AST 301Introduction to AstronomyJohn LacyRLM [email protected] LiRLM [email protected] JeonRLM [email protected] site: www.as.utexas.eduGo to Department of Astronomy courses,AST 301 (Lacy), course websiteTopics for this weekHow can we use the concept of thermal equilibrium tocalculate the temperature of the surface of a rock orbitingthe Sun?How does the result depend on the distance of the rock fromthe Sun?How does the Earth’s atmosphere affect the surfacetemperature of the Earth?Why do Venus and Mars have such different surfacetemperatures?How are we changing the Earth’s atmosphere, and how dowe think this will affect the surface temperature?Two common questionsI don’t curve tests separately or convert scores onindividual tests into letters. But I will curve the finalgrades. With my typical curve, you can figure that if youaverage 53/60 on the tests (and do about the same ofhomeworks and quizzes) you will have an A, 45/60 = B,37/60 = C, 30/60 = D.For extra credit, if you go to one of the observing nights onRLM or Painter Hall, and write a one-page description ofwhat you saw, it will replace a missed or low score on aquiz or in-class project.EquilibriumA balance between opposing influencesConsider a can with a hole in its bottom, held under afaucet.Is it possible for the level of water in the can to come to anequilibrium?What are the opposing influences?What would happen if you turned up the flow of water intothe can?The level of the water in the can would rise.If the can was very tall, would the water level just keep onrising or would it come to a new equilibrium level?A new equilibriumIf one influence changes, we could have a new equilibriumif that made the other influence change.If the flow of water into the can increased, the water levelwould rise.That would increase the pressure in the can causing theflow out of the can to increase too.If the flow out rose to equal the flow in, the water levelwould stop rising.We would have a new equilibrium.This is an example of a stable equilibrium.A rock in spaceConsider a black rock orbiting the Sun.Energy is flowing into the rock because it is absorbingsunlight.If there were no way for energy to flow out of the rock,what would happen?A. it would get hotter and hotter until it vaporizedB. it would get hot but it would never vaporizeC. it would be kept cool because space is coldA rock in spaceConsider a black rock orbiting the Sun.Energy is flowing into the rock because it is absorbingsunlight.If there were no way for energy to flow out of the rock,what would happen?A. it would get hotter and hotter until it vaporizedB. it would get hot but it would never vaporizeC. it would be kept cool because space is coldHow does energy flow out of a rock in space?A. by radiation from the rockB. by conduction into the surrounding spaceC. by reflecting sunlightFlow of energy = PowerThe temperature of the rock will come to an equilibrium if theflow of energy out of the rock (by radiation) balances theflow into the rock (by absorbing sunlight).The unit used to measure energy is the Joule.The unit used to measure the flow of energy, or power, isthe Watt.One Watt is one Joule per second.A 100 Watt light bulb has 100 Joules of electrical energyflowing into it each second.Less than 10 Joules of visible light come out of the light bulbeach second.The rest comes out as infrared radiation or is conducted intothe air around the light bulb.Calculating the rock’s temperatureTo calculate the temperature of the rock orbiting the Sun,we need to write down the formulas for the energy goinginto the rock and the energy going out each second.Power going in is the flux of sunlight multiplied by the areaof the side of the rock facing the Sun.Pin = Fsunlight x AfacePower going out depends on the temperature of the rockand its total surface area.Pout = σ T4 x AsurfaceIn equilibrium, Pout = PinDo the mathIf Pout = Pin:For a sphere, Aface / Asurface = ¼.The answer comes out to 279 K, or 6o C, or 42o F.444surfacefacesunlightsurfacefacesunlightfacesunlightsurfaceAAFTAAFTAFAT!!!===Different distances from the SunFlux = power per unit area, or the power hitting a squaremeter facing the Sun.I assumed that the flux of sunlight was that which wemeasure at the Earth.How does the flux of sunlight depend on distance from theSun?If the sunlight power hitting 1 m2 at a distance of 1 AU fromthe Sun is 1400 W, how much power hits 1 m2 at adistance of 2 AU from the Sun?Flux, Luminosity, and distanceNo light is lost between 1 AU and 2 AU, it just gets spreadout over a larger area.Since the area increases in both width and height, itincreases by a factor of 2x2 = 4.So 1400 W is now spread over 4 m2, and the flux ofsunlight is now 1400/4 = 350 W/m2.The formula is: Flux α 1/distance2Or Flux = Luminosity / 4π distance2Flux = the light power hitting each square meter.Luminosity = the total light power emitted by the Sun.Different distances from the SunI assumed that the flux of sunlight was that which wemeasure at the Earth.How would the calculation change if the rock were 4 AUfrom the Sun?First, how does the flux of sunlight depend on distancefrom the Sun?At 4 AU from the Sun, the flux of sunlight is…A. the same as at the EarthB. 1/4 that at the EarthC. 1/8 that at the EarthD. 1/16 that at the EarthDifferent temperaturesIf the flux of sunlight is 1/16 as large 4 AU from the Sun,the temperature is multiplied byWe can calculate the temperature at the locations of thedifferent planets:Planet distance predicted T actual surface TMercury 0.39 AU 450 K 100-700 KVenus 0.72 AU 330 K 700 KEarth 1.00 AU 280 K 290 KMars 1.52 AU 227 K 220 KJupiter 5.2 AU 123 K 130 K216/14=Include only sunlight absorbedOnly the sunlight absorbed (not reflected) by the planetcontributes to its heating.Recalculating the temperatures including only the absorbedsunlight we get lower temperatures:Planet black rock recalculated actual surface TMercury 450 K 440 K 100-700 KVenus 330 K 230 K 700 KEarth 280 K 250 K 290 KMars 227 K 217 K 220 KJupiter 123 K 103 K 130 KThe effect of the atmosphereWe assumed that all of the infrared radiation emitted by thesurface of the planet escaped to space, and so carriedheat away from the planet.This is not correct because the Earth’s atmosphere is nottransparent at all wavelengths.Molecules in the Earth’s atmosphere absorb manywavelengths of infrared radiation.Molecules absorb
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