Final Study Guide --- Astronomy 1101: Planets to Cosmos ------------------------------------------------------- Some example questions: The failure to detect the parallaxes of stars during Copernicus's time and before was used as evidence that A. the Earth orbits the Sun. B. the Earth does not move. C. the Earth is a sphere. D. the stars are nearer to the Earth than the Sun. E. None of these choices is correct. Object A has mass of 1 kg. Object B has mass of 20 kg. If the same force is applied to both, A. object A will have 1/20th the acceleration of object B. B. objects A and B will have the same acceleration. C. object B will have 1/400th the acceleration of object B. D. object B will have 1/20th the acceleration of object A. E. object A will have 1/400th the acceleration of object B. Two stars have the same apparent brightness and temperature, but different distances. The star that is closer to the Sun has a A. lower luminosity. B. higher luminosity. C. larger radius. D. bluer color. E. higher apparent brightness. What is the name of the sequence of nuclear reactions that generates the energy in the cores of main-sequence stars that are half the mass of the Sun? A. The CNO cycle. B. The ideal gas equation of state. C. Neon burning. D. The proton-proton (PP) chain. E. Silicon burning. The event separating the red giant phase from the horizontal branch phase of stellar evolution for low mass stars is the A. Silicon burning flash. B. Blue supergiant phase. C. Red supergiant explosion. D. Oxygen burning epoch. E. Helium flash. Taken together, our current estimates of the Hubble constant (H0) and the density parameter (Omega) tell us that the age of the Universe is about A. 14 trillion years old. B. 14 billion years old. C. 14,000 years old. D. 14 years old. E. 14 million years old. Imagine we knew the true luminosities of each of the objects below. Which would be the most generally useful for measureing the distances to very far-away galaxies? A. Red giants B. White dwarfs C. Household lightbulbs D. Main-sequence Sun-like stars E. Type-Ia supernova explosions Galaxy A has a redshift of 0.1. Galaxy B has a redshift of 0.2. From this information and the existence of the Hubble Law you can conclude that A. Galaxy B is two times further away than Galaxy A. B. Galaxy A is two times further away than Galaxy B C. Galaxy A is four times further away than Galaxy B. D. Galaxy B is four times further away than Galaxy A. E. Galaxy A and Galaxy B are at the same distance. ---------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------- Material from Quiz 1: --------------------- Astronomical Numbers, Scientific Notation 1 AU, 0.001 = 10^-3, 1,000,000,000 = 1 billion = 10^9 Metric system: meters, kilgrams, seconds. The Night Sky: The Constellations, true motions of the stars in the galaxy Measuring the Earth Aristarchus's derivation of the distance to the Moon and the distance to the Sun. Example of early heliocentrism The Spherical Earth Appeal to perfect symmetry Aristotle's arguments The circumference of the Earth Method of Eratosthenes Ptolemy's estimate and its influence Daily & Annual Motions Motions due to Earth's Daily Rotation, and due to Earth's orbit around the Sun. The latter gives us a different persepctive on the Sun and planets with respect to background stars. Motions of the inferior planets: always tied to the Sun Motions of the superior planets: not tied to the Sun Retrograde Motion: What is it, when does it occur for different planets? The Phases of the Moon The moon rotates synchronously: it rotates once for every orbit around the Earth. Main Phases of the Moon: Moonrise & Moonset times at the different Moon phases The orientation of the Earth-Moon-Sun system in different phases. Some important equations: F = ma (Newton's 2nd law) P^2 = a^3 (Kepler), and Newton's generalization. Note that Newton's generalization is important because it allows us to extend Kepler's relation to other masses of the bodies involved. For example, Newton's generalization shows that as the masses in the systems get larger, the period of the orbit decreases for fixed semi-major axis. V_circ = (G M / r)^1/2 (M is the central mass, r is the distance to its center) we have used this throughout the semester to measure the masses of astronomical objects. V_escape = 2^1/2 V_circ (velocity needed to escape the gravity of a body) a_1/a_2 = M_2/M_1 (determines center of mass between M_1 and M_2) L = m v r (the angular momentum of a body in orbit is conserved: L = constant). This is the physical reason for Kepler's "equal areas in equal times." In practice, I am more likely to ask you a question like "All else being equal, if the mass of a body increases, its escape velocity _____" (A) increases (B) decreases (C) stays unchanged than I am to