1• HW 5 due 11/16 before midnight• Take-home part of Midterm 2: DuenowAnnouncements:Astronomy 101Nov. 13, 2008Above: animation of a type of “variable star” that varies in brightness in a very regular and repeatable way.Sound waves are alternatingregions of high and low density,or equivalently as alternatingregions of high and low pressure.What happens when two sound wavescollide and mix with each other?• Waves add together in a simple way.• Examples:ADD:Wave 1 +Wave 2RESULTING WAVE:Case 1 Case 2At any givenpoint, theamplitudes justadd together(but we mustkeep track ofwhether an amplitude ispositive or negative)What happens when two soundwaves collide and mix with eachother?• If two waves are perfectly aligned, theywill add together to make another wavewith the same wavelength but a muchlarger amplitude• If two waves are exactly opposite, they willcancel each other out leaving nothing!2Close but no cigar: Whathappens if the waves are almostthe same but not exactly?Beat wavelengthPRS question:Hot areas onEnceladusAstronomers have determinedthat these Enceladus surface regions(from which the water is emerging)are hotter than the surroundingsurface. They learned this byusing spectroscopy to study whattype of light?1. Absorption lines2. Emission lines3. Continuum emissionThermal Radiation• Blackbody Radiation (a.k.a. Thermal Radiation)– Thermal radiation leads to a continuum spectrum– Every dense object with a temperature greater thanabsolute zero emits a continuum spectrum calledblackbody radiation. The properties of the thermalradiation only depend on the temperature of theobject, hence the name.– Hotter objects emit more total radiation per unitsurface area in a given amount of time. The amount ofthermal radiation emitted is given by the Stefan-Boltzmann law.– Hotter objects emit photons with a higher averageenergy. The wavelength at which the thermal radiationspectrum is given by the Wien law.The graph below shows the blackbody spectra of three different stars.All three stars have the same size. Which of the stars is at thehighest temperature?1) Star A2) Star B3) Star CABCWavelengthPRS question: Thermal Radiation• There are two differentways to approachthis problem.Brightness3The graph below shows the blackbody spectra of three different stars.All three stars have the same size. Which of the stars is at thehighest temperature?1) Star A2) Star B3) Star CABCWavelengthPRS question: Thermal RadiationSolution option 11. Hotter objects emit more total radiation per unitsurface area. Stephan-Boltzmann Law E = σT4BrightnessThe graph below shows the blackbody spectra of three different stars.All three stars have the same size. Which of the stars is at thehighest temperature?1) Star A2) Star B3) Star CABCBrightnessWavelength• Hotter objects emit bluer photons (with a higheraverage energy.) Wien Law λmax = 2.9 x 106 / T(K) [λmax in nm]T(K) = 2.9 x 106 / λmax [nm]λmaxλmaxPRS question: Thermal RadiationSolution option 21. Hotter objects emit more total radiation perunit surface area per time. Stephan-Boltzmann Law E = σT4Power = σT4Rules for Emission by Denseand Opaque ObjectsEvidence of thermalradiation?• We know that thermalradiation exists in thevisible part of theelectromagnetic spectrumbecause something like aprism disperses the lightfrom the Sun or an old-fashioned lightbulb into acontinuum spectrum.• If something is dense butrelatively cold (say,colder than a star like ourSun), then it emitsthermal radiation, but thecontinuum comes out inthe infrared and our eyescan’t see it. How can weprovide evidence of thisthermal radiation?4Saturn observed invisible lightMulticolor image of Saturnshowing both visible light and infrared lightThermal (aka Blackbody)RadiationHow did Edwin Hubble discoverthe expansion of the Universe?• Velocity = distance x constant• Velocity = distance x H0Hubble used sp e ctra todetermine the galaxy velocitiesNearby star:Using the best telescopes of the day, Hubble obtained spectrasomething like these:Nearby galaxy:Distant galaxy:Hubble noticed that the spectra of distant objects were shiftedtoward the red end of the visible wavelength range. Whatcaused the shift??Answer: The Doppler Effect5Doppler EffectThe first crest travels out incircle from the original positionof the planeAt a later time, a secondcrest is emitted from theplanes new position,but the old crest keepsmoving out in a circlefrom the planes originalpositionThe same thing happens again ata later timeLongerwavelength(more red)Shorter wavelength (more blue)Doppler EffectLongerwavelength(more red)Shorter wavelength (more blue)Which of these Dopplereffects was Hubble observingwhen he looked at galaxies?Galaxy spectra were shifted to the red, whichindicates that the galaxiesare moving away from us.By measuring the shift ofa spectral line, the velocityof the object can be measuredwith great precision.Doppler Effect Vocabulary• The “native” frequency at which an object isemitting is called the rest frequency.• You will see/hear frequencies higher than therest frequency from objects moving towards you.This is called a BLUESHIFT.• You will see/hear frequencies lower than the restfrequency from objects moving away from you.REDSHIFT.• The faster the object is mover, the greater thefrequency shift due to the Doppler effectPRS: The Doppler EffectTwo identical stars are moving towards the Earth. Star A’s emissionlines (that are normally at visible wavelengths) are observed to beat ultraviolet wavelengths. Star B’s emission lines are observed tobe at X-ray wavelengths. From these observations you concludethat:1) both stars are moving away from the Earth2) Star A is moving towards the Earth faster than Star B3) Star B is moving towards the Earth faster than Star A4) Star B is actually moving away from the Earth6Only the motion along theline-of-sight is important forthe Doppler effectMeasuring Rotational VelocityHow did Edwin Hubble discoverthe expansion of the Universe?• Velocity = distance x constant• Velocity = distance x H0Hubble measured the galaxy velocitiesby using the Doppler effect.How did he measure the galaxy distances?Power from the Sun• Power = energy/time, often measured in Watts• The Sun emits thermal radiation, so the Stefan-Boltzmann law applies:• Energy per area per time = σ T4• Total energy radiated by the Sunper second is the luminosity ofthe Sun.• Luminosity is the