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Astronomy 101 Course Review and Summary Main Topics: • • • • • • • The Night Sky History of Astronomy & Science Light and Matter The Solar System Structure and Evolution of Stars Structure and Evolution of Galaxies Structure and Evolution of the Universe The Night Sky The Celestial Sphere The sky as seen from Earth is divided into 88 constellations. It is convenient to pretend the stars are attached to a celestial sphere. The celestial sphere appears to rotate about the celestial poles (1 day). The Sun appears to move west to east relative to stars (1 year). The Moon appears to move west to east relative to stars (1 month). Celestial Sphere: A large imaginary sphere centered on Earth Season & Calendars The cause of the seasons is the tilt of the Earth’s rotation axis relative to its orbit around the Sun. The day is based on the time between one noon and the next. The year is based on the time between one vernal equinox and the next. The moon (month) is based on the time between one new moon and the next. Moon Phases & Eclipses: Key Concepts Lunar phases change as we see more or less of the Moon’s sunlit half. The Moon rotates about its axis as it revolves around the Earth. The sidereal month=27.3 days; the synodic month=29.5 days. A lunar eclipse occurs when the Moon passes through the Earth’s shadow. A solar eclipse occurs when the Earth passes through the Moon’s shadow. Solar eclipses occur when Moon is between Sun and Earth. Solar eclipses occur at NEW MOON. A lunar eclipse occurs when the Moon passes through the Earth’s shadow. Lunar eclipses occur when Earth is between Sun and Moon. Lunar eclipses occur at FULL MOON. From Ptolemy to Copernicus: Key Concepts Aristotle (4th cent BC) showed that the Earth is round. Greek astronomers developed a geocentric model for the universe. Ptolemy (2nd cent) used epicycles to explain retrograde motion of planers. Copernicus (16th cent) proposed a heliocentric model for the universe. In the model of Copernicus, retrograde motion is easily explained. The combination of small and large circles produces “loop-the-loop” motion. Tycho, Kepler, & Galileo: Key Concepts Tycho Brahe made accurate measurements of planetary motion. Planetary orbits are ellipses with the Sun at one focus. A line between planet & Sun sweeps out equal areas in equal times. The square of a planet’s orbital period is proportional to the cube of its average distance from the Sun. Galileo made telescopic observations supporting the heliocentric model. Kepler’s First Law of planetary motion The orbits of planets around the Sun are ellipses with the Sun at one focus. Kepler’s Second Law of planetary motion A line from the Sun to a planet sweeps out equal areas in equal time intervals. Kepler’s Third Law of planetary motion The square of a planet’s orbital period is proportional to the cube of its average distance from the Sun*: *A planet’s average distance from the Sun is equal to the semimajor axis of its orbit. Newton’s Laws Three Laws of Motion: (1)An object remains at rest, or moves in a straight line at constant speed, unless acted on by an outside force. (2) The acceleration of an object is directly proportional to force, and inversely proportional to mass. (3) For every action, there is an equal and opposite reaction. Law of Gravity: The gravitational force between masses M and m, separated by distance r, is proportional to the product of the masses divided by the square of the separation Applying Newton’s Laws Newton modified and expanded Kepler’s Laws of Planetary Motion. Kepler described how planets move; Newton explained why they move. Tides are caused by the difference between the Moon’s gravitational force on different sides of the Earth. Tidal forces are slowing the Earth’s rotation & enlarging the Moon’s orbit. Newton’s First Law of Motion: An object remains at rest, or moves in a straight line at constant speed, unless acted on by an outside force. Precise mathematical laws require precise definitions of terms: SPEED = rate at which an object changes its position. Example: 65 miles/hour. VELOCITY = speed plus direction of travel. Example: 65 miles/hour to the north. Newton’s Second Law of Motion: The acceleration of an object is directly proportional to the force acting on it, and inversely proportional to its mass. In mathematical form: Or alternatively: Newton’s Third Law of Motion: For every action, there is an equal and opposite reaction. Whenever A exerts a force on B, B exerts a force on A that’s equal in size and opposite in direction. All forces come in pairs. Kepler’s Third Law: Light Visible light is just one form of electromagnetic radiation. Light can be though of as a wave or as a particle. Light forms a spectrum from short to long wavelengths. A hot, opaque object produces a continuous blackbody spectrum. Light forms a spectrum from short to long wavelength Visible light has wavelengths from 400 to 700 nanometers. [1 nanometer (nm) = 10-9 meter] Color is determined by wavelength: Blue: 480 nm Green: 530 nm Red: 660 nm Visible light occupies only a tiny sliver of the full spectrum. Matter and Forces Matter can come in various forms that are composed of fundamental particles An element is known by it number of protons Isotopes of an element contain different number of neutrons Isotopes can be radioactive and spontaneously decay There are four fundamental forces (Gravity, Electromagnetism, Strong, and Weak) Hydrogen 1 proton 1H 2H 3He 4He 6Li 7Li Helium 2 protons Lithium 3 protons Proton: Neutron: 3H Spectra A hot, transparent gas produces an emission spectrum. A cool, transparent gas produces an absorption spectrum. Every type of atom, ion, and molecule has a unique spectrum. The most abundant elements in the universe are hydrogen and helium. The radial velocity of an object is found from its Doppler shift. Continuum Source Cloud Solar System Solar System Constituents The terrestrial planets are made primarily of rock and metal. The Jovian planets are made primarily of hydrogen and helium; also have large amounts of water, methane, and ammonia Moons (a.k.a. satellites) orbit the planets; some moons are large. The terrestrial planets are made primarily of rock and metal. Mercury, Venus, Earth, & Mars. The terrestrial planets are: low in mass (< Earth mass) high in density (> 3900 kg/ m3). Water = 1000 kg/m3 Air = 1 kg/m3 Rock = 3000 kg/m3 The Earth The study of seismic waves tells us about the Earth’s interior. The Earth is layered into crust, mantle, inner core, and outer core. The Earth is layered because it underwent differentiation when molten. The crust is broken into plates that move relative to each other. Seismic waves radiating through the Earth after an earthquake: Note: S waves do not travel through the outer core! The Moon The Moon’s surface has both smooth maria and cratered highlands. The surface was shaped by heavy bombardment, followed by lava floods. The Moon has a thick crust but a tiny ironrich core. The Moon may have been ejected when a protoplanet struck the Earth. Computer simulation of impact: Mantle of the colliding body was ejected to form the Moon. Iron core of the colliding body sank to the Earth’s center. Mercury Mercury has a 3-to-2 spin-orbit coupling (not synchronous rotation). Mercury has no permanent atmosphere because it is too hot. Like the Moon, Mercury has cratered highlands and smooth plains. Mercury has an extremely large iron-rich core. Radius of Mercury = 2400 km. Radius of iron core = 1800 km. Venus The surface of Venus is hidden from us by clouds of sulfuric acid. The atmosphere of Venus is hot because of a runaway greenhouse effect. The surface of Venus shows volcanic activity but no plate tectonics. The interior of Venus is similar to that of the Earth. The interior of Venus is similar to that of the Earth. Uncompressed density of Venus = uncompressed density of Earth = 4200 kg/m3. Venus probably has a metal core and rocky mantle, like the Earth. Mars Mars has a tenuous atmosphere, with little water vapor and few clouds. (Mars has large volcanoes and a huge rift valley, but no plate tectonics. Robotic “rovers” have given us a close-up look at Mars. Mars has two small irregular moons, Phobos and