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Final Exam Review Please press “1” to test your transmitter. The outer planets (Mars, Jupiter, …) are usually moving which way in the sky, against the background of the stars? 1. 2. 3. 4. 5. East to West West to East North to South South to North They remain stationary near the celestial poles. The Motion of the Planets • All outer planets (Mars, Jupiter, Saturn, Uranus, Neptune and Pluto) generally appear to move eastward along the Ecliptic. • The inner planets Mercury and Venus can never be seen at large angular distance from the sun and appear only as morning or evening stars. The moon’s siderial orbital period is … 1. the time it takes to orbit once around Earth, back to the same position with respect to the stars. 2. the time it takes to orbit once around Earth, back to the same lunar phase. 3. the time it takes to orbit once around the sun. 4. the time it takes to orbit once around a glass of cidre. 5. Both a) and b) are correct; those two orbital periods are the same. The Phases of the Moon 27.32 days • The Moon orbits Earth in a sidereal period of 27.32 days. Moon Earth Fixed direction in space The Phases of the Moon Fixed direction in space 29.53 days Earth Moon Earth orbits around Sun => Direction toward Sun changes! • The moon’s synodic period (to reach the same position relative to the sun) is 29.53 days (~ 1 month). What is the orientation of the moon’s orbit with respect to the Earth’s orbit around the sun? 1. They are exactly in the same plane. 2. The moon’s orbit is inclined by 5o against the Earth’s orbit. 3. The moon’s orbit is inclined by 23.5o against the Earth’s orbit. 4. The moon’s orbit is exactly perpendicular to the Earth’s orbit. 5. The moon’s orbit is identical to the Earth’s orbit. Conditions for Eclipses (I) The Moon’s orbit is inclined against the ecliptic by ~ 50. A solar eclipse can only occur if the Moon passes a node near New Moon. A lunar eclipse can only occur if the Moon passes a node near Full Moon. Conditions for Eclipses (II) Eclipses occur in a cyclic pattern. → Saros cycle: 18 years, 11 days, 8 hours What were the epicycles in the Ptolomaic model of the “Universe” supposed to explain? 1. The fact that the planets orbit the sun. 2. The fact that the planets always seem to move westward in the sky. 3. The fact that the planets always seem to move eastward in the sky. 4. The fact that the planets move westward for some time, while they usually move eastward. 5. The fact that the planets move eastward for some time, while they usually move westward. Epicycles Introduced to explain retrograde (westward) motion of planets The ptolemaic system was considered the “standard model” of the Universe until the Copernican Revolution. Kepler’s third law of planetary motion states: 1. 2. 3. 4. 5. The planets revolve around the sun in perfect circles. On its elliptical motion around the sun, a planet moves faster when it is far away from the sun, and slower when it is closer to the sun. The square of the orbital period of a planet’s motion around the sun is proportional to the third power of its average distance to the sun. The orbital period of a planet’s motion around the sun is proportional to its average distance to the sun. The mass of a planet is proportional to its average distance to the sun. Kepler’s Third Law 3. A planet’s orbital period (P) squared is proportional to its average distance from the sun (a) cubed: Py2 = aAU3 (Py = period in years; aAU = distance in AU) Orbital period P known → Calculate average distance to the sun, a: aAU = Py2/3 Average distance to the sun, a, known → Calculate orbital period P. Py = aAU3/2 You see the headlights of a relativistic train which approaches you with a speed of 150,000 km/s (i.e., half the speed of light, c = 300,000 km/s). You have a detector that can measure the speed of the light signal. What speed will it measure? 1. 2. 3. 4. 5. 450,000 km/s 45,000,000,000 km/s 150,000 km/s 300,000 km/s Depends on the wind speed between the train and the detector. Two postulates leading to Special Relativity (I) 1. Observers can never detect their uniform motion, except relative to other objects. This is equivalent to: The laws of physics are the same for all observers, no matter what their motion, as long as they are not accelerated. Two postulates leading to Special Relativity (II) 2. The velocity of light, c, is constant and will be the same for all observers, independent of their motion relative to the light source. Mercury’s orbit … 1. 2. 3. 4. 5. is a perfect circle whose orbital plane remains stable even over many centuries. is an ellipse whose orientation remains stable even over many centuries. is a perfect circle, and its orbital plane gradually becomes more and more inclined against the plane of the orbits of all other planets. is an ellipse whose orbital plane gradually becomes more and more inclined against the plane of the orbits of all other planets. is an ellipse whose major axis is slowly precessing in the plane of the orbit. Perihelion Precession Which of these forms of radiation can be observed directly with ground-based telescopes? 