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Didaktik der Physik Frühjahrstagung Frankfurt 014 How Old is the Universe? - A Teaching Unit Using the Novel Applet Spectrarium - Hans-Otto Carmesin*, Ellen Carmesin + * Gymnasium Athenaeum, Harsefelder

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Didaktik der Physik Frühjahrstagung Frankfurt 014 How Old is the Universe? - A Teaching Unit Using the Novel Applet Spectrarium - Hans-Otto Carmesin*, Ellen Carmesin + * Gymnasium Athenaeum, Harsefelder Straße 40, 1680 Stade and Studienseminar Stade, Bahnhofstraße 5, 168 Stade and Fachbereich 1, Institute for Physics, University Bremen, 8334 Bremen, + Institute for Mathematics, Technical University Darmstadt, Schloßgartenstraße 7, 6489 Darmstadt Abstract We present a teaching unit that offers the students the opportunity to discover the age of the universe by hands on model experiments also with applets. We present a novel software, worksheets and outlines of s. We present experiences with students and a teacher training. 1. Introduction We present a teaching unit in which the students discover the age of the universe by simulated observations using applets. So the students can form hypotheses, test them and achieve a high efficiency of learning [1]. We used the well known planetariumsoftware Stellarium [] and a software simulating astronomical spectroscopic observations. We developed the latter software and called it Spectrarium. The teaching unit is presented in three versions, a conceptual level, an expert level and a mathematical level. The units have been tested with students in Germany and in a teacher training in Lisbon. We present the teaching unit including corresponding work sheets and report about our experiences in s and teacher training. The software Spectrarium and a used zoom animation can be requested via .. Conceptual Level The unit for the conceptual level consists of five s. It has been tested in an astronomy club with students from classes five to 1. The outlines of the s including working sheets are as follows: Lesson 1: Investigation of the Large Magellanic Cloud LMC Goals: The students can find the LMC with Stellarium, describe the location of the LMC at the celestial sphere as well as essential contents of the LMC. 8 Introduction: Magellan Methodical Social form Story of his sailing around the world, his discovery of the strait of Magellan, his description of the LMC 50 Development of results: exploration 70 ulation of results: see exploration of further galaxies,, Question of the Stellarium, zoomanimation animation in the plenum Stellarium Studentpresentation : Where is the Large Magellanic Cloud at the Celestial Sphere and What Can We Find in It? Ideas: Southern Hemisphere LMC contains: stars, star clusters The LMC is in the constellation Dorado. It contains globular star clusters and open star clusters. It is a galaxy. Lesson : Discovery and use of the decrease of radiation with distance Goals: The students can explain the decrease of the intensity of a radiation source and its use for measurements of astronomical distances. 8 Introduction: Examples of distances see ) 0 Hypotheses: see 30 Experiment: Plan see 60 Development of results: performing the experiment 75 ulation of results: see Methodical Teacher instructs, Instruction students give a resume Question of the Conjecture,, Planning,, Some groups perform experiment, some develop the idea of the use of the decrease demonstration in the plenum 1 Carmesin, Carmesin Creative experimentation with more radiation sources Information: Distance to America: 5000 km Distance to the moon: km Distance to the sun: km How Can the Distance of a Galaxy be Measured? Hypothesis: we get only light, we use light The light brightness decreases with the distance. Design of model-experiments: Heater The intensity of a radiation source decreases with the distance. The galaxy is a radiation source. The intensity of the light of the galaxy decreases with the distance. Conversely, the astronomers measure the intensity of the light