Astronomy Final Exam
Astronomy Final Exam Astronomy 1020
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This 86 page Study Guide was uploaded by Emily Mason on Friday April 22, 2016. The Study Guide belongs to Astronomy 1020 at Clemson University taught by Dr. Flower in Winter 2016. Since its upload, it has received 221 views.
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Unit 1A Learning Objectives: Science Science- derives from the Latin scientia meaning to know. Science is a consistent body of knowledge about matter and energy, including the methods by which this knowledge is obtained and the criteria by which its truths are tested. o Science mainly relies on observations of nature, which are statements of high standards, composed in the precise language used in a particular science. o Examples: lead is 11.34 times denser than water, a lunar rock weighs 31.4 grams. o Observations of nature are obtained through experiments, observing, collecting, and cataloging. o Some sources of error involved in obtaining facts of nature are imperfections in instruments, human error, improper observational techniques, and poor observing conditions. Scientific Method- a system of securing and testing scientific knowledge described in a series of steps. o Steps: 1. Gather information/Observations: Observers and experimentalists gather, process, and store observations of nature relevant to the problem they are investigating through experimenting, observing, collecting, and cataloging. 2. Explain information with a hypothesis: Experimentalists try to explain observed phenomena with a hypothesis 3. Test the hypothesis with experiments Hypothesis- a preliminary explanation for a phenomenon that may or may not be supported by further observations or experiments. Uses human induction and data. o Induction- when our minds put together bits and pieces of information and uncover new lines of thought. Theory- describes a hypothesis that has considerable experimental support. They are hypothesis that have been confirmed. Scientific Laws- statements or mathematical relations founded on extensive observations of nature. These observations have clearly demonstrated that the scientific laws are always true, under certain conditions o Example: Boyle’s law states that the volume of a given amount of gas at a fixed temperature decreases as the pressure on it increases. This law applies under normal conditions on earth but may not on other planets. Sources of error in astronomical observations: o Often, radical results, ones that question our fundamental theories and paradigms, are the result of experimental errors Paradigms- it is basically an example, and consists of scientific laws, diagrams that give insight into the laws, and a group of calculations and solved problems that everyone agrees are done correctly. In order from least certain to most certain: Hypotheses (least), Theories, Scientific Laws (most) Learning Objectives: Basic Electromagnetic Radiation Electromagnetic Radiation- waves of a given wavelength (λ) with a certain energy traveling at the speed of light (c). The more energy an electromagnetic wave has, the shorter the wavelength. The approximate wavelength of red light is 780-622 nm (nanometers) The approximate wavelength of blue light is 492-455 nm One of the most important interactions in astronomy is between Electromagnetic Radiation (photons) and individual atoms. This interaction is the absorption of photons by atoms. The atom absorbs the energy of the photon of EMR and this causes electrons in atoms to move further away from the nucleus of the atom into outer orbitals. (Remember it like this: absorption, away) Emission – As the electron that has been removed from one orbital moves towards the center of another, it then emits and causes a photon to move further away from the nucleus of the atom into outer orbitals. Learning Objectives: Telescopes Refraction- when light changes direction or bends o Results from a change in the speed of light as it passes from one medium to another o Refraction is used in telescopes because light passes through the lens, is refracted, and meets a point called the focus. This light then goes through a second lens called the eyepiece. The focal lens, or the distance between the center of the lens and the point where the spot of light is smallest, determines how much the telescope magnifies. Reflection- when light bounces off a surface; the angle at which it bounces off is perpendicular to the surface the light strikes. o The curved nature of the lens made it able to also form a focus point. o Without alteration, this focus point is at an awkward location because it is nin the light path of the object being viewed. Types of Telescopes 1. Galileo’s Telescope- uses a refracting lens 2. Prime Focus- blocks only a small fraction of light 3. Newton’s Telescope- The focus of the primary mirror is to the side of the telescope tube because he added a small flat secondary mirror to reflect light. 4. Cassegrain Telescope- brings the focus of the primary mirror to the rear of the telescope by reflecting light with a secondary mirror back through a hole made in the primary mirror. 5. Coude Telescope- moves the focus away from the telescope to anywhere in the observatory. Magnification- the ratio of the focal length of the objective (lens at the front of the telescope) divided by the focal length of the eyepiece. In other words, Resolving Power- one advantage over the eye/one of the main functions of a telescope that measure how well a telescope can distinguish between two objects close together or how much detail it can show of extended objects such as surfaces of planets Light Gathering Ability- one advantage over the eye/another function of a telescope that refers to the capability of larger and larger telescopes to produce brighter and brighter images, allowing observers to see fainter objects. The largest telescopes built in the last century and today are reflectors because they applied a thin layer of shiny metal to the surface of glass, which makes the mirrors extremely reflective, reflecting more than 90% of visible light. Also, the mirror itself can be glass or another ceramic, which does not have to be optically perfect since light never passes through it. They are easier to shape and are lighter than metal. Atmospheric blurring- distortions in images caused by any misalignments in the telescope mirror and its supports and by atmospheric turbulence. Active Optics- methods that adjust for mechanical and optical misalignments due to manufacturing errors in the shape of the mirror and to the stresses on the mirror when the telescope is in different