1. 2. 3. 4. 5. Radio waves Infrared light Ultraviolet light X-rays Gamma-rays The Electromagnetic Spectrum Wavelength Frequency Need satellites to observe High flying air planes or satellites The Chandra Space Telescope observes … 1. 2. 3. 4. 5. Radio waves Infrared light Ultraviolet light X-rays Gamma-rays The Chandra X-Ray Observatory • Launched in 1999 • Extremely high angular resolution (< 1 arc second) • Very high sensitivity Most of the mass of an atom is … 1. 2. 3. 4. 5. Contained in the protons in the nucleus. Contained in the neutrons in the nucleus. Contained in both protons and neutrons in the nucleus. Contained in electrons. Equally distributed between protons, neutrons and electrons. Atomic Structure • An atom consists of an atomic nucleus (protons and neutrons) and a cloud of electrons surrounding it. • Almost all of the mass is contained in the nucleus, while almost all of the space is occupied by the electron cloud. Which of the following lists the layers of the sun in the correct order, from inner to outer layers? 1. 2. 3. 4. 5. Photosphere, chromosphere, core, radiation zone, corona Core, radiation zone, chromosphere, corona, photosphere Core, chromosphere, radiation zone, photosphere, corona Core, corona, radiation zone, chromosphere, photosphere Core, radiation zone, photosphere, chromosphere, corona The Sun’s Interior Structure Flow of energy Photosphere Energy transport via convection (explained soon) Energy transport via radiation Energy generation via nuclear fusion Temp, density and pressure decr. outward Structure of the Sun Apparent surface of the sun Heat Flow Only visible during solar eclipses Solar interior Temp. incr. inward How is energy produced in the sun’s core transported outward in the region immediately outside the core? 1. 2. 3. 4. 5. By radiative energy transport. By convective energy transport. By heat conduction. By microwave heating. By relativistic beaming. The Sun’s Interior Structure Flow of energy Photosphere Energy transport via convection (explained soon) Energy transport via radiation Energy generation via nuclear fusion Temp, density and pressure decr. outward Which of the following provides evidence that convective energy transport plays a role in the sun? 1. 2. 3. 4. 5. Spicules Granulation Prominences Sunspots The Aurora Borealis Granulation … is the visible consequence of convection How does the region around a sunspot appear when viewed in ultraviolet light? 1. 2. 3. 4. 5. Also as a dark spot, just like in visible light and exactly coinciding with the visible-light sunspot. As a small bright spot exactly coinciding with the visible-light sunspot. As a rather large bright region around the sunspot. As a rather large dark region around the sunspot. Sunspots do not leave any trace in the sun’s ultraviolet image. Sun Spots Active Regions Visible Ultraviolet Cooler regions of the photosphere (T ≈ 4240 K). Sirius A has an absolute magnitude of MA = 1.4, while Sirius B has MB = 11.6. This means that … 1. 2. 3. 4. 5. Sirius A is about 10 times more massive than Sirius B. Sirius B is about 10 times more massive than Sirius A. Sirius A is about 100 times brighter than Sirius B. Sirius B is about 100 times brighter than Sirius A. Sirius A is about 10,000 times brighter than Sirius B. The Magnitude Scale • Brightest stars: ~1st magnitude (mv = 1) • Faintest stars (unaided eye): 6th magnitude (mv = 6) More quantitative: • 1st mag. stars apear 100 times brighter than 6th mag. stars • 1 mag. difference gives a factor of 2.512 in apparent brightness (larger magnitude => fainter object!) The magnitude scale system can be extended towards negative numbers (very bright) and numbers > 6 (faint objects): Sirius (brightest star in the sky): mv = -1.42 Full moon: mv = -12.5 Sun: mv = -26.5 Magnitude difference DM ~ 10 DM = 5 Flux ratio 100 DM = 10 Flux ratio 1002 = 10,000 The stars Deneb and Vega have about the same spectral shape (and hence, surface temperature), but Deneb is 900 times brighter (more luminous) than Vega. What does this tell you? 1. 2. 3. 4. 5. Deneb’s diameter must be 900 times larger than Vega’s Deneb’s diameter must be 30 times larger than Vega’s. Deneb must be 900 times more massive than Vega. Deneb must be 30 times more massive than Vega. Deneb must have a 900 times stronger magnetic field than Vega. The Size (Radius) of a Star We already know: flux increases with surface temperature (~ T4); hotter stars are brighter. But brightness also increases with size: A B Star B will be brighter than star A. Specifically: Absolute brightness is proportional to radius (R) squared, L ~ R2. Example: Both Spica B and Sirius B are B-type stars, but Sirius B is a white dwarf star, with a radius ~ 560 times smaller than Spica B. Thus, since L ~ R2, Sirius B is intrinsically 5602 ≈ 320,000 times fainter than Spica B. The Hertzsprung-Russell (HR) Diagram organizes stars in a plot of … 1. 2. 3. 4. 