M(solar masses)^2.5
Conclusion: Massive stars live much shorter lives that low mass stars!
18:10
FORMATIONOFSOLARSYSTEM
18:10
Jupiter largest planet in our solar system
Very thick atmosphere
strong winds that circle the planet making the stripes
The different colors are created by different molecules at different depths in the atmosphere
Aurora at pole
Atmospheres of giant planets have strong winds which circulate around the planet and strong
convection which moves gas up and down
Differentiation is the process by which denser material sinks and less dense material floats to the
top for example: a rock in water
When the planets formed they were liquid so the denser material mostly sunk to the center of
the planet.
For the giant planets this meant that the rocky material and heavy elements mostly sunk to the
center.
Jupiter is highly differentiated with rock and heavy elements in the core.
Outside the core, Jupiter is mainly metallic and liquid hydrogen.
Jupiter mostly composed of Hydrogen
Jupiter is massive so gravity is strong can hold hydrogen in atmosphere which Earth could not
Hydrogen is the most common element in the Universe 90% of atoms are H!
Jupiter has 4 large moons comparable to size of our moon
The smaller moons of Jupiter are irregularly shaped mostly captured icy/rocky bodies leftover
from the formation of planets
FORMATIONOFSOLARSYSTEM
18:10
Jupiters rings are very faint compared to Saturns
Saturns rings are made of dust and ice is orbiting the planet.
The dust and ice comes from very small moons in and around the rings
The details gaps and grooves of the rings are created by gravitational interaction of the dust and
ice with the moons.
These moons are called Shepherd moons, as they herd the dust into rings.
Titan = Saturns only large moon
Solid ice on surface with ice rocks
Most small moons of Saturn also irregularly shaped
Titania and Oberon = largest moons of Uranus
Triton = smallest moon of Neptune
Jovian atmospheres mostly made up of Hydrogen
Asteroids are rocky bodies found on and inside the orbit of Jupiter which range in size from
rocks to almost 1000 km in diameter.
Leftover rocky bodies from formation of Solar System
Irregularly shaped
Craters and rough surface
Too small for atmospheres
Too warm for ice
The primary location for asteroids is the Asteroid Belt which is between the orbits of Mars and
Jupiter
FORMATIONOFSOLARSYSTEM
18:10
Why there? Safety from gravity of Mars and Jupiter.
Go closer to Mars or Jupiter and you get drawn toward the planet and then thrown out of the
Belt.
Some asteroids enter our orbit and can possibly hit us! orbits changed through interactions
with Jupiter
Called Apollo Asteroids
About 3000 of them
Evidence that impact has occurred: craters on the earths surface
Kuiper Belt:
Region from Neptunes orbit and beyond in the plane of the Solar System.
It contains millions to billions of kilometer and larger sized icy-rocky bodies
The dwarf planets (other than Ceres) are the largest of these Icy-rocky bodies
Oort Cloud:
stretches from the Kuiper Belt out 1000s of AU and contains billions of small icy bodies.
Most of these objects we will never see or know
Comets:
When objects in Kuiper and Oort change their orbits to bring them into the inner Solar Systems
are called comets.
Icy-rocky bodies spewing out gas and dust because sun heats surface
2 tails:
dust pointed along orbit
gas always pointed away from sun
FORMATIONOFSOLARSYSTEM
18:10
What are the important broad facts?
1. The Sun contains 99% of the mass in the Solar System and is composed mostly of hydrogen
and helium.
2. The orbits of the planets are nearly in a flat disk and all orbit in the same direction around the
Sun.
3. The asteroid belt and the Kuiper Belt objects orbit in the same plane and same direction as the
planets.
4. The planets and objects inside 4 AU are rocky with little hydrogen gas and small amounts of
hydrogen rich molecules (ammonia NH3 , methane NH4)
5. The planets outside 4 AU are larger than the ones inside 4 AU and are rich in hydrogen.
6. The rotation axis (spin axis) of the planets are not all the same and can be very different
from the orbital axis.
7. The terrestrial planets have few moons and the giant planets have many moons.
8. Comets are icy-rocky bodies that are generally found at the orbit of Jupiter and beyond out to
1,000s of AU
9. The ages of meteorites are uniformly 4.57 Billion year old.
The youngest stars have gas and dust associated with them. Often the material appears to be in a
disk which extends out 100s of AU.
How did solar system form?
Gas cloud, speeds up and flattens out, forms sun and frost line, planets form
The gravitational force of Jupiter kept a planet for ever forming in the region between Mars and
Jupiter and the asteroid belt is what is left of material that never formed that planet
he formation of the Sun took 1-3 Million years.
The total formation of planets took 10-100 Million years.
The icy and rocky planetessimals all formed early so all of the oldest material bears the same old
age.
To detect stars/planets:
FORMATIONOFSOLARSYSTEM
18:10
Astrometric technique physical movement of one star across the sky
Transit/eclipse periodic dip in brightness that tells us how fast a planet is moving about star
Doppler effect
Most effective
Light turns blue when traveling towards you and red when traveling away