of the galaxy and therefrom calculate the distance. Example: The galaxy M66 has the distance 80 Zm = m. If each human travels the distance to the sun, then they travel a distance of 1 Zm altogether. Lesson 3: Discovery and use of the Wave nature of Light WNL Goals: The students can illustrate the WNL. Time Didactical Commentments Methodical Com- Social form 5 Introduction: Question, Teacher presents see the 10 Ideas: see Students suggest,, 0 Instruction: Diffraction experiment, Photo of watewaves, Students describe the diffraction pattern and the photo of water-,, 40 Development of results: Analogy 75 ulation of results: see, hand spectrograph if available creative experiments with waterwaves Hand Smartphone, Light Sensor illustration in the plenum waves. Students discover common property of waterwaves and light, see Studentpresentation How can We Measure Properties of the Galaxy? Ideas: no probes analysis of light An experiment illustrates: Light propagates like a wave and has a wavelength λ. λ red λ green Screen Light spreads behind a hole. Waterwaves spread behind a hole. Light has properties of waves. The wavelength corresponds to the colour. The wavelength can be observed with a so called spectrograph. Perhaps the wave property of light gives more information about a galaxy. Lesson 4: Discovery and use of the redshift Goals: The students can explain the redshift and its use for the determination of velocities. 8 Introduction: M66 in Stellarium, increase of wavelength 15 Hypotheses: see 50 Development of results: performing the control experiment 55 ulation of results: see Correspondence of wavelength increase and velocity Methodical Students suggest measurements of D and spectrum Question of the Conjecture,, Students perform experiment animation in the plenum Students work with worksheet or observe ducks in a lake Studentpresentation Why is the Wavelength Increased? Hypothesis: Motion changes the wavelength Control experiment: - We move a toy duck in water - Behind the duck the wavelength is increased - In front of the duck the wavelength is decreased Result: The wavelength of M66 is increased, because M66 moves away from us. Information: From the increase of the wavelength, the velocity v of the galaxy can be determined with help of a spectrograph. The velocity is v = 0 Zm/Gy. 1 Gy = 1 billion years ½ number of Europeans. Laser How Old is the Universe? Worksheet, Astronomy Club, Dr. Carmesin 013 Wavelength of a Moving Source Worksheet, Astronomy Club, Dr. Carmesin 013 Exercise 1: Describe the wavelengths of the swimming baby duck (Photo from MINT Zirkel, September/October 013, p. 18, hoc.). Exercise : Find out what you can tell about the velocity of the duck by observing the wavelength. Lesson 5: Discovery of the Equality of Start Times EST and Measurement of the Age of the Universe Goals: The students can explain their discovery of the EST and calculate the age τ of the universe. 8 Introduction: D, v, see 0 Model experiment: see 30 Development of result: τ 35 ulation of result: see 40 Development of the. 60 Development of result: τ 65 ulation of result: see 80 Metacognition: see Investigate the proportionality of D and v Social form Main of the Plan,, Methodical Pupils explain Calculation ulation Pupilpresentation. Interpretation, Reflexion Worksheet M66: D = 80 Zm; v = 0 Zm/Gy Where Has M66 Been Before? Design of model experiment: Calculation, worksheet ulation Pupilpresentation Result: 14 Gy ago M66 was here. The start time is 14 Gy. When Have Other Galaxies Been Here? Result: All distant galaxies move away from us and started 14 Gy ago. Interpretation: Everything began to expand 14 Gy ago. This is called the Big Bang. The age of the universe is 14 Gy. NGC37: HST, D = 700 Zm; v = 50 Zm/Gy NGC3516: Photo by pupils in Stade with 11 - telescope [3]. D = 1400 Zm; v = 100 Zm/Gy Exercise: When have the galaxies been here? 3. Spectrarium On the expert level the students simulate the astronomical spectroscopy of distant galaxies. For this purpose we developed the novel software