positions. o First, it divides the image of a star into cells. If there were no distortion, the parts in image of each cell would be exactly centered. A computer then determines the necessary correction to the shape of the primary mirror to center the image in each cell. Adaptive optics- a new technique that corrects in real time for blurring caused by atmospheric turbulence. o The system divides the light from a star into pieces. Lasers then excite atomic sodium, causing it to emit at a wavelength of 5890A. The sodium “star” then appears as a point of light and is high enough in the atmosphere to be above the distorting effects of the atmosphere. Radio Telescopes- a parabolic dish that acts like the mirror of an optical telescope by focusing the radio waves from the sources it is pointed toward onto the dipole. The dipole at the focus produces electric currents, which receivers amplify and record. o A major disadvantage is their poor resolving ability, or the ability to separate two images. Interferometry- the technique in which telescopes far apart synthesize a telescope with a diameter equal to the Earth’s diameter. Observers record the data from each telescope on magnetic tapes. Researchers then paly the tapes back into a computer that combines the signals as if they were from a single telescope. Major advantage of Space telescope over an Earthbound: o It’s ability to reach its theoretical resolving unit. Unit 1B Learning Objectives: Magnitudes Brightness/Intensity- used to describe the amount of energy emitted each second (Measured in: ????????????????/????/???????? or ????????????????????????/????/???? ) 2 Energy Flux- the rate of flow of energy Inverse Square Law- brightness diminishes with the square of the distance Brightness o Implies that if a star were 10 times farther away than we see it now, it would appear 1/ 10 , or 1/100 time as bright. (Or, 100 times fainter) Magnitude/Luminosity- a measure of the brightness of a star o The terms “brightness” and “intensity” are considered everyday terms, where “Magnitude” and Luminosity” are technical terms Intrinsic Brightness- the intrinsic brightness of a star is the energy flux at its surface. o The energy from a star’s surface is diminished as the square of the distance to the observer increases o In other words, Intrinsic Brightness is the amount of light an object actually emits, as opposed to how the object may look from Earth. o *Note: intrinsic brightness varies on the object. For instance, the intrinsic brightness of a light bulb is its wattage. Apparent Brightness- When the measured brightness at the Earth of any star depends of both intrinsic brightness and its distance Photometer- instrument used to measure the brightness of individual stars by electronically counting the number of photons from each star. o Photons deliver energy, so the intensity of light from a star is proportional to the number of photons it emits (AKA: the more photons, the brighter the star) Apparent Magnitude (m) Groups Visible to the Naked Eye: 1. First Magnitude Stars (m= 1) 2. Second Magnitude Stars (m= 2) 3. Third Magnitude Stars (m= 3) 4. Fourth Magnitude Stars (m= 4) 5. Fifth Magnitude Stars (m= 5) 6. Sixth Magnitude Stars- The faintest group (m= 6) Calculating Magnitude Difference: o Star A…m =1 o Star B…m = 2 o 2-1 = 1 o ** The difference in magnitudes corresponds to a brightness factor of 2.512 o So, since 2-1 =1, the Star B is 2.512 times fainter. If the difference of the magnitudes equaled 2, then it would be 5.024 (0r 2.512 x 2) times fainter. Negative Magnitudes- the necessity for negative magnitudes arises because some objects, including some stars, are many time brighter than first- magnitude stars. Only negative magnitudes can represent the observed brightness ratios for these stars. Brightness Ratio Between 2 Stars Formula: ????2−????1 b1/b2 = 2.512 Learning Objectives: Distances AU- represents Astronomical Units (the mean distance from the center of the earth to the center of the sun) Light Year- describes how far light travels in one year. o 1 Light Year = 9.4 x 10 km2 o Light years represent both time and distance because it is used like a travel time, such as 60 mph. You can do 60 miles (the distance) in one hour (time). Parsec- A parsec is the distance a star would be at if its measured parallax were 1/(3600 degrees), called an arcsecond. o Abbreviated “pc” o 1 parsec = 1 pc = 206265 AU o Light years to PC: 1 Light year= 0.30661pc o PC to light years: 1 pc = 3.26156 light years Alpha Centauri- closest star in the solar system o Distance of 4.3 light years from earth o Distance of 1.33 parsecs from earth o Distance of 271400 AU = 4.1 x 10^13 km) from earth Parallax- 3 definitions: 1. a name used to describe a method to obtain distances 2. an apparent motion of stars on the sky due to Earth's orbital motion 3. an angle used in the distance estimation. o Measured in arcseconds o Thumb Experiment: You extend your arm and act like you’re giving a thumbs up. When you blink one eye, then the other, it looks like your thumb is moving back and forth. This motion simulates parallax motion. PARALLAX EQUATIONS: o The angle p is called the parallax angle or just the parallax. The distance between the star and the sun is d. o The two equations in the drawing are two equivalent ways of determining the distance, d, from the measured parallax p. o The first equation gives the distance measured in astronomical units, the second in another unit, the parsec. o p” represents the parallax in arc seconds o Recall: 1 parsec = 1 pc = 206265 AU o 1 degree = 60’ (arcminute) = 60 arcminute o 1 degree = 60” (arcseconds) = 60 arcsecond o 1” (arcsecond) = 1/(3600 degrees) o ***No known stars have parallaxes larger than 1" and parallaxes are always measured in arcseconds*** Learning Objectives: Radiation Laws Planck Curves- represent the supply of photons emitted by a star o Shows how the intensity of emitted radiation is distributed over the electromagnetic spectrum o Tend to rise steeply at short wavelengths, reach a maximum, then gradually decrease at longer wavelengths Energy flux (F) - represents the total energy the star emits each second from each square meter of its surface. o The amount of energy flux is dependent on temperature. o Energy flux from a hotter star is greater than from a cooler star The Planck Curve of the hottest object lies completely above the Planck Curve of both the cooler objects. Stefan-Boltzmann Law- gives the relationship between energy flux (????) and the temperature (T) of the surface of the starepresents the proportionality constant. o ????????????????????????represents the amount of energy passing through a surface each