ask you about the actual scaling of the escape velocity equation. Nevertheless, I will sometimes put in harder questions that ask you about the scaling, and the consequences of an equation. For example, "All else being equal, if the mass of a body were to increase by a factor of 4, its escape speed would (A) increase by a factor of 2. (B) increase by a factor of 4. (C) decrease by a factor of 2. (D) decrease by a factor of 4 Short review of gravity and orbits: Two bodies with masses M1 and M2 are separated by a distance d. If M1 increases by a factor of 4, the force increases by a factor of ____. If M2 increases by a factor of 4, the force increases by a factor of ____. If d increases by a factor of 4, the force decreases by a factor of ____. If d decreases by a factor of 4, the force increases by a factor of ____. The above can be understood knowing the equation F = G M1 M2 / d^2. Two bodies with masses M1 and M2 are in a gravitationally bound orbit. All else held equal, if either M1 or M2 increases, the period of the orbit ____. A small asteroid is in orbit around the Sun with semi-major axis A and period P. All else being equal, if A is increased by a factor of 4, the P increases or decreases by a factor of 2, 4, 8, 16, 32? Aristotelian World View Assumptions (uniform circular motion, fixed unmoving earth) Early Geocentric Systems Eudoxus, Pythagoras, Aristotle Epicyclic Systems Hipparchus & Ptolemy Early Heliocentric System Aristarchus Ptolemaic Geocentric System Epicycles and so on. Preserving Appearances - especially the retrograde motion & change in brightness of superior planets at "opposition." Opposition is when we are closest to asuperior planet in its orbit. It is the same configuration for the superior planet as it is for the Full Moon: The planet, the Earth, and the Sun lie on a line, in that order. Problems: complex, no way to measure planetary distances with epicycles. Copernicus Motivations & Assumptions (disliked equant, wanted to **restore** Aristotelian ideal of uniform circular motion) Copernican Heliocentric System Sun at the center! Earth rotates on its axis every 24 hours! Earth orbits (revolves) around the sun once a year! His use of epicycles and why he used them. Successes: a) explains superior & inferior planets b) explains retrograde motion c) gives a geometric way to measure planetary distances Problems: (a) the Earth is not apparently moving (b) stellar parallaxes are not observed Should they have been able to measure stellar parallaxes at that time? (c) stars do not get brighter at "opposition" It is true that we do get a bit closer to and farther away from certain stars as we orbit the Sun, but the effect is TINY since the stars are actually so far away. Tycho Brahe: his observations & their significance Johannes Kepler: his theoretical work & its significance Kepler's Three Laws of Planetary Motion First Law (Ellipses!) Second (Equal Areas) Law Third (Harmonic) Law: P^2 = a^3 (where P is measured in years and a is measured in AU). Galileo's telescope observations & their significance The Moon Sunspots Phases of Venus Moons of Jupiter Isaac Newton: work and its significance Laws of Motion First Law (Law of Inertia) Second Law (F=ma) Third Law (Action & Reaction) Newtonian Gravity Inverse-Square Law Force Dependence of the gravitational force on masses and distance of the two bodies. Newton's Generalized forms of Kepler's Laws Shapes of Orbits Orbit about the Center of Mass Circular and Escape Velocity Measuring Masses with Newton's form of Kepler's 3rd Law Gravitational Interactions among objects What is Stellar Parallax? General Solar System --------------------- Names of the 8 planets Dwarf Planets Order of planets in the Solar System Main types of planets & other bodies Extrasolar Planetary Systems ---------------------------- Searches for planets around other stars Doppler Wobble Planetary Transits Extrasolar planetary systems Jupiter-sized planets close to their parent stars Prospects for finding Earth-like planets Basic conditions for Life The Habitable Zone Material from Quiz 2: --------------------- Stellar Brightnesses: Luminosity Apparent Brightness Inverse Square Law of Brightness : B = L/(4 pi D^2) Stellar Spectra: Colors of stars and relation to Temperature Main Spectral Types: O B A F G K M L T The Hertzsprung-Russell Diagram: Plot of Luminosity vs. Temperature for stars. Main Sequence Stars Giant Stars Supergiant Stars White Dwarfs Luminosity-Radius-Temperature Relation: L = 4 pi R^2 sigma T^4 Stellar Structure & Evolution ----------------------------- The Internal Structure of Stars: Mass-Luminosity Relationship: on the Main Sequence : L ~ M^4 Hydrostatic Equilibrium : balance of pressure and gravity. Energy Generation in Stars Hydrostatic equilibrium Nuclear Fusion Energy