Spectrarium. The underlying concept is outlined in the following. Overview of the concept of Spectrarium First the spectral flux densities are determined for the radiation coming from the galaxy [4] and for the radiation originating from the light pollution [5]. These calculations are based on data from the literature. Second the user can simulate his specific observation. Thereby the user can choose the diameter D of the telescope, the temperature T of the cooled camera, the exposure time t and the location with a light pollution described by a parameter L. For this purpose the incoming spectral flux densities of the galaxy and of the light pollution are transformed to the spectrum generated by the chosen parameters D, T, t and L. This transformation is realized by the software in two steps. In a first step we calculate the spectrum for the observatory in Stade equipped with the telescope Celestron C11, the spectrograph DSS7 form SBIG and the camera ST-40 from SBIG. In a second step we scale the spectrum according to the chosen parameters D, T, t and L. Fig.1: Spectrum of the galaxy NGC3516 [4]. 3 Carmesin, Carmesin Radiation from a galaxy From the literature we get the incident spectral flux density F λ coming from a galaxy. For instance, the H α -radiation of the galaxy NGC3516 arrives at the earth with a spectral flux density of F λ = erg s cm Ǻ -1 W or F λ = m Ǻ -1 or F λ = aw 500 m nm (see Fig. 1). Fig.: Construction for light entering the telescope Spectral flux of the light pollution From the literature we get the sky brightness or visual luminance L V in candela per square meter [5]. For instance, the sky above the city of Stade emits cd light with a luminance of L V = m. At the bottom there arrives the same luminance. In order to get the illuminance E V that enters the telescope, we multiply the luminance L V with the solid angle Ω of the galaxy (see Fig. ). This solid angle is the solid angle of the area presented on the photo (see Fig. ) multiplied by the percentage of the area covered by the galaxy on the photo. For example, the telescope C11 with the camera ST-40 from SBIG produces a photo with a solid angle of rad. The galaxy covers an area of 0.1 % of this photo (see Fig. 3). Thus the solid angle of the galaxy is rad and the illuminance E V of the light pollution is E V = cd rad lm m or E V = m. Next we convert this visual or physiological illuminance E V to an energetic illuminance E e. For this conversion we use the fact that the illuminance of the sun is E e = 800 W m corresponds to 0,008 or E V = W m lm m lm. So 1 m and the energetic illuminance of the light pollution is E e = 54 m. This illuminance of the light pollution is an average over the visual wavelength interval [400 nm; 800 nm] with λ = 400 nm. So we obtain the spectral energetic illuminance alias the spectral flux density F λ by dividing the illuminance by λ = 400 nm. Thus we get F λ = 135 aw. m nm fw Fig.3: Photo of the galaxy NGC3516 (upper right) taken by pupils with an 11-inch-telescope. Transformation to the spectrum for the observatory in Stade We present the spectrum for the wavelengths 365 nm, 366 nm, 367 nm, 709 nm. The opening of the telescope has a diameter of D 0 = 0,75 m. With our observatory we took a reference spectrum at a clear night from the sky in Stade (see Fig. 4) at a temperature of T 0 = 70 K with an exposure time of t 0 = 300 s. This spectrum exhibits a maximum of the light pollution at 11 counts and λ = 544 nm originating from mercury in the street lamps. Moreover this spectrum shows a stochastic noise characterized by the standard deviation σ 0 = 97. Fig.4: Reference spectrum In order to produce a light-pollution-spectrum, we subtracted the noise from the reference spectrum and rescaled this spectrum so that the mean spectral flux aw m nm is F λ = 135. As a result we obtained a maximum spectral flux of 145 m nm at 544 nm. So the aw standard deviation of the stochastic noise should be aw aw σ = /11 m nm or σ = 108 m nm. We generate such a noise-spectrum with the help of random numbers. Thereby we add ten random numbers for each wavelength and rescale appropriately. We take the galaxy-spectrum from the literature. Finally we obtain the displayed spectrum by adding the above three spectra. Shortly speaking, we form the sum displayed spectrum = galaxy-spectrum + noise-spectrum + light-pollution-spectrum. 