second. o Units: joules/???????? or watt/????????2 ???? ???????????????????? = ???? ???? Wein’s Law- the mathematical relationship between the wavelength of the intensity maximum and temperature (***See graph above as well***) o T represents the temperature of a radiating surface o o Units: meters or angstroms Å) o Conversions: 1 Å = 10 -1m Learning Objective: Spectra Spectrographs- prisms that disperse starlight into individual wavelengths Absorption Spectra- show dark lines on a continuous spectrum/continuum o The dark lines represent individual wavelengths buy they are due to an absence of photons at those wavelengths o Occurs when atoms in cooler outer layers of a star absorb continuum photons emitted from the hot interior. Every time an atom absorbs a photon, an electron moves to a higher orbital. Emission Spectra- exhibit bright lines, the colors of which indicate their wavelength. o Occurs when atoms in a hot gas have electrons in orbitals farther away from the nucleus than normal, or when it is in an excited state. Doppler Shift- when motion causes the wavelengths of spectral lines to shift. o Moves relative to us o Stars usually only shift only a fraction of an Angstrom o Blueshift is when the source is moving towards us (**Wavelengths become shorter) o Redshift is when the source is moving away from us (**Wavelengths get longer) o Represents the observed/measured wavelength of an absorption or emission line in a spectrum source o Represents the measured wavelength of the same absorption/emission line from a source at REST Radial Velocity- the amount of velocity that is necessary to produce these Doppler Shifts. Equation for Radial Velocity: 5 o Speed of light= c = 3x10 km/s o The larger is, the larger ,the larger the velocity Astronomy Unit 2A Learning Objectives: Sun’s Interior The Sun o 150 kilometers from earth (300,000 times closer than the closest star) 3 o Central density: 160 g/???????? (due to extreme pressure) o Average density: 1.41 g/???????? 3 o Surface temperature: 5800K o Interior temperature: 16,000,000K o Composed of Hydrogen, Helium, and partially of “more massive elements” o The sun is a GAS How Energy is Generated Inside the Sun: o The amount of fuel the sun has is its mass (1.99 x 10 kg) This is over 330,000 times that of the Earth. o Nuclear reactions create this energy when matter is destroyed and energy is released. Any source of energy from destroying matter is called nuclear energy High temperatures are required for nuclear reactions Because of the high temperatures in the center of the sun, this is the most likely location for nuclear energy generation. o Only a small fraction of the hydrogen (and therefore the total mass) of the Sun is converted to energy o Only hydrogen is the fuel Einstein’s Equation: the equation relates the destruction of mass and the energy released. E represents energy, m represents mass, and c represents the speed of light. E = mc 2 Proton-Proton Chain: A set of nuclear reactions in which four hydrogen nuclei fuse into a helium nucleus and release energy (a) (TWICE) (b) (TWICE) (c) (ONCE) 2 A) In reaction a, two protons fuse to form a deuterium ( ????) nucleus consisting of one proton and one neutron. It also produces a positively charged electron (???? ) called a positron and a neutrino (v) The number to the upper left of a chemical symbol is the total number of neutrons and protons in the nuclei. B) Reaction b is the fusion of a proton and the created deuterium nucleus into a helium-3 nucleus. Helium-3 is an isotope and contains two protons and one neutrons. A high energy photon, or gamma ray is also produced. C) Reactions a and b must occur twice before reaction c can occur. Six protons and Hydrogen fuse to form a helium nucleus, and two protons. The two remaining protons in reaction c are available for further nuclear reactions. Luminosity- the measure of how fast the Sun uses its fuel o Tells us the total amount of energy the Sun emits each second at all wavelengths in all directions outward from its surface. Luminosity and Lifetime of the Sun ???????????????????????? o Use the formula (time = ???????????????????????????????????????? o When calculated using the total energy generated by the Sun during the proton-proton chain over its lifetime and present luminosity, it results in an expected lifetime of about 30 billion years. o The current age of the sun is 4.6 billion years. Solar Constant- A measure of the tiny fraction of energy the Earth intercepts from the Sun. o Found by the amount of energy passing through 1???????? of space at Earth’s orbit. ???? ???? ???? o Equals either 0.136 watts/???????? OR about ???? of a joule per second per ???????? Why Can’t the Sun Convert all of its Mass to Energy? o Too far from the center of the Sun, temperature are so low that the protons are not moving fast enough to ensure nuclear reactions. o Therefore, only 40% or so of the mass of the sun ever experiences temperatures high enough for nuclear reactions. Learning Objectives: Sun’s Atmosphere Surface of the Sun: o The atmosphere of the sun (the layers in which emitted photons have a good chance of passing through the gas without being absorbed again) is used to describe the layers of the sun since it is gaseous and doesn’t have a solid surface separating an interior from an atmosphere. The sun’s atmosphere is as deep as you can see into the sun o The atmosphere is separated into three layers: 1. Photosphere- the brightest of the three layers. Lies at the top of the Sun’s convection zone and extends only a few hundred km beyond it. Has a temperature of 6000K. The deepest layer of the photosphere is called the surface because we can’t see below it. 2. Chromosphere- A thin layer of gas just above the photosphere; it is a transition region between the cool photosphere and hot corona. We can see the faint pink chromosphere only during total solar eclipses. Has a temperature of 100,000K 3. Corona- Outermost distinct layer in the Sun’s atmosphere. we can only see the white corona during total solar eclipses as well. Has a temperature reaching millions of K. Granules- bright spots surrounded by narrow dark lanes in a honeycomb pattern. o Caused by rising gas. The dark lanes are where the gas sinks after cooling o Typically hundreds of kilometers across and the gas can rise up to 300km high. o Their lifetime is only a few minutes. o Reside in the photosphere Granulation- the honeycombed pattern of granules and dark lanes Sunspots o Reside in the photosphere o A typical sunspot is about 1500km across, and the largest can be 50,000km in diameter o Their lifetime is much longer than granules, lasting anywhere from a few hours to a few