The Solar Age crisis: Is the Sun powered by Chemical Reactions? Gravitational energy? Proton-Proton Chain Neutrinos CNO Cycle Hydrostatic Thermostat, thermal equilibrium Energy Transport: Radiation, Convection The Main Sequence Burn Hydrogen into Helium in their cores. In Hydrostatic & Thermal Equilibrium Mass-Luminosity Relationship for M-S stars The Main Sequence is a Mass Sequence Lower M-S: M < 1.2 Msun Burn H via p-p chain Upper M-S: M > 1.2 Msun Burn H via CNO cycle Dependence of M-S Lifetime on stellar Mass. Larger Mass = Shorter Life. Typical lifetimes of O-stars, M-stars, & the Sun t_MS ~ 1/M^3 Minimum and Maximum masses of stars Brown Dwarfs (M < 0.1 Msun) The Evolution of Low Mass stars (M < 4 Msun) --------------------------------------------- Main Sequence phase through H exhaustion in core He core formation & H shell burning Ascent of the Red Giant Branch Helium Flash & the Triple-Alpha Process Descent to the Horizontal Branch He core burning & H shell burning C-O core formation Asymptotic Giant Branch star He and H burning Shells Onset of instability Envelope Ejection & Formation of a Planetary Nebula Core evolves into a White Dwarf star What are the timescales for these phases? Which way do stars move on the HR diagram? Stages of Evolution of High Mass O & B Stars (M > 4 Msun) --------------------------------------------------------- Stars with 4 < M < 8 Msun Burn Hydrogen, then Helium, then Carbon Blow off their envelope after exhaustion of Carbin Burning Core becomes an O-Ne-Mg White Dwarf Stars with M > 8 Msun Burn Hydrogen up through Carbon, Neon, Oxygen & Silicon What are the timescales for these burning phases? Iron Core Formation & burning shells Catastrophic collapse of Iron Core leading to Iron core bounce & supernova explosion ejecting envelope core collapses to a neutron star or black hole BHs may come from stars with M > 20-30 Msun, but uncertain Supernovae Nucleosynthesis in Supernovae (main source of heavy elements) Role of supernovae in seeding interstellar space with heavy elements Role of supernovae in producing neutron stars White Dwarfs: ------------- Remnant cores of low-mass stars (M < 8 Msun) About the size of the Earth R ~ 5000 km Held up by Electron Degeneracy Pressure Different from the Ideal Gas Law Equation of State: does not depend on temperature. Allows bodies that are cold to remain in hydrostatic equilibrium. Maximum Mass ~1.4 Msun (Chandrasehkar Mass) White dwarf just cools off over a long time. Can accrete from a binary companion, or run into another (collision, merger) white dwarf to produce a Type Ia supernova; thermonuclear detonation; run-away C burning. Produces a lot of Iron, most of the Iron in the universe. Neutron Stars: -------------- Remnant cores of massive stars (M > 8 Msun) About the size of a city: R ~ 10 km. Held up by Neutron Degeneracy Pressure: does not depend on temperature, allows cold neutron stars to stay in hydrostatic equilibrium Pulsar = rapidly spinning neutron star Neutron stars cannot support themselves above 2-3 Msun. Neutron degeneracy pressure fails. Gravity wins. Black hole formation Black Holes: ------------ Black Holes are totally collapsed objects gravity so strong not even light can escape predicted by General Relativity theory remnant cores of very massive stars (M > 20-30 Msun?) Singularity Schwarzschild Radius & Event Horizon Find them by their Gravity X-ray Binary Stars & Black Hole Candidates Hawking Radiation & Black Hole Evaporation Tests of Stellar Evolution: --------------------------- H-R Diagrams of Star Clusters Why clusters are good for testing stellar evolution Changes in the H-R diagram of a star cluster as it ages Estimating cluster ages from the Main-Sequence Turn-off Open Clusters Young clusters of few 100s - 1000s of stars Blue Main-Sequence stars & few giants Shapes of their H-R diagrams Range of ages from Few million to few billion years Globular Clusters Old clusters of a few 100,000 stars No blue Main-Sequence stars & many giants Shapes of their H-R diagrams 10-13 Billion years old Star and Planet formation: ------------------------- Star formation & the main sequence --------------------------------- raw material for stars are giant molecular clouds cold and dense blobs of gas in galaxies steps in star formation: gravitational collapse establish hydrostatic equilibrium (proto-star phase) establish thermal equilibrium (pre-main sequence phase) land on the main sequence planets-forming debris disks around newly formed stars what energy source powers a protostar? what is the Kelvin-Helmholz timescale? which stars reach the main sequence the fastest? are low or high-mass stars intrinsically rarer? what are the minimum and maximum masses of stars Planet formation ----------------- The importance of the "frost Line" or "ice line", the distance form the central star where the temperature drops below the temperature to form water ice. Beyond the frost line, ice can form, rapidly accumulate H from the disk, make the Ice and Gas Giants (Jupiter, Saturn, Uranus) Planetesimals We are Star Stuff ----------------- Where do the elements come from? Nucleosynthesis. H and He come from the Big Bang. Virtually everything else from stars and/or stellar processes. Massive stars: fuse H to He and then on up to Fe Intermediate mass stars: fuse up to ONeMg, eject He, CO Low-mass stars: fuse H to He, leave behind CO white dwarf Supernova remnants carry out the ejecta of massive stars, slow down on long timescales, pollute the interstellar medium. Seed new planet and star formation. Most Fe from Type Ia supernovae (thermonuclear detonantion of a White Dwarf) Most O and C from core-collapse supernovae of massive stars. Most N from AGB stars: mix C and protons, make N, then eject. What about Gold, Platinum, Uranium? Unknown, but maybe during the formation of a black hole when two neutron stars merge. Maybe in exotic supernovae. Material from Quiz 3: --------------------- Cosmic Distances: ----------------- Trigonometric Parallaxes RR Lyrae Variables Cepheid Variables Period-Luminosity Relation The Milky Way Galaxy -------------------- The Milky Way is our Galaxy Diffuse band of light crossing the sky Galileo: Milky Way consists of many faint stars The Nature of the Milky Way Philosophical Speculations: Wright & Kant What is the geometry of the Milky Way? A spherical shell, or a disk? Size of the MW from Star Counts: Herschels Star Gauges Kapteyn Model Globular Cluster Distribution: Shapley, RR Lyrae stars First to locate the Sun outside the center of the Galaxy. The importance of dust obscuration in calculating the luminosity distance. Nature of the "Spiral Nebulae" The Great Debate! ------------------------------ Two hypotheses: spiral nebulae are external, or internal to Milky Way? Island Universe Hypothesis (Kant & Humboldt) Nebular Hypothesis (Laplace) Role of finding distances in resolving the debate Leavitt: Cepheid Period-Luminosity Relation, distances Shapley-Curtis Debate (1920) Hubble: Cepheids in Andromeda The Milky Way & Andromeda ------------------------- Common Properties of the Milky Way & Andromeda Galaxies Disk & Spheroid Structure of the Galaxy Pop I Stars: Young, metal-rich, disk stars Ordered, nearly circular orbits in the disk Pop II Stars: Old, metal-poor, spheroid stars Disordered, elliptical orbits in all directions Chemical Evolution, connection to stellar populations Supermassive Blackholes Spiral Galaxies --------------- Disk & Spheroid Components Thick disk of stars, thin disk of dust, spiral arms Spheroid: bright central Bulge and faint extended Halo Rotation of the Disk Orbital period of the Sun in the Galaxy Measurement of Galaxy Masses from Rotation Curve, Doppler effect Spiral Arms: Outlined by O&B Stars, Gas & Dust clouds Sites of recent star formation. Why O&B stars don't move very far from their birthplaces? Types of Galaxies ----------------- Three basic types of Galaxies: Spirals Ellipticals Irregulars Dwarf Galaxies Differences between the types of galaxies in terms of Relative Gas content Star Formation History Internal Motions of stars: ordered rotation vs. disordered. Structure Groups & Clusters of Galaxies ----------------------------- Galaxies tend to group into Clusters The Milky Way is part of the Local Group Hierarchy of Structure: Groups: < 30 bright galaxies, many dwarfs Clusters: 30 - 100's of bright galaxies, many dwarfs Where Ellipticals & Spirals are found in Rich Clusters Superclusters: Clusters of Clusters Voids, Filaments, & Walls, porous structure of the universe Large scale structure reflects the initial perturbations to the density and temperature of the universe. Interacting Galaxies -------------------- Tidal Interactions occur between Galaxies Frequency of occurence: the relative distance between galaxies is small, particularly in comparison with stars. Cause of most of the "peculiar" galaxies observed Tidal distortion in encounters Types of interactions Close Tidal Encounters Galaxy-Galaxy Collisions Starbursts induced by interactions Stars pass through during a collision, but the gas shocks and forms lots of stars. Drive metal-rich winds into the inter-galactic medium. Mergers & Galactic Cannibalism How we think massive ellipticals and clusters are made. Special Relativity: ------------------ First Postulate (uniformly moving observers) Second Postulate (speed of light) Newton's conception of absolute space & absolute time Einstein's conception of space & time as relative How time appears to different observers (the photon clock experiment) General Relativity: ------------------ Explanation