Spectra, Doppler Shifts, and Exoplanets: A Novel Approach via Interactive Animated Spreadsheets

Transcription

1 FULL VOLUME TITLE ASP Conference Series, Vol. *, 2011 Editor 1, Editor 2, and Editor 3, eds. Spectra, Doppler Shifts, and Exoplanets: A Novel Approach via Interactive Animated Spreadsheets Scott A. Sinex 1 1 Department of Physical Sciences and Engineering, Prince George s Community College, Largo, MD Abstract. Students investigate spectral line generation, discover the red and blue shifts of the spectral lines of moving objects, and analyze the periodic signal for exoplanet discovery. All of this is accomplished using pre-build animated spreadsheets. 1. Introduction Atomic spectroscopy is a powerful tool for determining the elemental composition of materials. In astronomy, atomic spectroscopy is done remotely using the light emitted by stars and combining this with the light passing through other materials in space to derive composition and even temperature (Robinson 2007). When atomic spectroscopy is united with other concepts such as the Doppler Effect, astronomers have an even more powerful tool to derive information. In this article, an approach used with astronomy students in a general education course is presented using interactive animated spreadsheets. The students will discover how spectral lines are generated, how the Doppler shift affects lines from moving stars, and how the sinusoidal signal of an exoplanet can be analyzed. The approach brings some astronomical tools and concepts to students without belaboring the mathematics using an off-the-shelf piece of software, Microsoft Excel. All the spreadsheets are constructed using computational formulae with much of it hidden under the graphs (no programming) (Sinex 2007, 2011). A number of the forms tools, which function on both Mac and PC platforms, are used to add interactivity. The three spreadsheets discussed are available at 2. Discovering Atomic Spectra Using gas discharge tubes and diffraction glasses, students are introduced to atomic emission line spectra. They observe the spectra of hydrogen, helium, neon, mercury, and nitrogen and then identify two unknowns using the spectral drawings they made. Students quickly see that each element has a unique spectral fingerprint and is demonstrated further using the Java applet at This applet contains the absorption and emission spectra of the elements of the periodic table. Now how do you explain the generation of the spectra lines? In the Generating Atomic Line Spectra spreadsheet, students review the relationship between energy and wavelength and explore the visible spectrum of light 1

2 2 Sinex including the UV and IR regions at the extremes. Then students go to the H spectrum tab to examine how absorption lines and emission lines are generated by an electron changing energy levels in a hydrogen atom. Students move a single electron to see the generation of a single line. The wavelength of each line is given. After seeing how each line is generated and what electron transition is involved, all the visible lines can be shown and this is illustrated in Figure 1. For the absorption spectrum, the continuous spectrum of visible light is in the background. Comment boxes (little red triangles in upper right corner of cell) are used to supply information, hints, and explanations to aid students. Students discover how the electronic transitions generate the various spectral lines and the difference between absorption and emission lines. Since the energy levels are different for each element, an element has a distinctive spectrum that allows its identification. Students examine this on the element spectra tab. Figure 1. Generating the Line Spectrum of Hydrogen 3. Spectroscopy in Motion The Doppler Shift What happens to the spectral lines if the observed object is moving? To an observer on Earth, an object may be moving away from the Earth (increasing distance between Earth and object), toward the Earth (decreasing distance), or parallel to the Earth s motion (no change in distance). In the Spectroscopy in Motion: A Method to Measure Velocity spreadsheet, students review element spectra and mixtures to identify and then they are introduced to the effect of the Doppler shift. Figure 2 illustrates how a student would discover the red and blue shifts of spectral lines by changing the velocity and whether the object moves away or toward the observer. Students discover how astronomers can tell if the star is moving away (red shift) or toward (blue shift) the Earth. With a click of a check box, students can examine the

3 Spectra, Doppler Shifts, and Exoplanets 3 calculations and see how the radial velocity is determined. On the relativity tab (not shown) students can investigate the relativistic velocity as well. Hubble (1929) essentially discovered that most objects in the universe are moving away from each other. This indicates the expansion of the universe. Figure 2. Discovering the Doppler Shift Determining Hubble s Law is a major use of redshift data for a variety of astronomical objects. Hubble s Law shows that the radial velocity is a linear function of the distance the object is from Earth, or, the farther an object is from the Earth, the faster it recedes away. The radial velocity is determined by the redshift of spectral lines. Astronomers then can use this as a distance measuring tool. To get accurate distances, we need an accurate value for the Hubble constant. The Hubble tab has students examine a number of data sets for deriving the Hubble constant and allows then to quickly use the constant to estimate the age of the universe (Figure 3). Figure 3. Modeling Hubble s Law Data