months o The sun rotates differentially (spinning faster at its equator once every 25 than near its poles). This rotation helps identify the lifetimes of sunspots as they move across the surface of the sun. o They are regions of intense magnetic fields o Appear in pairs or groups; one sunspot has north magnetic polarity and the other has south magnetic polarity Sunspot cycle 1. At the beginning of an 11 year period, sunspots form predominantly at northern and southern latitudes of about 35 degrees 2. As time progresses, new spots form closer to the Sun’s equatorial regions as the older, higher latitude spots disappear 3. Near the end of an 11 year period, sunspots form predominantly close to the Sun’s equator. o Butterfly Diagram shows the variation in the location of sunspot formation for several 11 year periods. It also shows that the time between successive sunspot maxima or minima averages about 11 years. Three Phenomena Linked with the Sun’s Sunspot Cycle: 1. The location of newly formed sunspots 2. The number of sunspots 3. The polarity of leading sunspots Magnetic Cycle o The north magnetic pole of the Sun switches to a south magnetic polarity for 11 years, then switches back to a north magnetic polarity for another 11 years, and so on. Hale Polarity Law o Groups of Sunspots exhibit these distinct magnetic relationships to each other and to the Sun’s magnetic poles: 1. Sunspot groups are oriented in an east-west direction 2. The leading spots (the ones leading in the direction of rotation) or a group are of one magnetic polarity, and the trailing spots are of the opposite polarity 3. Polarities of leading (and trailing) spots are reversed in opposite hemispheres 4. All the leading spots in one hemisphere have the polarity of the hemisphere’s magnetic pole 5. Polarities of the leading spots in each hemisphere reverse approximately every 11 years. Heating of the Corona o Satellite observations show the Sun covered by magnetic loops. Because the loops are not as strong as in sunspots, the temperature reduction is much less. o Because the Sun’s gas is highly ionized, the magnetic loops are sources of strong electrical currents. If two loops touch, they release bursts of energy called microflares. o Microflares can raise the temperature to a million K. There is enough energy in the microflares to easily heat the entire corona to millions of K. Solar Winds- represents a loss of matter at a rate of around a million tons per second, and causes the perpetual outflow of matter from the Sun’s gravity o Fast solar wind originate in coronal holes (immense low temperature regions that are found near the north and south poles of the Sun but often extend to the equator). o Slow solar wind originates in coronal streamers (consists of looped magnetic fields, and above these loops are long, narrow stalks of magnetic field lines that extend tens of millions km away from the sun) Quiescent Prominences- huge luminous structures of hot gas in the corona that appear anchored to the chromosphere and photosphere. o Form over sunspot groups and look like curtains. o They are coronal gases suspended and trapped by huge magnetic flux tubes arching into the corona between sunspots. o Seem to be prevented from expanding upward by intense magnetic fields in the upper corona. o Can exist for days to weeks, and re typically 40,000 km high Eruptive Prominences- when quiescent prominences erupt in dramatic events that last only a few hours o Coronal gases surge upward several hundred thousand to a million km above the photosphere o The magnetic structure above the ionized gas of a prominence appears to disappear so that the gas is free to surge upward Coronal Mass Ejections- When the sun heaves off billions of tons of matter in a single eruption o Punctuate the steady flow of the solar wind along coronal streamers and prominences o Ejected matter speeds away from the sun as a bubble of gas and magnetic fields at speeds up to 8 million km/h. Flares- sudden intense brightening over regions of the Sun’s surface o Reach maximum intensity in minutes and then fade in minutes of hours o Release X-rays and radiation across the electromagnetic spectrum o The reconnection of magnetic field lines when flux tubes make contact forms these flares. Astronomy Unit 2B Temperatures and Abundances: Collecting the light from a star without dispersing it into its individual wavelengths allows us to determine distances and luminosities Dispersing starlight into a spectrum (wavelengths) allows us to determine surface temperature and abundances of chemical elements making up the atmosphere of a star. Astronomers can determine the chemical compositions of stars from their spectra from identifying the chemical elements responsible for the absorption lines of their spectra Temperature Classification of Stars: o Based on the appearance of absorption lines. Each letter represents a temperature range: O, B, A, F, G, K, M, or L stars Hottest-----------------------------------Coolest Why stars can have the same chemical composition but their spectra can look very different? o The spectra look different because temperature determines the supply of photons passing through a star's atmosphere, where the atoms that can absorb reside. o The energy of the photons determines which atoms can absorb or not. o Too much energy results in no absorption because of ionization. o Too little energy results in no absorption due to there not being enough energy to cause transitions. Luminosity of Stars Luminosity determines a star’s lifetime Luminosity is a star’s wattage (how much energy a star is emitting per second) We can find a stars luminosity without using distance; we use the Sun’s Magnitude (-26.5), the Sun’s luminosity(3.8 x ???????? ), and the Star’s apparent magnitude. o To do this, we must line the stars up at the same distance of 10 pc o We see this taking place and in the examples of the Stellar Lineup below Stellar Lineup Drawing A depicts all the Drawing B shows four stars stars at 10 pc, the red line. at different distances from Next to the stars are the Sun and their apparent their absolute magnitudes magnitudes. (5.0, 6.0, 0.0, etc.) (-26.8, 2.5, 1.2, etc.) Compare the magnitude of star 1 in Drawing B with star 1 in Drawing A. Since star 1 moves from about 5pc in Drawing B to 10pc in Drawing A, the magnitude becomes larger, making the star fainter. Compare the magnitude of star 2 in drawing B with star 2 in Drawing A. Since star 2 moves closer from 15pc in Drawing B to 10pc in Drawing A, its magnitude becomes smaller, making the star brighter. Example: How to find how much brighter a star is to another: ***Recall from Unit 1B, the difference