of gravity as curved spacetime Matter tells spacetime how to curve, Curved spacetime tells matter how to move. Experimental verification of GR: Perihelion shift of Mercury Bending of Starlight near the Sun Strong gravitational lensing of galaxies by clusters Upcoming experiments to image the event horizon of a black hole and gravitational waves from merging neutron stars and black holes. Einstein's Cosmology: -------------------- Cosmological Principle: Universe is Homogeneous and Isotropic on Large Scales Cosmological Constant Evidence of large-scale homogeneity & isotropy Observational Cosmology: ----------------------- Hubble's Law Hubble Parameter, H0 How it is measured Uncertainties in measuring H0 Current rate of expansion of the Universe We are not at the center: raisins in expanding cake, points on expanding balloon, etc. Redshift distances Redshift maps How is Hubble's Law --- V = H_0 D --- related to the approximate age of the universe? If H_0 were found to be smaller or larger than it currently is, would that immediately imply a younger or older universe? Tests of the Big Bang, Cosmic Timeline, Early Universe Big Bang Theory: ----------------------------------------------------------------------- Basic features of the theory Expansion of the Universe (Hubble's Law) Density Parameter (Omega0) Critical Density: Omega0 determines the geometry of the Universe Age of the Universe (Hubble Time), road trip analogy, the 'unit' of 1/H0 is time, the age of the universe. Primordial (Big Bang) Nucleosynthesis Production of Deuterium, Helium, and light metals (Li,Be,B) Predictions for observed abundances Comparison with predictions Cosmic Background Radiation Blackbody Spectrum & Temperature Observed properties Conditions at the Epoch of Recombination Dark Matter ----------- Observational evidence for dark matter: Rotation curves of galaxies, M = V^2 R/G Hot gas bound to galaxy clusters Motions of galaxies in galaxy clusters Gravitational lensing of background galaxies by clusters of galaxies. The physical nature of dark matter: MACHOS: massive compact halo objects: ancient, cold white dwarfs, neutron stars, black holes, brown dwarfs WIMPS: weakly interacting massive particles: something like a neutrino: interacts weakly with normal matter, but also gravity Other possibilities? Dark Energy ----------- Observational evidence for dark energy: The deviation of the Hubble diagram from a straight line indicates acceleration of the expansion of the universe. Explanantion: possibly the vacuum energy of the universe: the 'cost of having space' The overall budget of the universe. Physics of the Early Universe ----------------------------- The Cosmic Timeline Unification of the forces just after the Big Biang Separation of the forces as the Universe cools and expands Inflationary Epoch explains the smoothness and flatness of the Universe Emergence of matter at 10^-6 seconds after the Big Bang Recombination and the emergence of the visible Universe The critical role of the binding energy. In the epoch before nucleons, it was too hot for them to exist. In the era before nuclei (like He), it was too hot for them to exist. In the era before neutral Hydrogen, it was too hot for electrons to bind to nuclei. In all cases, as the universe cools, new things can happen. Fate of the Universe -------------------- The role of the density parameter in determining the expansion history of the Universe. If the universe was dominated by normal matter and energy, Omega tells you the future: If Omega > 1, the universe collapses and ends in a Big Crunch; if Omega < 1, the universe expands forever at an ever-decreasing rate. But, we live a universe with a lot of dark energy. This causes the acceleration of the expansion of the universe. How we measure the matter density: starlight, dark matter Evidence for an accelerating Universe (non-zero Cosmological Constant) Type Ia supernova results Baryon-acoutic Oscillations Future Evolution of an Open, Accelerating Universe: Cold, dark, disordered if a Cosmological Constant 1 - Sun gets brigher as it evolves, causes runaway greenhouse effect in 1-3 Gyr. 2 - In about 10^12 yr the era of star formation ends as more and more matter gets 'locked up' in white dwarfs, neutron stars, and black holes. 3 - Solar system dissolves. 4 - Galaxies disolve. 5 - Protons may decay, leading to the end of normal matter. 6 - Stellar mass black holes evaporate. 7 - Supermassive black holes evaporate. Other flavors of dark energy (e.g., Phantom energy) lead to very different cosmic end games. For Phantom Energy, the energy density in dark energy groes everywhere as a function of time, eventually ripping everything apart. Life in the Universe --------------------- Requirements for (intelligent?) life Drake Equation Fermi Paradox