4 4 Sinex 4. Spectroscopy in Motion Exoplanet Detection In the Spectroscopy in Motion II: A Method for Finding Exoplanets spreadsheet, students examine what the Doppler signal can reveal about possible exoplanets around a star. This spreadsheet starts with the concept of center of mass since the occurrence of any exoplanet(s) will cause the center of mass to shift from the star s center. This causes the star to wobble which will induce a periodic signal in the radial velocity (for a near circular orbit viewed edge on, the signal is sinusoidal). Students discover this on the signal detection tab and can explore how the period, p, and amplitude, K, influence behavior (Figure 4). Students further fit the data for 51 Pegasi b with a sine wave while minimizing the sum of the squared error and discover the exoplanet s mass in multiples of Jupiter and its orbital distance in AU s which they compare to the actual values. All the mathematics is camouflaged in the spreadsheet and the instructor can decide if it needs to resurface for discussion or not. Figure 4. Discovering the Signal from an Exoplanet Once the simple system is examined, instructors can decide if more complicated orbital systems need to be explored. A variety of websites provide the orbital information. We go one step further by looking at how our solar system would behave if an alien astronomer were to examine it from afar. What would the Doppler shift data look like for our solar system as observed by an alien astronomer? How many planets could be detected in our multi-planet system? On the our solar system tab (Figure 5), students examine the individual signal for the four Jovian planets. When they set the scale to maximum for comparing to Jupiter s signal, students see how minor the other planets are (LoPresto & McKay 2004, 2005). Only Saturn s signal has any significant addition to the total signal, so are alien astronomer might assume we only have two planets orbiting our Sun.

5 Spectra, Doppler Shifts, and Exoplanets 5 5. Student Assessment Figure 5. Viewing Our Solar System from Afar The activity and spreadsheet for the Spectroscopy in Motion: A Method to Measure Velocity were used in introductory astronomy laboratory in the fall of 2010 and the results for 20 of 21 students are shown in Figure 6. A mean score of 40 out of 50 was obtained. Figure 6. Student Performance (n = 20 students) 6. Constructing Interactive Excel Spreadsheets or Excelets The wherewithal for producing Excelets can be found at the Developer s Guide to Excelets (Sinex 2011), which includes a tutorial, illustrated instructions, and many more examples. Take the interactive features tour to see what you can do in Excel. The forms toolbar provides a variety of features (spinners, scroll bars, checkboxes,

6 6 Sinex etc.) that are easy to use, and when combined with logical functions, lookup tables, conditional formatting, and a number of simple tricks provides a wealth of interactivity and dynamic display. The use of the forms toolbar allows Excelets to function on both PC and Mac platforms. All of this is done using computations (a.k.a. - formulas and available functions) in the cells. The use of comment boxes adds explanation, hints, and answers for students as well. Always look under the graphs, as many of the tricks, such as turning lines on graphs on and off or tracer points are explained there. 7. Some Final Thoughts The interactive animated spreadsheets produce an engaging pedagogy for students in the classroom. Through the predict-test-analyze and explain method of questioning, students can discover a vast array of concepts. The mathematics can be incorporated in as the instructor deems necessary. Using these interactive spreadsheets as part of assessment is the next step (LoPresto 2010). The spreadsheets and accompanying activities discussed plus others that explore topics in astronomy are available for free download at Acknowledgements. The author wishes to thank Barbara Gage of Prince George s Community College for providing comments on this article. 8. References Hubble, E. 1929, A Relationship between Distance and Radial Velocity among Extra-Galactic Nebulae, Proc Natl Acad Sci USA 15 (3) LoPresto, M.C. 2010, Using Visual Assessments and Tutorials to Teach Solar System Concepts in Introductory Astronomy, Astronomy Education Review 9. LoPresto, M.C. & McKay, R. 2004, Detecting Our Own Solar System from Afar, Physics Teacher 42 (4), LoPresto, M.C. & McKay, R. 2005, An Introductory Physics Exercise using Real Extrasolar Planet Data, Physics Education 40 (1) Robinson, K. 2007, Spectroscopy: The Key to the Stars, Springer-Verlag London Limited, 160pp. Sinex, S.A. 2007, Excelets: Excel's Excellent Adventure, (accessed 03 June 2011). Sinex, S.A. 2011, Developer s Guide to Excelets, (accessed 03 June 2011).