in magnitudes corresponds to a brightness factor of 2.512*** o Compare Star 2 and the Sun in Drawing A o We see Star 2 is brighter since its magnitude is smaller. o Subtract the magnitude of Star 2 and magnitude of the Sun: Magnitude of the Sun (5) minus magnitude of Star 2 (0) equals 5 o To determine how much brighter Star 2 is, square the brightness factor (2.512) by the number you have just calculated through subtraction (5) 5 Your calculation should look like this: 2.512 This comes out to be about 100 o Therefore, in this example, Star 2 has a luminosity 100 times greater than the Sun. Radii of Stars (HR Diagram) These are HR Diagrams, which shows how radii vary. The dashed lines, running diagonally from the upper left to the lower right, represent the radius of are lines of the Sun’s constant radius. Stars with plotted radii are names and represented with a ‘+’ The green circles show radii of different sizes, to represent how the radius changes. The radius increases from left to right in the HR diagram, and diagonally from lower left to upper right. The largest stars are in the upper right of the diagram, and the smallest stars are in the lower left. Key for graph on the right: a= spectral type (coolest to hottest from right to left), b= decreasing absolute magnitude, d= decreasing radius, e= main sequence (top left are the hottest and faintest stars, bottom right the faintest and coolest), A= where white dwarfs are located, C= where to find a supergiant, D= low mass main sequence star, E= low giant star How to Calculate the Radius Use the equation: Ratio of luminosities between the star and Ratio of radii between the sun the star and the sun Ratio of temperature between the star and the sun Example: Calculate the radius of a star with: Ratios needed: ***Even if these ratios weren’t given to us, we could still figure them out. We know the temperature of the sun (5800K), and we can simply rearrange the equation given to us for the luminosity of the star ( ), and solve for the luminosity of the sun, resulting in these same ratios. Next, insert the ratios into the blue equation for the radius Reduce and solve for Double Stars Binary/Double Stars- two stars that orbit each other. We describe this orbit using 2 main parameters: 1. The Semi major axis (a)- distance from center to the point on the orbit along longest diameter (equals half of the longest axis) - this is the size or "radius" of an orbit 2. Eccentricity- the shape of the orbit (value of 0 for a circle and approaching 1 for a very flat orbit) o Also important is the orbital period (time once around) and the velocity in orbit The masses of the orbiting stars control the periods and velocities through the force of gravity If you observe two of the parameters, it is possible to extract the value of the masses of the stars Gravity and Orbits Force of gravity between two masses separated by a distance d F= G(m1Xm2/d^2) G is the gravitational constant Newton’s 2 nd law: F= mass x acceleration Smaller mass experiences greater acceleration (faster motion) Stars orbit around each other—motion prevents collision Relative orbits- the motion of the brighter star is ignored o Astronomers make continuous measurements of the position of the fainter star relative to the brighter o Relative orbits don’t provide enough info to determine individual masses (only the sum of the masses are known) Absolute orbits- individual orbits of the two stars about the center of mass of the system o If the masses of the two stars are the same, the center of mass is exactly between them (same distance away) o If one star is more massive, the center of mass shifts closer to the more massive star o The more massive star has the small orbit (stars orbit about the center of mass) Binary Star Orbits Binary stars: pairs of stars that orbit about each other Gravitationally bound to each other Their orbits are the result of their interaction through the gravitational force High masses, strong gravitational forces Must have high orbital velocities to maintain their orbits Leads to short orbital periods Periods and velocities are related to orbital sizes, or semimajor axes o The radius of the orbit equals the semimajor axes, a o The orbital period, P, is the circumference of the orbit divided by the orbital velocity o P= 2pia/v Types of Binary Systems: o Visual binary stars- visible as two individual stars - A= Alpha Centauri A and B= Alpha Centauri B - Over 70,000 visual binaries - Orbital periods range from 2 to many thousands of years o Astrometric binaries- close enough to earth that astronomers deduce their binary nature from the motion of the visible companion about the center of mass of the pair - Change of position of the visible star of the astronomic pair gives away the presence of the unseen companion - Can distinguish binaries from single stars through Doppler shifts (shift will vary if a star is orbiting another0 o Spectroscopic binaries- binaries detected through variations in their spectra - Orbital period is the time it takes for the observed spectral lines to cycle through the red and blue variations - Radial velocity curve shows the periodicity of the orbital motion o Eclipsing binaries - Primary minimum: hotter star is eclipsed, greater decrease in light. Times between 1 and 2 and 3 and 4 measures the size of the cool star - Secondary minimum: cooler star is eclipsed, less of a decrease in light. Times from 1 to 3 measures the size of the hot star - Light curve: light variation in eclipsing binaries is plotted against time Radial Velocity Curve Velocity of the system through space: o The dashed line that cuts through the wave-like line (km/s) Orbital velocity of stars: o Where the wave-like line hits the dashed line or how much time is spent on the positive side of the dashed line (km/s) Points where star is moving toward or away from us: o Towards: when the velocity(wave-like line) is under the dashed line o Away: when the velocity (wave-like line) is above the dashed line Mass-Luminosity Relation: The main sequence is a progression in mass as well as in temperature and luminosity Faint, cool main sequence stars have low masses Bright, hot main sequence stars have high masses There are deviations though ex: white dwarfs are underluminous rd Kepler’s 3 Law: Relates the semimajor axis to mass Allows astronomers to determine masses of stars Two gravitationally interacting objects are needed for us to determine the mass of one or both Evidence of stellar mass is in the effects of the gravitational interaction between stars M + A = a Bp 3 2 The a= the semimajor axis in AU The p= orbital period in years The final answer should be in solar mass