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Lecture14_note

Course: ASTR 5, Spring 2011
School: Mt. SAC
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Interiors 10/18/10 Saturn The of the Gas Giants Mass: ~ 1/3 of mass of Jupiter Radius: ~ 16 % smaller than Jupiter Av. density: 0.69 g/cm3 Would float in water! Please insert figure 43.3 Rotates about as fast as Jupiter, but is twice as oblate No large core of heavy elements Mostly hydrogen and helium; liquid hydrogen core Saturn radiates ~ 1.8 times the energy received from the sun Probably heated by...

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Interiors 10/18/10 Saturn The of the Gas Giants Mass: ~ 1/3 of mass of Jupiter Radius: ~ 16 % smaller than Jupiter Av. density: 0.69 g/cm3 Would float in water! Please insert figure 43.3 Rotates about as fast as Jupiter, but is twice as oblate No large core of heavy elements Mostly hydrogen and helium; liquid hydrogen core Saturn radiates ~ 1.8 times the energy received from the sun Probably heated by liquid helium droplets falling towards center Storms on Saturn Saturn, though it appears calmer, has storms as well Higher wind speeds than Jupiter Storms are deeper in its atmosphere Uranus and Neptune Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 10/18/10 The Discovery of Uranus In 1781 a new planet was discovered by W. Herschel Originally thought to be a comet! Herschel named it Georgium Sidus (Georges Star) after King George III Name changed to Uranus to stay consistent with the mythological names of the other planets A New Method of Discovery It was noted that Uranus was not following its calculated orbit Another planet must be influencing its orbit Two scientists calculated where the new planet should be Astronomers looked at this location, and found Neptune! Galileo saw Neptune while looking at Jupiters moons, but didnt realize what it was The Atmospheres of Uranus and Neptune Interior of Uranus The atmospheres of both Uranus and Neptune are rich in hydrogen and helium Both have larger amounts of methane, giving them their blue color Methane crystals scatter blue light, and methane gas absorbs red light Please insert figure 44.3 Both planets are very cold Uranus: 80K Neptune: 75K Densities: Uranus: 1.3 kg/liter Neptune: 1.6 kg/liter Their interiors are probably ordinary water mixed with methane and ammonia, surrounding a core of rock and iron-rich material 2 10/18/10 Storms Uranuss Axial Tilt High winds lead to storms on Neptune Neptune has the Great Dark Spot, which disappeared recently Uranus is tipped almost 90 degrees to the ecliptic plane Possible that a collision early in its history tipped the axis, and splashed out material for its moons Odd Magnetic Fields Both Uranus and Neptune have magnetic fields Stronger than Earths Uranus: 47x Neptune: 25x Probably generated by currents in the liquid water in their interiors Tipped in odd directions! Not centered on the center of the planet, as with Earth, Jupiter and Saturn Titan This inclination means that for half of Uranus orbit, one hemisphere is in uninterrupted daylight, and the other hemisphere is in darkness! About the size of Jupiters moon Ganymede Rocky core, but also large amount of ice Thick atmosphere resembling early Earths -> Potential life supporting place 3 10/18/10 Titans Atmosphere Titans Surface Explored in detail by the Cassini spacecraft and the Huygens probe, which landed on Titans surface in 2005 Huygens discovered outflow channels, possibly of liquid methane Atmosphere consists mostly of nitrogen, methane and ethane and grapefruit sized rocks on the surface. Surface pressure: 50% greater than air pressure on Earth Surface temperature: 94 K (-290 oF) methane and ethane can condense and lead to rain of methane ethane Methane and is gradually converted to ethane in the Atmosphere Methane must be constantly replenished, probably through breakdown of ammonia (NH3). Neptunes Moon Triton Uranuss Moon Miranda Triton is larger than Pluto and almost as big as Europa Orbits backwards relative to Neptunes rotation Miranda appears to have been shattered by an impact Likely a captured icy planetesimal The leading hypothesis for Mirandas appearance is that the complex pattern arose as the result of strong tectonic activity that broke the surface into plates Has an atmosphere that freezes out on the night side of the planet Odd surface features Long cracks or faults riddle its surface Huge 20 km cliffs Rolling hills adjacent to wrinkled terrain 4 10/18/10 Ring Systems Ringlets A close examination of Saturns rings shows that they are composed of tiny ringlets Galileo first saw the rings of Saturn, but didnt know what they were Huygens observed that the rings were detached from Saturn Maxwell realized that the rings were not solid, and were made up of small particles all following Keplers Laws! Saturn has three main rings Outermost ring is the A ring Middle ring is the B ring Inner ring is the C, or crepe ring, and is very dark The separation between the A and B ring is called the Cassini division All of the Gas Giants Have Ring Systems These might be caused by gravitational influences of very small moons, creating waves in the main rings (spiral density waves) Larger gaps (Cassini and Enke divisions, for example) are caused by orbital resonances with some of Saturns moons Shepherd Satellites The thin rings of the gas giants are maintained by shepherd satellites The gravitational pull of these small moons keeps ring particles in line! 5 10/18/10 The Origin of Planetary Rings If a body held together only by gravity gets too close to a planet, tidal forces pull it apart Planetary Rings The Roche limit is where the tidal forces of the planet are too strong for a moon to survive; this is where rings are formed. This distance is called the Roche