4 How Old is the Universe? Rescaling of the spectra The user of the software may simulate the observation with a location with a pollution factor L, with a telescope with diameter D, with a temperature T and with an exposure time t. As a consequence the three spectra are scaled by the following factors: - The galaxy-spectrum is obviously multiplied by the following galaxy-factor: g f = (D/D 0 ) t/t 0 - The light-pollution-spectrum is obviously multiplied by the following pollutionfactor: p f = (D/D 0 ) t/t 0 L/L 0 - The noise-spectrum is multiplied by a noisefactor of the following form 1 : z f = (t/t 0 ) 0.5 max( 1; [(T-70)/6.3] ). Thereby T is the temperature in K and we obtained the parameters of this formula from a series of experiments. 4. Expert Level On the expert level the students can simulate and evaluate all observations. The unit has been tested with students in an astronomy club from classes six to 1. The unit consists of six s outlined as follows: The first is the same as on the conceptual level. Lesson : Discovery and use of the Inverse Square Law of Flux Density ISL Goals: The students can explain the Inverse Square Law of Flux Density and use it for calculations of astronomical distances. 8 Introduction: Information about α1 Centauri, see 0 Hypotheses: see 30 Experiment: Plan see 60 Development of results: performing the experiment 75 ulation of results: see Calculation of fluxes and distances Methodical Teacher instructs, Instruction students give a resume Question of the Conjecture,, Planning,, Some groups perform experiment, some groups derive formula animation in the plenum Worksheet 1 The exponent 0.5 is a consequence oft he central limit theorem. The denominator 6.3 describes the fact that the noise is increased by a factor two if the temperature is increased by 6.3 K. The maximum describes the fact that the thermal noise dominates for temperatures above 70 K, while the read-outnoise dominates for temperatures 70 K. Information: α1 Centauri emits the same spectrum as the sun. So α1 Centauri has the same physical properties as the sun. So α1 Centauri emits the same power as the sun P sun = W. The sun appears brighter than α1 Centauri. A modern measure of brightness is the power P per area A, the so called flux density F = P/A. Why has α1 Centauri a smaller Flux Density than the Sun? Hypothesis: light spreads in space. The light brightness decreases with the distance. Experiment design: Smartphone, Light Sensor Inverse Square Law of Light Brightness ISL: The flux density F decreases with the distance D proportional to 1/D. The flux density F of a source with power P alias flux L at a distance D is F=P/(4πD ). The flux density F of a source with an apparent brightness m is: F = 1367 W/m (6.83+m) Calculation of the distance of α1 Centauri: P = W F = 5.6 nw/m D = (P/[4πF]) 0,5 = 34.6 Pm = 3.6 Ly (Stellarium: 4.39 Ly) Calculation of the flux of β Centauri for comparison: Stellarium: Apparent Brightness m = 0.55 F = 1367 W/m (6.83+m) = 15.3 nw/m Worksheet, Astronomy Club, Dr. Carmesin 013 Usual stars are spherical gas balls performing a nuclear reaction. As a consequence the colour of a star corresponds to its flux L or emitted radiation power P. This is conventionally expressed by the following classification: Class Colour Flux or power in multiples of the power of the sun, P in P sun O Blue Larger B Blue-white A White 5-5 F Yellow-white 1,5-5 G Yellow 0,6-1,5 K Orange 0,08-0,6 M Red er 0,08 P sun = W This is the basis fort he spectroscopic distance measurement, illustrated for Sirius: Exercise 1:Determine the apparent brightness m with Stellarium. Exercise : Determine the spectral class with Stellarium. Exercise 3: Determine the flux density F from the apparent