units, M☉-- But now we only have the sum of the masses Use Absolute Orbit to get the distances o Plot the location of both stars relative to a more distant background Newton’s Laws: 1. Constant speed in straight line unless unbalanced force acts o Force- any push or pull o Frictional force slows the object o Collisional force changes direction and speed of the object 2. Force= mass x acceleration o Acceleration- any change in speed/direction o If F is the same, m and a inversely correlated 3. Action-Reaction Newton on Planetary Motion: Newton’s 1 law tells us that a force acts on planets—makes the planets circle the sun This force is called gravity Newton’s 3 law tells us why the sun is the center of the solar system— Sun feels force from planets (action-reaction) o Sun and planets experience acceleration but the sun is more massive o Sun’s acceleration is very small, planets move not Sun o Sun is at center of planetary motion Law of Gravity o F= (mass of sun x mass of planet)/ distance 2 o Force decreases with the square of distance Kepler’s Laws of Planetary Motion: 1. Orbits are ellipses/ sun at one focus 2. Planets move faster closer to the sun o Perihelion- closest to sun o Aphelion- farthest from sun 3. P a= 3 o P= orbital period in years o The a= semimajor axis in AU Shape of ellipse= eccentricity= e= F/A Astronomy Unit 3A Learning Objectives—Interstellar Medium Interstellar Medium- what lies between stars o Includes gas, dust, Electromagnetic radiation between stars, magnetic fields and cosmic rays o The density of the interstellar medium is very low o Much of the interstellar medium’s mass is concentrated in diffuse clouds (made up of atoms and molecules) and molecular clouds (denser than diffuse clouds and made up of mainly molecules) o Intercloud medium- a hot gas between the diffuse atomic and dense molecular cloud 1. Explain why it is difficult for astronomers to piece together the lives of the stars. With the unaided eye, stars look more or less the same except for brightness and subtle color variations. Careful observations then reveal many differences between the stars, such as those embodied in the spectral and luminosity class More detailed observations reveal signs of extreme youth and evidence of old age 2. Describe how interstellar dust contributes to extinction and reddening Extinction- Immense clouds of dust and gas completely block out the light from stars behind them. This can cause distant stars to appear much fainter than they really are Reddening- interstellar dust grains are the right size to scatter blue light more than red light. So, more red light than blue light passes through a cloud of dust, causing reddening of starlight and changing a star’s color index. ***Dust does not affect the observed spectral type of a star because the pattern of spectral lines does not change*** 3. Name the different components of the interstellar medium Diffuse clouds (see above description) Molecular clouds (See above description) Intercloud Medium (See above description) H II Regions/emission nebulae- the largest visible structures in the interstellar medium which are the bubbles supernovae create. oThey are cavities of ionized hydrogen gas. o When a hydrogen ion recaptures and electron, the electron is “kicked” from the third to second orbital, emitting a red photon. Because of this, H II regions glow from the red light of photons. Reflection Nebulae- Nebulae that reflect starlight from nearby hot stars off dust particles oSince spectrum of a reflection nebula is the same as that of the stars generating the light, and these stare are hot, main sequence stars (therefore emitting intensely in the blue part of the spectrum), reflection nebulae are blue as well. Dark nebulae- huge, dark, opaque, dense clouds of dust oExist within the gaseous component of the interstellar medium 4. List the visible features of the interstellar medium (Largest to smallest) H II Regions (huge bubbles and supernova remnants- x rays and extremely hot gas) Reflection nebulae / emission nebulae Dark nebulae 5. List the largest structures of the interstellar medium H II Regions Learning Objectives—Star formation Protostar- collapsing condensations in a molecular cloud that are not yet capable of generating nuclear energy but are on their way to doing so. 1. State the physical property of stars that determines how long the different phases of stellar evolution last Mass determines how long different phases of stellar evolution last. Larger stars go through longer evolutions. 2. The phases that occur during the formation of a star from beginning to end: Dynamic collapse, slow contraction, bipolar molecular outflows, T Tauri phase, Main sequence Self Gravity- the tendency for atoms, molecules, and dust particles in a molecular cloud or a dense core to feel an attractive gravitational force between each other binding them together. 3. What forces are balanced in a cloud of dust and gas? A balance between gravity and gas pressure 4. How does mass and temperature control these forces seen above? Greater massed stars require more pressure to obtain hydrostatic equilibrium (definition below), and to get more pressure they must be hotter. These hot temperatures produce more nuclear reactions/energy, therefore making these stars brighter. 5. Describe the two different triggers of star formation occurring in and near molecular clouds The supernovae- a gigantic stellar explosion in which most of the mass of a massive star is blasted to space oThe ejected material becomes an expanding shell that compresses gas and dust as it moves through the interstellar medium and can encounter molecular clouds oWhen the shell intercepts a molecular cloud, it can cause the edge of the cloud to implode and initiate star formation. Galactic Scope o Spiral arms are sites of star formation o Astronomers interpret these arms as being a density wave o When a density wave crosses a molecular cloud, it compresses it and reduces its mass, leading to star formation. 