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Ch 5-6, 15-18
Is light a wave or a particle?
Light is an electromagnetic wave (both a wave & a particle: wave-partical duality which is justified by quantum mechanics)
It contains packets of wavelengths called photons, which act as particles
Does light need a medium to travel?
No; Light is generated by the motion of charged particles and does not need a medium
Characteristics of a wave
Wavelength (λ): length between crests
Frequency (f): number of cycles/sec (wave speed)
Speed (c ): waves travel at speed of light (3.e8 m/s)
c=λf
Amplitude: height of wave crests
Electromagnetic Waves
The motion of a charged particle causes the electric field and magnetic field to oscillate, producing an electromagnetic wave, or light.
ex. Varying electric field cases varying magnetic field, which repeats again causing wave
Photon
A particle of light that carries energy (basically a packet of waves)
Photon is emitted when an electron transitions between energy levels in an atom (excited state>ground state or vice-versa)
Inverse Square Law for Light
the intensity of light decreases with the square of the distance from the source. This means that as you move away from a light source, the brightness diminishes rapidly
(light spreads out of a greater area>decreases concentration of electromagnetic radiation)
What has a lower frequency, gamma rays or infrared rays on the electromagnetic spectrum?
Infrared rays have a lower frequency than gamma rays on the electromagnetic spectrum because they have a longer wavelength (i.e. there are less waves/second)
What is the correlation between temperature and wavelength?
As temperature increases, the wavelength of emitted radiation decreases, indicating that hotter objects emit radiation at shorter wavelengths.
Hotter objects also emit more light at all wavelengths, especially shorter wavelengths.
Wien’s Law
The higher the temp, the shorter the wavelength at which the peak amount of energy is radiated
Relates the temp of a blackbody to wavelength.
Stefan-Boltzmann Law
Hotter obj radiate more total energy at all wavelengths
sigma=5.67e-8 W/m²K^4
Flux (F)= rate of energy/particles across a surface
Luminosity
Total amount of energy a star emits at all wavelengths
Luminosity of the Sun is used as a unit (i.e. 25 L sun rather than 900000 etc.)
Light speed & Energy)
speed light travels in a year in a vacuum
Light carries energy (the ability to do work)
Atomic Structure
Atoms make up matter (anything that occupies space and has mass).
They are made of Protons (positive charge), Neutrons (no charge), Electrons (negative charge)
Atoms carry most of their mass in their nucleus (made up of nucleons: protons, and neutrons). The nucleus is surrounded by a less dense electron “cloud”
The model of the proton we know is the Bohr model.
Electron Energy Lvls
Electrons in an atom are quantized (can only have certain energy levels). Like how elevators only go to certain floors.
Ground state (1) is electrons lowest energy lvl. Excited states are electrons not at the ground state.
When electrons change energy lvls, they absorb (going to higher lvl) or emit (going to lower lvl) a photon of light.
What happens when electrons move to a lower energy lvl in an atom?
A photon is emitted. The photon’s energy is equal to the energy difference between the 2 lvls.
Individual atoms decay to a lower energy lvl spontaneously (happens all at once).
Half-life: time it takes for half of initial atoms to decay
Absorption & Absorption lines
White light contains all colors, so when it passes through a prism, it produces a continuous spectrum.
If the spectrum passes through cool gas, electrons in the atoms of the gas absorb the energy of a photon and move to a higher, more excited state. That photon contains a specific wavelength or color.
Absorption is electron moving from LOW to HIGH.
This produces Absorption lines that appear on the spectrum (can tell us chemical makeup of gas).
Absorption lines are produced from a cold gas, because cold gases is in a less excited state and can absorb energy/radiation.
Emission Lines
Hot gas emits photons as its energy decreases.
When light/photons from the gas is collected through a lens/prism, it shows up as an emission line, whose wavelength corresponds with the photon energy.
Emission electrons are moving from HIGH to LOW energy lvl. (able to emit a photon).
Hot gas in the process of cooling creates an emission line, because its excited atoms produce photons as they move to lower states, which can be measured as an emission line.
What is the most abundant element in the Sun?
Hydrogen (91.2%), followed by helium (8.7%). Percents of total # of atoms.
The sun contains a very low amount of heavy metals.
Properties of Light
Light can be reflected, emitted, or refracted.
Reflected: what we see of other people (light reflecting off obj)
Emitted: what we see through infrared (the light an obj like our bodies emit)
Refracted light: light passing through a prism (bent/scattered light)
All light is bent through a prism, but violet light is bent more than red light because its at a shorter wavelength
What holds an atom together?