Deimos. Mars interior : Jupiter and Saturn Jupiter and Saturn consist mainly of hydrogen and helium. Jupiter and Saturn have belts and zones of clouds, plus circular storms. Jupiter and Saturn have magnetic fields created in metallic hydrogen. Differences between Jupiter and Saturn are due to Jupiter’s higher mass. All Jovian planets have rings. Jupiter and Saturn are differentiated. Moons of Jupiter and Saturn The Galilean Moons of Jupiter: Callisto: heavily cratered Ganymede: larger then Mercury Europa: covered with smooth ice Io: volcanically hyperactive The Giant Moon of Saturn: Titan: wrapped in an atmosphere 4 of the moons of Jupiter are large (> 3000 km across) and spherical (like our Moon). These are the four Galilean moons: Io, Europa, Ganymede, Callisto Titan: Saturn’s ATMOSPHERIC moon Nearly the same size as Ganymede: escape speed is the same. Twice as far from the Sun as Ganymede: temperature is lower. Titan, alone among moons, has a Uranus and Neptune Uranus and Neptune are nearly identical in their internal structure. The rotation axis of Uranus is tilted by about 90 degrees, causing extreme seasons. Neptune has surprisingly strong storms, driven by internal heat. Triton, the giant moon of Neptune, is a cold world with nitrogen geysers. 1) 2) 3) 4) Interiors of Uranus and Neptune Gaseous atmosphere: hydrogen, helium, methane Liquid outer layer: hydrogen, helium Liquid or slushy mantle: water, ammonia Solid core: rock, metal Triton: Neptune’s Frosty Moon Surface temperature = 38 Kelvin. Covered with “frost” at poles: frozen methane, frozen nitrogen. Pluto and its moon Charon are icy worlds that resemble Triton. Eris, the troublemaker (Greek goddess of strife). The Kuiper belt, beyond Neptune, contains small, icy, Plutolike objects. The icy Kuiper Belt Objects are leftover planetesimals. Comets are “dirty snowballs”: ice mixed with dust & carbon compounds. Most comets are in the Kuiper belt or the Oort cloud, far from the Sun. A comet or asteroid impact may have caused the extinction of dinosaurs Studies of the Outer Solar System continue. Pluto and Charon have many properties in common with Neptune’s moon Triton. • Cold surfaces (about 40 Kelvin) • Icy mantles and rocky cores (about 2000 kg/m3) • Pluto has a thin atmosphere (like Triton); Charon has none. Eris (“Xena”), the troublemaker. Discovered in 2005 by Mike Brown and collaborators. It has a moon. It is BIGGER than Pluto! Led to re-definition of what a Planet is Created new class of object called “Dwarf Planets Most comets are in the Kuiper belt or the Oort cloud, far from the Sun. Comets with short orbital periods come from the Kuiper belt, 30-50 A.U. from the Sun. We know the Kuiper belt is full of icy objects – we have seen them! Origin of the Solar System: Key Concepts How the Solar System formed: A cloud of gas & dust contracted to form a disk-shaped solar nebula. The solar nebula condensed to form small planetesimals. The planetesimals collided to form larger planets. When the Solar System formed: Radioactive age-dating indicates the Solar System is 4.56 billion years old. The contraction of the solar nebula made it spin faster and heat up. (Compressed gas gets hotter.) Temperature of solar nebula: > 2000 Kelvin near Sun; < 50 Kelvin far from Sun. How does this “nebular theory” explain the current state of the Solar System? Solar System is disk-shaped: It formed from a flat solar nebula. Planets revolve in the same direction: They formed from rotating nebula. Terrestrial planets are rock and metal: They formed in hot inner region. Jovian planets include ice, H, He: They formed in cool outer region. Radioactive age-dating Radioactive decay: Unstable atomic nuclei emit elementary particles, forming a lighter, stable nucleus. Example: Potassium-40 (19 protons + 21 neutrons = 40) 89% of the time, Potassium-40 decays to Calcium-40. 