brightness m. Exercise 4: Determine the flux P approximately from the spectral class. Exercise 5: Determine the distance D from F and m. 5 Carmesin, Carmesin Intended solution: Stellarium: m = F = 1367 W/m 10 (-0.4 (6.83+m)) = 96 nw/m Stellarium: Spectral class A approximately we get P = 15 P sun D = (P/(4π F)) 0.5 = 69 Pm = 7. Ly (Stellarium: 8.6 Ly) Lesson 3: Measurement of the distance of a galaxy with an 11 telescope Goal: The students can simulate with Stellarium the measurement of the distance of a galaxy with an 11 telescope. Methodical Social form 8 Introduction: Locate Simulation NGC3516 in Stellarium Main of the 15 Ideas: see Conjecture,, 0 Info 1: Measures of Instruction Instruction brightness 30 Development of Calculation result 1: F = 0.58 pw/m 40 ulation of result 1: see ulation 45 Development of the. of the 60 Info : Galaxy Worksheet, Survey exercise 70 Development of Calculation result : D = 1300 ZM 75 ulation of result : see ulation galaxies found in Stellarium Calculation of distances How Can We Measure the Distance D of the Galaxy NGC3516? Ideas: We only get light from NGC3516 we analyse light we analyse the brightness We use Stellarium: m = 11.6 Measures of brightness observed at the earth: The magnitude m is an ancient unit. Example: Polaris observed at the earth: m = 1.95 Further Examples: Vega: m=0. (Mizar; Alcor) (.; 3.95). ηumi: m = Just visible: m = 6 The flux density F has the modern unit W/m. Polaris observed at the earth: F = 4. nw/m Conversion m to F: F = 1367 W/m (6.83+m) NGC3516: F = 1367 W/m ( ) = 0.58 pw/m What is the Radiation Power P alias Flux L of a Galaxy? Galaxy survey (Yee, H. K. C. u. a.: The CNOC Field Galaxy Redshift Survey. I. The Survey and the catalogue for the Patch CNOC The Astrophysical Journal Supplement Series, 19, , 000): With P = 13 trillion YW = W the distances have a mean error of 33.8%. Exercise solution: D = (P/[4πF]) 0,5 = ( W/[4π 180 fw/m ]) 0,5 = 397 Zm Result 1: Using the typical galaxy flux W, we get a mean distance error of 34 %. NGC3516: D = (P/[4πF]) 0,5 = ( W/[4π 0.58 pw/m ]) 0,5 = 1300 Zm (Lit.: 1140 Zm) Result : Using Stellarium, we measured the distance 1300 Zm. Info: Using an 11 inch-telescope, pupils measured: m = 11.1; F = 0.9 pw/m ; D = 1060 Zm Worksheet, Astronomy Club, Dr. Carmesin 013 Table: Columns 1-3: Galaxy Survey Column 4: D theoretical = (P/(4πF)) 0,5 with: P = 13 quadrillion YW or P = W Column 5: D measured D theoretical 100% Exercise: Control D theoretical for Nr. 1. with P = 13 quadrillion YW D measured D theoretical Error Nr. F in fw/m in Zm in Zm in % 1 180, ,0 5, ,4 3 4, ,7 4 3, ,3 5, ,3 6, ,8 7, ,5 8 1, ,0 9 1, ,4 10 1, ,4 11 1, ,3 1 1, ,7 13 1, ,9 14 1, ,4 15 1, ,9 16 1, ,8 17 0, ,1 18 0, ,0 19 0, ,5 0 0, ,8 1 0, , 0, ,8 3 0, , 4 0, ,6 5 0, ,1 6 0, ,6 7 0, ,1 8 0, ,4 9 0, ,6 30 0, ,9 31 0, ,8 3 0, ,7 33 0, ,4 34 0, ,8 35 0, ,8 6 How Old is the Universe? 36 0, ,7 37 0, ,8 38 0, ,9 39 0, ,8 40 0, ,9 41 0, ,1 4 0, , 43 0, ,3 44 0, ,3 45 0, ,6 46 0, , 47 0, ,7 48 0, ,5 49 0, ,1 50 0, ,6 51 0, ,7 5 0, ,6 53 0, , 54 0, ,0 55 0, ,7 56 0, ,3 57 0, ,0 58 0, ,4 59 0, ,9 60 0, ,0 61 0, ,6 6 0, ,0 Means ,8 Lesson 4: Discovery and use of the Wave nature of Light WNL Goals: The students can illustrate the WNL and use it for the identification of discrete spectral lines, especially the H α -line. Time Didactical Commentments Methodical Com- Social form 5 Introduction: Teacher presents Question, see the 10 Ideas: see Students suggest,, 15 Instruction: Diffraction experiment Students describe the diffraction pattern and suggest the wave,, 40 Instruction: Measurement of the wavelengths of a hydrogen lamp and of a neon lamp 60 Development of results: Determining the matter on Vega 75 ulation of results: see observation of spectra with the hand-spectrometer nature of light Students calculate the wavelengths according to a given procedure Determination of the spectrum with Spectrarium, identification of Hydrogen by comparison animation in the plenum For experts:

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