Limit Solid bodies (chunks of rock or ice, or even the space station) are safe, as they are held together by forces other than gravity The fragments of the brokenup satellite go into orbit around the planet, forming a ring Roche Limit stage 1 Consider an orbiting mass of fluid held together by gravity, here viewed from above the orbital plane. Far from the Roche limit the mass is practically spherical. Credit: Wikipedia Roche Limit stage 2 Closer to the Roche limit the body is deformed by tidal forces. Credit: Wikipedia 6 10/18/10 Roche Limit stage 3 Within the Roche limit the mass's own gravity can no longer withstand the tidal forces, and the body disintegrates. Roche Limit stage 4 Particles closer to the planet move more quickly than particles farther away, as represented by the red arrows. Credit: Wikipedia Roche Limit stage 5 Credit: Wikipedia How does tidal force work? Differential Forces The varying orbital speed of the material eventually causes it to form a ring. Credit: Wikipedia 7 10/18/10 Planetary Rings All observed ring systems are within this limit. Conservation of Angular Momentum |L|= msv d v d 8
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Mt. SAC - ASTR - 5
10/24/10 Pluto and its Moons Pluto is a mix of water ice,rock, methane and frozennitrogen When Pluto is within Neptunesorbit, it has an atmosphere!Ice Worlds, Pluto andBeyond As the planet moves further out into the solar system, theatmosphere
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10/25/10 The Heating of Meteors When a meteoroid (small chunk of rock inspace) travels through the Earthsatmosphere, it begins ionize the atmospherearound it. The vaporized material andionized gas begins to glowImpacts on Earth It is now called a
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11/1/10 The Solar AtmosphereSunsAtmosphere &Sunspots Regions of the Sun abovethe photosphere are calledthe Suns atmosphere Just above the photospherelies the chromosphere Above thechromosphere isthe coronaThe ChromosphereThe Chromosphere (2
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A123456789101112131415161718192021222324252627BDiscount ratePresent valueCDE10%$379.08 <- =NPV(B2,B7:B11)12345012345YearIRRNPVYearGDiscount rateNet present valueCashflow1001001001001007.931% <-
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A12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576BCDEFShare value and anticipa
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A12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667BCDEFGCHAPTER 3 TEMPLATE-JUST TO SAVE YOU SOME TYPINGS
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A12345678910111213141516171819202122232425262728293031323334353637383940BCDEFSETTING UP THE FINANCIAL STATEMENT MODELSales growthCurrent assets/SalesCurrent liabilities/SalesNet fixed assets/SalesCosts of
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Page 90A1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859BCFARMERS BAGELS, INC.Financial Results for First Two Years of Existence1
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Page 102Misleading analysis: This is the analysis of the first section of the chapterAsset costInterest rateLease rental paymentAnnual depreciationTax rateNPV(leasing)NPV(buying)540,00012%130,00090,00038%these numbers are copiedfrom the nex
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ABCDEFGHIJKLBASIC LEVERAGED LEASE EXAMPLECost of assetLease termResidual valueEquityDebtInterestAnnual debt paymentAnnual rent receivedTax rateYear1,000,00015300,000200,000800,000 15-year term loan, equal payments of interest an
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UN-5BAMonth0123456789101112BCStock pricesStock AStock B25.0045.0024.1244.8523.3746.8824.7545.2526.6250.8726.5053.2528.0053.2528.8862.7529.7565.5031.3866.8736.2578.5037.1378.0036.8868.23DEFGHIJCALCULATI
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UN-6AA1234567891011121314151617181920BCDEFGHRETURN DATA FOR VARIANCE-COVARIANCE CALCULATIONS1974197519761977197819791980198119821983AMR-0.35050.70830.7329-0.20340.1663-0.26590.0124-0.02641.06420.1942BS-0
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Feasible Port folio0.11Por t f oli o me a n r e t ur n0.10Efficient andenvelope0.090.08Feasible, not efficient0.070.060.050 .00Envelope5.0010.0015.00Port folio st andard deviat ion20.0025.00Finding Envelope Portfolios1200%1000%Por
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UN-11CA12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152BCDEFGHIJKTWO-DATE BINOMIAL OPTION PRICINGUpDown10%-3%Initial stock priceInterest r
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UN-13BA123456789101112131415161718192021222324252627282930313233BCDEFGHIJKBlack-Scholes Option-Pricing FormulaSXrTSigma25 Current stock price25 Exercise price6.00% Risk-free rate of interest0.5 Time to
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A123456789101112131415161718192021222324252627282930313233343536373839404142BCDEFGHIJTHE OPTION TO EXPANDYearCF of single machine0-1000Discount rate for machine cash flowsRiskless discount rateNPV
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UN-11IA12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485
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Page 432A1234567891011121314150.56430.92190.47250.72770.80050.01280.97480.41280.9670B0.85070.52730.88680.10370.18460.02580.05440.59690.1379CDE0.50780.01300.83450.35170.48280.32060.62440.19990.02120.8786 <- R
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UN-15I2.6T erm Structures, 19482.42.2Pur e discount r a t e %21.81.61.41.210.80mo 1mo 2mo 3mo 4mo 5mo 6mo 9mo1yrMat urit y2 yr3yr4yr5yr10yr 15yr 20yrUN-15J18T erm Structures, 19811716Pur e discount r a t e, %1514131211109
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