11% of the time, Potassium-40 decays to Argon-40. Age of oldest Earth rocks = 4 billion years Age of oldest Moon rocks = 4.5 billion years Age of oldest meteorites (meteoroids that survive the plunge to Earth) = 4.56 billion years This is the age of the Solar System The Structure and Evolution of Stars • Distance is important but hard to measure • Trigonometric Parallaxes – direct geometric method – only good for the nearest stars (~500pc) • Units of distance in Astronomy: – Parsec (Parallax second) – Light Year Parallax decreases with distance Closer stars have larger parallaxes: Distant stars have smaller parallaxes: Parallax Formula p = parallax angle in arcseconds d = distance in “Parsecs” • Luminosity of a star: – total energy output – independent of distance • Apparent Brightness of a star: – depends on the distance by the inverse-square law of brightness. – measured quantity from photometry. Flux-Luminosity Relationship: Relates Apparent Brightness (Flux) and Intrinsic Brightness (Luminosity) through the Inverse Square Law of Brightness: • Color of a star depends on its Temperature – Red Stars are Cooler – Blue Stars are Hotter • Spectral Classification – Classify stars by their spectral lines – Spectral differences mostly due to Temperature • Spectral Sequence (Temperature Sequence) • O B A F G K M L T The Spectral Sequence O B A F G K M LT Hotter 50,000K Bluer Cooler 2000K Redder Spectral Sequence is a Temperature Sequence • Types of Binary Stars – Visual – Spectroscopic – Eclipsing • Only way to measure stellar masses: – Only ~150 stars • Radii are measured for very few stars. Center of Mass • Two stars orbit about their center of mass: a1 a2 M2 a M1 • Measure semi-major axis, a, from projected orbit and the distance. • Relative positions give: M1 / M2 = a2 / a1 Measuring Masses Newton’s Form of Kepler’s Third Law: • Measure Period, P, by following the orbit. • Measure semi-major axis, a, and mass Ratio (M1/M2) from projected orbit. Summary of Stellar Properties • Large range of Stellar Luminosities: – 10-4 to 106 Lsun • Large range of Stellar Radii: – 10-2 to 103 Rsun • Modest range of Stellar Temperatures: – 3000 to >50,000 K • Wide Range of Stellar Masses: – 0.1 to ~50 Msun • The Hertzsprung-Russell (H-R) Diagram – Plot of Luminosity vs. Temperature for stars. • Features: – Main Sequence (most stars) – Giant & Supergiant Branches – White Dwarfs • Luminosity Classification Luminosity (Lsun) H-R Diagram Supergiants 106 104 102 Giants 1 10 -2 10 -4 40,000 White Dwarfs 20,000 10,000 Temperature (K) 5,000 2,500 Main Sequence • Most nearby stars (85%), including the Sun, lie along a diagonal band called the • Main Sequence • Ranges of properties: – L=10-2 to 106 Lsun – T=3000 to >50,0000 K – R=0.1 to 10 Rsun Giants & Supergiants • Two bands of stars brighter than Main Sequence stars of the same Temperature. – Means they must be larger in radius. • Giants R=10 -100 Rsun L=103 - 105 Lsun T<5000 K • Supergiants R>103 Rsun L=105 - 106 Lsun T=3000 - 50,000 K White Dwarfs • Stars on the lower left of the H-R Diagram fainter than Main Sequence stars of the same Temperature. – Means they must be smaller in radius. – L-R-T Relation predicts: R ~ 0.01 Rsun (~ size of Earth!) • Main Sequence: – Strong correlation between Luminosity and Temperature. – Holds for 85% of nearby stars including the sun • All other stars differ in size: – Giants & Supergiants: Very large radius, but same masses as M-S stars – White Dwarfs: Very compact stars: ~Rearth but with ~Msun! Mass-Luminosity Relationship • For Main-Sequence stars: In words: “More massive M-S stars are more luminous.” Not true of Giants, Supergiants, or White Dwarfs. • Observational Clues to Stellar Structure: – H-R Diagram – Mass-Luminosity Relationship – The Main Sequence is a sequence of Mass • Equation of State for Stellar Interiors – Perfect Gas Law – Pressure = density × temperature • Stars are held together by their self-gravity • Hydrostatic Equilibrium – Balance between Gravity & Pressure • Core-Envelope Structure of Stars – Hot, dense, compact core – cooler, low-density, extended envelope • Stars shine because they are hot. – need an energy source to stay hot. • Kelvin-Helmholtz Mechanism – Energy from slow Gravitational Contraction – Cannot work to power the present-day Sun • Nuclear Fusion Energy – Energy from Fusion of 4 1H into 1 4He – Dominant process in the present-day