An electron has 2000x less mass than a proton, but it also has an equal & opposite charge. That electric force created from the electron/proton holds an atom together.
What defines an element? What are isotopes?
The number of protons in their nuclei.
An isotope is the same element with the same # of protons but a different number of neutrons.
The Doppler Effect
If a wave source is moving toward you, then the wavelength has to shrink. That is because as the source moves toward you, the next peak of the wave covers a shorter distance.
Wavelength shrinks for a source coming at you, and increases for a source moving away from you.
This is relevant for starlight as all stars have some motion. Thus, we can use the Doppler Effect to measure how a star moves.
Telescopes
Telescopes collect and focus light. Collecting light is from mirrors, and focusing light is from optics afterwards.
If the mirror of the Hubble Space Telescope has a diameter 500x wider than a human eye’s pupil, how much more light can it collect?
500² = 25,000x more light
This is due to the opposite effect of the inverse square of light.
How is a telescope image formed? (refracting/reflecting)
Light can be refracted and focused by a lens into an eyepiece (refracting telescope).
Light can be reflected by a lens or mirror and focused into an eyepiece (reflecting telescope).
What telescope is easier to make, refracting or reflecting?
Reflecting; it’s easier to make large mirror than large lenses. This is because while lenses need to be perfect on both ends, for light to pass through perfectly, mirrors only need to be perfect on one side.
What matters for a telescope to work well?
Size of lens or mirror
Site (less cloud cover, clearer atmosphere, LESS HUMIDITY)
Radio telescopes
Radio telescopes detect and amplify radio waves from space, turning them into signals that astronomers use to enhance our understanding of the Universe.
A larger diameter means a greater resolution. Single wave radio telescopes have poor resolution due to the long wavelengths being measured.
Radio telescopes can be amplified in networks, interferometric arrays, that combine the signals from many telescope, increasing the diameter of the telescope and thus increasing its resolution.
Is the sun a solid, liquid, or gas?
None of the above; the sun is a large ball of ionized fluid (gas or liquid) called plasma.
When atoms of ionized, the electrons are separated from the atoms.
The gas becomes ionized because the sun is so hot (surface temp 5,800K)
What layer of the sun can we see?
Photosphere: visible surface of the sun; part of sun’s atmosphere
Contains sun spots (cooler areas that appear dark due to the other relative heat of the sun)
Granulation
The surface markings of the convection cells on the sun create a granulation pattern.
This is caused from hot gases rises while cold gases fall.
What parts of the sun make up its atmosphere?
Photosphere, or surface of the Sun visible in ordinary light (also contains convective cells); 4,400 - 6,600 K (around 5800K)
chromosphere, which can be seen during solar eclipses and is hotter than the photosphere 4,000 - 8,000K
corona, also visible during solar eclipses and extending beyond the sun (hotted than both previous layers), 1-2 million K
Solar Wind
Solar wind particles leave the Sun at a rate of 400 km/s, or about 1 million miles per hour.
The Sun is losing 1 or 2 million tons of material every second, which for the Sun is tiny. These charged particles are responsible for the Aurora.
Label the parts of the sun
What is the hottest part of the sun?
The core (15 million kelvins; hot enough for nuclear fusion)
Core
Corona
Chromosphere
Photosphere
Why do the magnetic fields on the sun “wind up”?
The sun spins faster at the equator than near its poles. As such, the magnetic fields of the sun “wind up,” causing loops that create sun spots.
This irregular spinning is called differential rotation.
Sunspots
Cooler regions of the sun (temp is 3,800 K rather than 5,800K). They are caused by magnetic field loops in the sun (traps hot gas from rising to the surface).
Only appear dark relative to the bright sun. Observed on the photosphere
Galileo tracked how sunspots rotate and determined they have a rotational period of around 25 days at the equator, 28 at the latitude 40, and 36 days at the latitude 80.
This is because of differential rotation, sun rotates fastest at the equator.
How does the solar cycle contribute to climate variations on Earth?
The around 11-year cycle in solar activity causes slight variation in Earth’s climate that is separate and smaller than global warming.
Types of Solar Phenomena
Sunspots: cold, dark spots on the sun caused by blockages in the magnetic field
Plages: bright parts around sunspot
Prominences: plasma loops near the surface of the Sun
Solar flare is an intense burst of radiation coming from the release of magnetic energy associated with sunspots
An observer on Mars in watching the Earth, following its phases. When will they see Earth in the “New Earth” phase?
Mars will see Earth in “New Earth” phase when it is opposite Earth in its orbit.
Where does most of the sun’s energy come from?