6. Describe how astronomers detect the existence of recently formed protostars They initially become visible indirectly as embedded infrared sources of radiation within molecular clouds 7. Describe how astronomers detect the thin disks surrounding T Tauri stars The infrared excess of T Tauri stars is much less than that of embedded protostars, and indicates the existence of only a thin disk. The disk is what remains after nearly all the dust and gas have fallen onto the protostar or have been blown away Stellar Birthline- connects the birthpoints for stars of different masses/ the time when the protostar becomes visible. o Most T Tauri stars fall on or below the predicted stellar birthline HR Diagram Luminosity o ***Higher masses collapse faster!! (10000 to 100000 years)****** o Massive stars, brighter, and hotter stars are located in the top left o T Tauri stars are plotted above the main sequence 8. Describe what stops a protostar from contracting The protostar reaches hydrostatic equilibrium, in which nuclear reactions at the center provide the energy for its support and supply all the energy that it radiates away, making it a main-sequence star. 9. Describe how astronomers explain the trend in mass and luminosity of the observed mass-luminosity relationship. Mass-Luminosity relationship- high-mass main sequence stars are more luminous than low-mass stars oAstronomers observed that that the mass-luminosity relationship is dependent on the central temperature of mass oGreater massed stars require more pressure to obtain hydrostatic equilibrium, and to get more pressure they must be hotter. These hot temperatures produce more nuclear reactions/energy, therefore making these stars brighter. Learning Objectives—Stellar Evolution Main Sequence Stars- any star that is fusing hydrogen in its core and has a stable balance of outward pressure from core nuclear fusion and gravitational forces pushing inward. 1. How do Astronomers determine the age of star clusters? o Star clusters are the result of the collapse of a large segment of a molecular cloud that fragments into hundreds to millions of protostars o We can infer the relative ages of star clusters by the location of the brightest main-sequence stars. Must compare the brightest main sequence stars in each cluster: Whichever one is brightest is younger o We determine the absolute age of star clusters by determining the luminosities and masses of the brightest main sequence stars, then using the lifetime-equation to estimate the cluster’s age. 2. Describe the main sequence turn off of a star cluster o Main sequence turn off- where the brightest stars have already shifted away from their original main sequence positions. o The upper part of the main sequence decreases in luminosity as the stars in the cluster age (this is when they turn off) 3. Order the sequence of events for a star as it becomes a red giant Core hydrogen exhaustion, ignition of nuclear shell source, atmosphere and envelope expand, contraction of the core 4. List the main composition of the cores of: o The main sequence: Nuclear reactions occur, and the core is made of hydrogen. The amount of hydrogen is decreasing because the proton-proton chain is gradually converting it to helium. When the hydrogen is eventually exhausted, the core is completely helium and contractions of the star heat it until nuclear burning occurs. o Stars right after hydrogen exhaustion: The core contracts until it is heated to 100 million K (making it a red giant) and how has a helium core which undergoes helium burning ( now the core is made of helium) o Stars right after helium exhaustion: Burn carbon, but this is only if their masses were big enough to keep contractions going Helium flash- when temperature reach hundreds of millions of K, and the amount of energy generated in the core reaches a hundred time the luminosity of an entire galaxy, creating an enormous outburst of nuclear energy. o After this happens, helium burning is able to occur. “D” represents the main sequence. Line “7-8-9” represents the least massive protostar Line “1-2-3” represents the most massive protostar “B” represents the birthline Lines points 4 and 6 represent helium burning, with 4 being the helium flash Point 2 represents hydrogen core exhaustion Astronomy Unit 3B Learning Objectives –Supernovae & Nucleosynthesis Nuclear Burning Cycle in Massive Stars 2 3 4 1 Diagram showing the layering of the core of a massive star o This shows the end of silicon burning. A shell source burns and adds mass to the layer below it. o The Core Collapses within seconds of the end of silicon burning o Once at the iron core, the iron core contracts but does not burn. Iron nuclei are the most strongly bound of all nuclei. Since no further nuclear reactions can occur, the core must collapse. Cepheid Variables- a type of variable star that occupy the instability strip (place where star undergoing evolution is unstable an pulsates) o 2 types: Type 1 Cepheids- relatively massive stars with high metalicities, similar to the sun and found in young star clusters. They are core-helium burning giants and have masses between about 4 and 20 M. Astronomy Unit 3B Type 2 Cepheids- metal poor, low mass stars found in the oldest star clusters. They have already exhausted their helium cores, thus they are more luminous giants. o Pulsation periods for Cepheids range from a couple of days to a couple hundred of days. They are longer because they have a larger radii. Larger Cepheids pulsate slower than smaller Cepheids. Period-luminosity relation- correlation between luminosity and pulsation periods that says brighter Cepheids (which are larger) have longer pulsation periods than Cepheids that are less bright (which are smaller) o The longest period Cepheid are nearly 100 times brighter (5 magnitudes brighter) than the shortest period Cepheid. o Useful for determining distances to Cepheids. o The distance to the Cepheid is the same distance to the cluster or galaxy in which it resides. Type II Supernova o This is a mechanical explosion 1. the neutron core rebounds 2. the neutrons degenerate at the center first 3. the degeneracy causes a sudden halt in the inner core 4. inward momentum compresses the inner core 5. the inner core rebounds 6. Collision between the inner and outer halves of the core occur 7. This causes a shock wave, which move the air at the speed of sound and ejects matter beyond the inner core. This causes and explosion which is a type II supernova Type Ia Supernova o White dwarf explosions o Made up of a double star system and there is a transfer of mass from the companion onto the white dwarf. When this additional mass puts the white dwarf over the Chandrasekhar limit, it collapses and blows itself up Diagram for the phases of evolution of stars of different masses Astronomy Unit 3B Where all of the elements in the universe are created o Elements are created 4 ways: 1. Nuclear reactions in the first few minutes of the universe 2. Nuclear burning in the cores of stars 3. Nuclear burning during supernova 4. Neutron capture during supernova o Neutron Capture is the process of building isotopes and new elements from capturing electrons. This usually happens after an explosion. o Nucleosynthesis- the creation of elements through nuclear processes Learning Objectives: Planetary Nebulae & White Dwarfs AGB