Sun • Energy generation in stars: – Nuclear Fusion in the core. – Controlled by a Hydrostatic “thermostat”. • Energy is transported to the surface by: – Radiation & Convection in normal stars – Conduction in white dwarf stars • With Hydrostatic Equilibrium, these determine the detailed structure of a star. • Main Sequence stars burn H into He in their cores. • The Main Sequence is a Mass Sequence. – Lower M-S: p-p chain, radiative cores & convective envelopes – Upper M-S: CNO cycle, convective cores & radiative envelopes • Larger Mass = Shorter Lifetime Putting Stars Together • Physics needed to describe how stars work: • • • • • Law of Gravity Equation of State (“gas law”) Principle of Hydrostatic Equilibrium Source of Energy (e.g., Nuclear Fusion) Movement of Energy through star Proton-Proton Chain: 3-step Fusion Chain CNO Cycle: Main Sequence Membership • For a star to be located on the Main Sequence in the H-R diagram: – must fuse Hydrogen into Helium in its core. – must be in a state of Hydrostatic Equilibrium. • Relax either of these and the star can no longer remain on the Main Sequence. The Main Sequence is a Mass Sequence. • The location of a star along the M-S is determined by its Mass. – Low-Mass Stars: Cooler & Fainter – High-Mass Stars: Hotter & Brighter • Follows from the Mass-Luminosity Relation: • Luminosity ~ Mass3.5 Main Sequence Lifetime • How long a star can burn H to He depends on: – Amount of H available = MASS – How Fast it burns H to He = LUMINOSITY • Lifetime = Mass ÷ Luminosity • Recall: Mass-Luminosity Relationship: • Luminosity ~ Mass3.5 Main Sequence Lifetime • Therefore: • Lifetime ~ 1 / M2.5 • The higher the mass, the shorter its life. • Examples: Sun: ~ 10 Billion Years 30 Msun O-star: ~ 2 Million years 0.1 Msun M-star: ~ 3 Trillion years Low Mass Stellar Evolution: • Stages: • Energy Source: • Main Sequence • Red Giant • Horizontal Branch • Asymptotic Giant • White Dwarf • H Burning Core • H Burning Shell • He Core + H Shell • He Shell + H Shell • None! HighMass Stellar Evolution: • Similar Stages as Low Mass Stars initially: • Main Sequence • Red Giant • Horizontal Branch • SuperGiant • Additional Stages as ever heavier elements are used as fuel • Ne, O, Si also can be used • Elements up to Iron (Fe) • Fe not useful though, because nucleus is too tightly bound Interior Structure of High Mass Star towards the end of its life: H Burning Shell He Burning Shell Core Radius: ~1 R C Burning Shell Ne Burning Shell Inert Fe-Ni Core O Burning Shell Si Burning Shell Envelope: ~ 5 AU End of the Road • At the end of the Silicon Burning Day: – Star builds up an inert Fe core – Series of nested nuclear burning shells • Finally, the Fe core exceeds 1.2-2 Msun: – Fe core begins to contract & heat up. – This collapse is final & catastrophic End of Life for a High Mass Star: • End of the Life of a Massive Star: – Burn H through Si in successive cores – Finally build a massive Iron core. • Iron core collapse & core bounce • Supernova Explosion: – Explosive envelope ejection – Main sources of heavy elements Stellar Remnants: • White Dwarf: – Remnant of a star <8 Msun – Held up by Electron Degeneracy Pressure – Maximum Mass ~1.4 Msun • Neutron Star: – Remnant of a star < 18 Msun – Held up by Neutron Degeneracy Pressure – Pulsar = rapidly spinning neutron star Using Clusters to Test Stellar Evolution • Cluster H-R Diagrams give us a snapshot of stellar evolution. • Observations of clusters with ages from a few Million to 15 Billion years confirms much of our picture of stellar evolution. • Remaining challenges are in small details, but the big picture seems secure. Using Clusters to Test Stellar Evolution: • H-R Diagrams of Star Clusters • Ages from the Main-Sequence Turn-off • Open Clusters – Young clusters of few 1000 stars – Blue Main-Sequence stars & few giants • Globular Clusters – Old clusters of a few 100,000 stars – No blue Main-Sequence stars & many giants The Structure and Evolution of Galaxies The Milky Way: • 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 – Star Counts: Herschels & Kapteyn – Globular Cluster Distribution: Shapley The