Nuclear fusion (forming small nuclei into larger ones)
Mostly Hydrogen fusion (hydrogen into helium)
Explain the premise of the debate between Kelvin & Darwin
Kelvin calculated that the Sun could be no more than 30 million years old. Darwin thought that the Earth had to be at least a few hundred million years old for things to evolve.
Kelvin ended up being wrong because he didn’t know about nuclear physics; the sun is around 4 billion years old.
Mass, Energy, and the Theory of Relativity
Energy and mass are equivalent, as proportional to the speed of light squared.
ex. 1 g of water creates almost 90 trillion J of energy
Albert Einstein derived the equation E=mc²
Nuclear Fusion vs Fission
In fusion (a), light atomic nuclei join together to form a heavier nuclei, releasing energy in the process.(i.e. LIGHT to HEAVY)
In fission (b), energy is produced by the breaking up of heavy, complex nuclei into lighter ones. (i.e. HEAVY to LIGHT)
ex. The first atomic bombs (Hiroshima and Nagasaki) were fission bombs, fusion bombs were developed in the 1950s, where they used a fission bomb to create enough heat for fusion
How does the sun get its energy? How does it work?
The Sun gets most of its energy from nuclear fusion, the only source of power great enough to sustain the sun this long.
Nuclear fusion happens in the sun’s core and involves the fusing of atomic nuclei to form heavier elements.
Nuclei consist of protons (positive charge) and neutrons (no charge). Electric forces pushes protons apart (like repels like) but fusion needs protons to be slammed together at high speed. They come together at short distances because of strong nuclear force.
When protons slam together, it creates a more massive nuclei from the less massive one but it loses mass in the process. Lost mass is converted to energy using E=mc².
Because the sun’s core is dense, it’s more likely for protons to collide than on Earth.
Where does nuclear fusion take place in the sun?
Fusion takes place in the core, where it is hot enough to push the nuclei close together (15 million K).
The rate of fusion is sensitive to temperature and density of the gas (sun has high temp and higher density required for fusion).
Hydrogen is the most abundant element and requires the lowest temperature for fusion.
Hydrogen fusion converts four hydrogen nuclei into one helium nucleus and is the most significant energy source in main sequence stars.
What is the most common type of fusion in the sun’s core?
Hydrogen>Helium fusion
Proton-Proton Chain: 4 H nuclei are converted to He nucleus.
Required high temp and high density (doesn’t happen spontaneously on Earth)
What keeps the sun together?
Hydrostatic equilibrium: balance between pressure & gravity. Gravity pushes INWARD to the center of the sun, but nuclear reactions & thermal pressure push OUTWARD. This keeps the sun stable.
If gravity won, the Sun would get smaller and the pressure of nuclear reactions at its core would increase, making it get bigger again.
If pressure won, the sun would expand, then the nuclear reactions would drop causing the pressure to drop, and the sun would contract again.
How long does it take for a photon to reach the surface of the sun?
For a photon to reach the surface of the sun from the sun’s dense core, it would take around 6e5 years.
This is because the sun’s core is dense and the photon bounces off other photons.
Apparent Brightness vs Magnitude
Apparent brightness gets greater as stars are brighter. Magnitude gets smaller as star is brighter.
The apparent brightness of a star is how bright a star’s light shines on Earth. Stars can have greater apparent brightness either due to having greater luminosities, or being closer. Brightness is inverse to distance, so the further the obj the fainter it is.
Apparent Magnitude is a classification for the brightest stars. It uses a logarithmic equation (see photo). Magnitude is backwards, so brighter stars have a smaller magnitude.
How do we determine the color of stars?
Stars are classified by their temperature. Hotter stars are more violet/blue and colder stars are more red/orange.
Color, unlike brightness, does NOT depend on distance of the obj.
What are the min/max temp of stars? How do we know?
The hottest stars have temperatures of 50,000 Kelvin, and the coldest stars have temperatures of 2,000 Kelvin.
We know the min temp of stars from the min temp needed to sustain nuclear fusion. The max temp of star is dependent on things we haven’t figured out yet.
Proper Motions & Radial Velocities
Radial velocities inform if a star is moving toward or away from us, but it can also be moving in a direction perpendicular to us.
Radial velocity is along our line of sight, proper motions are transverse to our line of sight.
Ex. Radial velocity is professor moving toward class. Proper motion is professor moving side to side.
Star A has a proper motion of 1”/year. Star B and Star A have the same physical motion in space, but star B is 4x further away. What is the proper motion of Star B?
If a star is twice as far, its proper motion is HALF as much for the same transverse velocity.
Thus, Star B is around 0.33 arcseconds/year (less than 1 due to being twice as far>1/4 proper motion).