star- stars that become more luminous after exhaustions in the cores of giants and supergiants, and their calculated evolutionary tracks asymptotically approach the first red giant branch o Have a helium shell source Planetary Nebulae- Shells of glowing gas o When intense ultraviolet radiation from the core begins to ionize the expanding envelope, causing the gas to shine by emission because ionization frees electrons that ions capture. o Consists of a central star which is the star in the middle of the ring. o Estimated more than 20 thousand exist in the Galaxy o Green-blue due to emission from oxygen ions and have a disk like shape o Range in size from a few hundredths to a few tenths of a parsec across White Dwarf- What remains of planetary nebulae by the time their shell sources run out of fuel, which are remnants cores of AGB stars o They are faint and hot—much fainter than main sequence stars of similar temperatures o The hottest white dwarf have spectra similar to those of centrals stars of planetary nebulae o Typically have small radii (0.o1 solar radii) compared to the sun, hence they are dwarf (however, this radii is about the size of earth) o Have masses between 1.1 and 0.4 (the greater the mass, the smaller the radius) o Have high densities (between 3 x 10^6 and 2.5 x 10^5 gm/cm^3) Chandrasekhar limit- A mass that exists at which degenerate electrons apply the maximum pressure possible (1.4) Astronomy Unit 3B o Explains how a white dwarf can have twice as much mass as another white dwarf but only 1/3 of the volume o All white dwarfs are less than 1.4, because cores greater than this number cannot support themselves and must collapse and produce supernova. o Pressure from degenerate electrons is sufficient to support the star’s structure and maintain their radii at a constant value without nuclear reactions. Since white dwarfs can’t contract and have no nuclear energy supply, they can’t heat up—they only become cooler and fainter. So, since the pressure from degenerate electrons is independent of temperature, cooling causes no change in radius. ***Sun’s end state will most likely be a white dwarf*** Astronomy Unit 3B Information from the Sample Test 1. What kind of Cepheids have larger radii? The more massive Stars i. Cepheids are core-helium burning giants, where they make “loops” in the HR diagrams. 2. What is the most likely evolution for a star of 5 solar masses? MS->RG->PN->WD i. Stars below 8 solar masses become red gains, not super red giants ii. Stars above 8 solar masses and less than about 25 would evolve like this: MS->RSG->SN->WD 3. What is most likely the evolution for the sun? MS->RG->PN->WD 4. What is the most likely evolution for a 25 solar mass star? MS ->RSG -> SN ***See page two for a graph of this*** 5. , 6. , and 7. 1-2 is hydrogen burning, 2-3-4 is single shell source burning, 5 is helium burning in the core with 4-6 as the beginning and end processes of helium burning in the core with a surrounding hydrogen shell source, 6 is the exhaustion of helium in the core and the creation of the helium shell source, 6-7 is the period in which the stars envelope dissipates, 8 is the location of planetary nebulae with 7-8 as the period of these nebulae forming, 7 is where a star has lost nearly all of its envelope, and 8-9 are the white dwarfs ***I think the graph below is actually much more useful for these questions.*** More detailed information for the HRD of the evolutionary track Astronomy Unit 3B 8.. Which of the following is a possible last visible phase of a star, with a main sequence mass below 8 solar masses, before it reaches its end state? Planetary Nebula o The End states for more massive stars are black holes 9.. What is the difference between a white dwarf and a planetary nebula? Planetary nebula are the ejected envelops of low mass stars and white dwarfs are the remaining cores of low mass stars after envelope ejection 10. How many nuclear burning phases are possible for the most massive stars? 6: Hydrogen, helium, carbon, neon, oxygen, silicon o 2 or 3 for smaller stars 11. What is the Chandrasekhar limit and what is its value It is the maximum mass that degenerate electrons can support: 1.4 solar masses 12. Why doesn’t electron degeneracy hold up the iron core in a massive star? The core and overlying envelope is too massive for electron degeneracy o The mass of the iron core and the star are higher than the Chandrasekhar limit 13. What causes a supernova? Rebound of the inner core 14. What process in a supernova helps create heaviest elements in the universe? Neutron capture 15. Which of the following best describes a Type II supernova? Explosion initiated by the collapse of the iron core 16. Which is one way iron in the universe is formed? By explosive nuclear burning in SN shock waves 17. Which gives the correct statement concerning the length of time of the different phases of nuclear burning in the core> Neon-Burning takes longer than oxygen burning o The further inward the shell, the less time it takes that phase to occur 18. 3 represents the relative abundances of elements in the universe created by neutron capture 1 represents the relative abundances of elements created by the core burning 2 represents the relative abundances of elements during the first few minutes of the universe ***See page 3 for a more detailed graph*** 1 Astronomy Unit 4A Neutron Stars Neutron star- the remnant core of the exploded star o Extremely compact/dense and tiny o Diameters (size) are less than 35 km, the size of a large city (still tiny in comparison to other stars) o Difficult to detect o The largest mass is about 3 M, but scientist don’t know for sure. o In binary stars, the maximum is about 2M. o The average mass is about 1.5M, slightly more massive than white dwarfs o It’s surface gravity is 100 billion times greater than Earth’s Composition of the Neutron Star o The crust is about 1-2km thick Consists of an iron nuclei o The core is a neutron superfluid in which the sea of neutrons become frictionless fluid Very dense region Pulsars- celestial radio sources o Rotation increases as the core shrinks and the magnetic field increases in strength. o Produce radio waves o Discovered these signals from the Crab Nebula o Glitches are rare speed ups, and about 30 of the 1500 known pulsars exhibit these This means they spin more rapidly Glitches are produced when the rotational motion of vortexes is deposited to the crust, speeding up its rotation Happens every few years o The slowing down of pulsars is probably the result of strong magnetic fields surrounding pulsars. Magnetic fields and Pulsars o 2 observa
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