5. distance vs. luminosity. mass vs. luminosity. mass vs. surface temperature. luminosity vs. spectral type. luminosity vs. distance. Organizing the Family of Stars: The Hertzsprung-Russell Diagram We know: Stars have different temperatures, different luminosities, and different sizes. To bring some order into that zoo of different types of stars: organize them in a diagram of Luminosity Luminosity versus Temperature (or spectral type) Hertzsprung-Russell Diagram Spectral type: O Temperature B A F G K M What is the minimum mass that a protostar has to have in order to ignite Hydrogen fusion and become a real star? 1. 2. 3. 4. 5. 0.1 % of a solar mass. 1 % of a solar mass. 8 % of a solar mass. 25 % of a solar mass. 1 solar mass. Minimum Mass of Main-Sequence Stars: Mmin = 0.08 Msun Gliese 229B At masses below 0.08 Msun, stellar progenitors do not get hot enouth to ignite thermonuclear fusion. → Brown Dwarfs Which is the latest fusion process that will occur in the sun before it “dies”? 1. 2. 3. 4. 5. Proton-proton chain CNO cycle Triple-alpha process Oxygen -> Neon burning Silicon -> Iron burning Red Giant Evolution (5 solar-mass star) C, O Inactive He What will happen to the sun when it has used up its hydrogen supply in the core? 1. 2. 3. 4. 5. Hydrogen burning will continue in a shell around a Helium core, and the sun will expand to become a red giant. The Helium core will collapse onto a white dwarf, and Hydrogen burning will continue in a shell around the white dwarf. The sun will explode in a supernova explosion. Hydrogen burning will continue in a shell around a Helium core, and the sun will become a hot, O or B-type star. Hydrogen burning will cease, and the core will begin to burn Helium into Carbon instead. Evolution off the Main Sequence: Expansion into a Red Giant H in the core completely converted into He: “H burning” (i.e. fusion of H into He) continues in a shell around the core. Expansion and cooling of the outer layers of the star → Red Giant In Cepheid variables, what is correlated with what? 1. 2. 3. 4. 5. Luminosity with distance. Luminosity with size. Mass with pulsation period. Mass with rotation period. Luminosity with pulsation period. Cepheid Variables: The Period-Luminosity Relation The variability period of a Cepheid variable is correlated with its luminosity. The more luminous it is, the more slowly it pulsates. => Measuring a Cepheid’s period, we can determine its absolute magnitude! A “planetary nebula” is … 1. 2. 3. 4. 5. The remnant of the protostellar disk around a newborn star out of which planets may form. The remnant of the explosion of a sun-like star at the end of its life. The remnant of the explosion of a very massive star (more than 8 solar masses) at the end of its life. The combined image of many planets around a newborn star, which can not be inidividually resolved in telescopes with moderate resolution. A giant molecula cloud, out of which new stars and planets might form. The Formation of Planetary Nebulae Two-stage process: Slow wind from a red giant blows away cool, outer layers of the star Fast wind from hot, inner layers of the star overtakes the slow wind and excites it => Planetary Nebula Formation of a Planetary Nebula What is a “nova”? 1. 2. 3. 4. 5. The birth of a new star. The birth of a new planet. The explosive disruption of a very massive star at the end of its life. The explosive onset of Hydrogen fusion on the surface of a white dwarf in a binary system. The explosive onset of Carbon/Oxygen fusion in a white dwarf in a binary system. Nova Explosions Hydrogen accreted through the accretion disk accumulates on the surface of the WD Very hot, dense layer of nonfusing hydrogen on the WD surface Explosive onset of H fusion Nova Cygni 1975 Nova explosion In many cases: Cycle of repeating explosions every few years – decades. Which of the following will NOT result in a supernova explosion? 1. 2. 3. 4. 5. The core-collapse of a 20-solar mass star. The accretion-induced collapse of a white dwarf. The onset of the triple-alpha process in the Helium core of a Red Giant. The merging of two white dwarfs in a binary system. None of the above. – I. e., all of the above will result in supernova explosions. A different kind of Supernova: Type Ia Supernovae White Dwarfs can not be more massive than ~ 1.4 solar masses. White Dwarf in a binary system accreting matter from a companion star. Untill it becomes too massive to be a White Dwarf Collapse! Supernova Type Ia Supernovae Alternative Scenario: Merger of two white dwarfs What will become of the core of a 15-solar-mass star at the end of its life? 1. 2. 3. 4. 5. It will collapse to form a white dwarf. It will collapse to form a neutron star. It will collapse into a black hole. It will collapse to form a brown dwarf. It will collapse to form a planet. The Death of a Massive Star Properties of Neutron Stars Typical size: R ~ 10 km Mass: M ~ 1.4 – 3 Msun Density: r ~ 1014 g/cm3 → Piece of neutron star matter of the size of a sugar cube has a mass of ~ 100 million tons!!!