What is the relationship between energy of electromagnetic radiation and its wavelength?
They have an inverse relationship.
As energy decreases, wavelength will increase.
As wavelength decreases, energy will increase.
Where does most mass in an atom lie? Where does most size lie?
Most mass is in the nucleus, but very little of its size.
Most size comes from an atom’s electron cloud, which is much larger in volume than the nucleus.
Is an electron at the 3 state close or far from ground state?
Far; ground state is 1
Does it take more, less, or the same amt of energy to ionize a H atom in the n=3 state than ground state?
Less
A H atom in the n=3 state will take less energy to ionize (remove electrons) because the electron has already gained energy to reach the excited state (not starting from ground 0).
What color shift would we see if an object moved toward, away, and transverse to the viewer?
All shifts are formed from radial velocity, or movement toward the viewer. Proper motion, or movement transverse the viewer, causes no shift in color.
Color shifts are due to the Doppler Effect compressing the wavelengths. An object going toward you would have a more compressed/smaller wavelength and appear as a blueshift.
An object moving away from you would have a less compressed/longer wavelength and appear as a redshift.
Why are most professional telescopes reflectors, not refractors?
A lens has to be supported only around its edges (harder to build)
It’s easier to make a large reflecting telescope rather than refracting (making large mirror is easier than lens)
Only front surface of a mirror has to be perfect whereas lens needs both sides
Why are radio telescopes larger than optical telescopes?
Radio wavelengths are much longer than optical wavelengths
Why is the Sun’s corona hotter than the photosphere, but not as bright?
The density of the corona is much lower, so it doesn’t emit as much light.
Which element was first discovered on the Sun?
Helium
How long is the solar cycle? What phenomena vary with the cycle?
Solar cycle is 11 years.
Sunspots, flares, and the magnetic field vary in the solar cycle because they are affected by differential rotation.
Zeeman Effect
Splitting of spectral lines in the presence of a magnetic field.
The absorption lines split into 3 when there’s a sunspot. That’s because magnetic fields cause energy levels in atoms to split. This is how we know that sunspots occur in regions of stronger magnetic fields.
Types of heat transfer
Conduction: involves direct contact between surfaces (i.e. burner on electric stove heating up pot)
Convection: involves the movement of a fluid/gas; movement of hot air (rising) and cool air (sinking) in heat transfer; (i.e. convection oven)
Radiation: can travel through vacuum of space; any light is radiation (i.e. sunlight)
As viewed on Earth, would a star of magnitude 5 appear dimmer, brighter, or the same as a star of magnitude 1?
Dimmer; magnitude is backwards (brighter=lower lvl)
What characteristic of a star’s spectrum dictates its spectral class?
The strength or weakness of the H absorption lines (depends on temperature)
What stellar properties are measured by a star’s spectrum?
Composition (absorption lines)
Radial Velocity & Rotational Velocity (Doppler Effect)
How do you find the number of protons, neutrons, and electrons in an atom?
Protons are found using the atomic number. If the atom is neutral, the number of electrons is equal to the number of protons.
Neutrons can be found by subtracting the atomic mass from the number of protons.
Blackbody
A blackbody is an idealized obj that absorbs all electromagnetic energy that falls onto it.
The Stefan-Boltzmann law is a formula from which the rate at which a blackbody radiates energy is found.
Charge-coupled device (CCD)
Array of high-sensitivity electronic detectors of electromagnetic radiation, used at the focus of a telescope/camera lens to record an image or spectrum
Color index
Temperature is difficult to measure in stars, so scientists use color indices.
Difference between the magnitudes of a star/other obj measured in light of 2 different spectral regions
ex. Blue minus visual (B-V) magnitudes
Spectral class
classification of stars according to their temp using characteristics of their spectra
Most stars have different spectra than the sun. The most important difference is temp and the second most important is elemental abundances.
From hottest to coldest: O, B, A, F, G, K, & M (Oh Be A Fine Girl, Kiss Me)
L, T, & Y added later
(order of letters reclassified by Annie Cannon)
What determines the thickness of spectral lines?
Size
Larger stars have less pressure in their atmosphere, thus fewer collisions (less density), thus narrow spectral lines.
Larger stars also have more ionized atoms. Atoms can be ionized in any stellar atmosphere but they stay ionized longer is a giant star’s atmosphere.
Stellar Census
Stars within 21 light years of the sun are catalogued in this census.
M-Dwarfs are most common (1/10 and ½ mass of sun)
G-dwarfs like the sun aren’t common or rare
The stellar census probably misses low-mass objects like brown dwarfs and is as such not representative of the Milky Way.