Milky Way and Other 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 • Gives clues to the formation of the Galaxy. Other Galaxies: • Three basic types of Galaxies: – Spirals • Disk and spheroid component • Rotation of disk allows measurement of galaxy mass – Ellipticals – Irregulars • Differ in terms of – Relative Gas content – Star Formation History – Internal Motions • Galaxies tend to group into Clusters – Groups, clusters, and superclusters – Galaxies can collide and merge • Some galaxies have “active” nuclei – Powered by large Black holes in the center The Structure and Evolution of the Universe Special Relativity: • Postulates of Special Relativity: – The laws of physics are the same for all uniformly moving observers. – The speed of light is the same for all observers. • Consequences: – Different observers measure different times, lengths, and masses. – Only spacetime is observer independent. General Relativity: • General Relativity: – Modern Theory of Gravitation – Matter tells spacetime how to curve. – Curved spacetime tells matter how to move. • Tests of General Relativity: – Perihelion Precession of Mercury – Bending of Starlight near the Sun – The Binary Pulsar (Gravitational Waves) Expansion of the Universe: • Hubble’s Law: – Galaxies are receding from us. – Recession velocity gets larger with distance. • Hubble Constant: – Rate of expansion of the Universe. • Cosmological Redshift: – Redshift distances – Redshift maps of the Universe. Cosmology: • Cosmological Principle: – The Universe is Homogeneous and Isotropic on Large Scales. – No special places or directions. • General Relativity predicts an expanding universe. • Cosmological Constant Big Bang: • Big Bang Model of the Universe – Starts in a hot, dense state – Universe expands and cools • Expansion and Redshift • Critical Density – Geometry of the Universe • Hubble Time = Maximum age of the Universe Evidence for the Big Bang: • Fundamental Tests of the Big Bang • Primordial Nucleosynthesis – Primordial Deuterium & Helium – Primordial light elements (Li, B, Be) • Cosmic Background Radiation – Relic blackbody radiation from Big Bang – Temperature: T = 2.726 K First 3 Minutes in the History of the Universe: • Physics of the Early Universe – Informed by experimental & theoretical physics • The Cosmic Timeline: – Observations go back to t~3 minutes – Reasonably firm physics back to t~10-6 sec – Speculative back before t~10-12 sec – Present theories stop at t~10-43 sec Critical Density • All galaxies attract each other via gravity. – Gravitational attraction slows the expansion. • How it behaves depends on the density: – High Density: Expansion slows, stops, & reverses. – Low Density: Keeps expanding forever. • Dividing Line = “Critical Density” Density Parameter: Ω • Ω>1: High Density “Closed” Universe • Ω=1: Critical Density “Open” Universe • Ω<1: Low Density “Open” Universe End of Universe: • The Fate of the Universe depends on the density of matter. • Closed Universe: – Enough matter to stop the expansion – Collapses in a “Big Crunch” • Open Universe: – Expands forever – Ends in a cold, disordered state – Dark Energy seems to make this outcome more likely Physics • Gravity – Newton & Relativity – Dynamics (how things move) • Radiation – Photons – Electromagnetic spectrum • Thermodynamics – Pressure, density, temperature – Degenerate electron/neutron gas • Thermonuclear fusion Connect to stuff here at home • Gravity – Things fall! – Things move! • Radiation – How we see – How we manipulate “light” • X-rays • Radio • microwaves Connect to stuff here at home • Thermodynamics – How refrigerators work – The “pressure” you feel on your ears at the bottom of a pool • Thermonuclear fusion – Boom! Three Questions: 1) What is it? – Describe it: how bright, far, energetic, etc. 2) How does it work? – Underlying Physics (testable theories) 3) How does it evolve? – How does it form, develop & end its existence? Scientific process • Answer questions – Look for inconsistencies – Alter ideas – Look for things not understood • New things to investigate – Dark matter – Dark energy – New forms of matter and energy