Is it easier to measure the mass of single stars or binary stars?
Binary stars. Binary Stars’ masses can be measured using Newton’s generalization of Kepler’s third law.
However, single stars is hard to infer mass because we often don’t know their distances or size.
Visual Binary Stars vs Optical Double Stars
Optical double stars appear to be binary from Earth (close/orbiting each other) but this is an illusion. They’re usually far away from each other.
Visual binary Stars are actually orbiting each other and appear as such from Earth.
Visual Binaries
2 Stars that actually orbit a center of mass (not just optically).
Visual Binaries orbit with proper motion so their motion can be traced with telescopes over time (track movement of star’s center of mass & orbit)
Spectroscopic Binary Stars
appear as 1 star but can be measured as binary stars on a spectrum (track blue/redshift of their orbital motion)
Absorption lines vary based on brightness (more bight=better line)
Blue=toward; Red=away (Doppler Effect)
Spectroscopic stars move radially (toward/away) from Earth. That’s how we measure their shift (proper motion could be observed as visual binary).
Star that has more motion (greater blue/redshift) on graph is less massive star (further from center of mass that the stars are orbiting=less mass).
Can you find the mass of binary stars?
Yes, Newton’s generalization of Kepler’s 3rd shows sum of masses of a binary system, to its orbital period, to the length of its semi-major axis.
Visual binary stars: You can find the orbital period by watching over time and ratio of masses by seeing which star is further from center of mass (more massive stars=closer to center of mass)
Spectrscopic binary Stars: More massive star has less movement on graph.
What’s the relationship between mass and luminosity? What about mass and temperature?
Stars that are more massive are brighter/have more luminosity. They also have a higher temperature.
This varies on a plot due to stellar outliers like white dwarf stars (super dense, small)
L~M³.5
How do you measure the diameter of a star? What about a binary star?
Our sun’s diameter can easily be measured because we know its angle in the sky (and can use its distance from earth to find the radius, and thus the diameter).
Other stars have such a small angular size in the sky that we cannot measure their diameter without knowing their distance.
Eclipsing binary stars’ diameters can be measured by the time it takes one star to pass in front of the other. We can solve for this using velocity (v=d/t) where t=time it takes for 1 star to pass in front of another star.
How do you tell which star is hotter in a pair of binary stars
Temperature of binary stars can be measured during their eclipse. This is because not all eclipses are equal in depth, one star may be more hot.
Less hot stars are less bright, and will have less of an effect on the overall brightness when they pass in front of the other star.
Thus, the avg temp of stars in a binary pair can be measured by seeing which star causes a greater shift on the brightness graph during an eclipse.
Are all of the brightest stars in the sky nearest to Earth?
No, only some of them. Some very distant stars are more luminous, thus they could be further away but look more bright than closer stars.
Is an obj with negative velocity moving toward or away from earth?
Objects with negative velocities (less than 0) are moving TOWARD earth.
Objects with positive velocities (greater than 0) are moving away from earth.
Absolute vs Apparent magnitude
absolute mag: how bright a star is intrinsically (if it were positioned at a standard distance of 10 parsecs (about 32.6 light-years) away)
apparent mag: how bright is and how far as viewed from earth
relative luminosity: about how bright a star is from Earth
What did Cecilia Payne-Gaposchkin figure out?
Her 1925 doctoral thesis laid the foundations for understanding the composition of the Sun and the stars.
Found that Hydrogen was most abundant element on Sun followed by Helium.
What did Annie Jump Cannon do?
Annie Jump Cannon is well-known for her classifications of stellar spectra
Hertzprung-Russell Diagram
Plot of luminosity vs temperature. Position determined by mass (more massive in upper left, less massive in lower right)
Hot luminous stars are at upper left
Large, luminous stars are in upper right
Faint, small, cool stars are in lower right.
What type of stars are on the main sequence in an H-R Diagram?
Stars burning Hydrogen in their cores are on the main sequence. (i.e. Sun is on the main sequence)
Runs from O-type to M-type (coolest); (“Oh Be A Fine Girl, Kiss Me)
Position determined by mass.
How can the main sequence be used to find distance through spectroscopic parallax?
Measuring the spectral type to determine surface temperature.
Estimating luminosity from the H-R diagram.
Comparing luminosity and brightness to obtain distance.
What is measured and inferred on an H-R Diagram?
Measured:
Temperature
Distance
Composition (spectrum)
Inferred
Luminosity
Size
Mass
Age
Distance
Chromatic Apperation
All colors have different focal lengths, and imperfect mirrors/lens in a telescope can only capture so many.
Creates fuzzy image.
Note 
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