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CU-Boulder ASTR 1120 - Problem Set 5

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Fall 2005 ASTR 1120-001 General Astronomy: Stars & Galaxies.Problem Set 5. Due Th 17 NovYour name:Your ID:Except for the tutorial, for which you should submit answers on line, please write youranswers on this sheet, and make sure to show your working. Attach extra sheets if youneed them. If you mess up, you can get another copy of the problem set at http://casa.colorado.edu/~ajsh/astr1120_05/prob.html.1. Tutorial on Detecting Dark Matter in Spiral GalaxiesGo to http://www.astronomyplace.com, press on the Cosmic Perspective 3rd Editionicon, log in. You should already have joined our class ‘cm651430’, so that you can record yourwork and submit it for grade on line. Click on Tutorials, and do the tutorial on DetectingDark Matter in Spiral Galaxies. You can redo the tutorial as often as you like, to improveyour grade.Your score should be recorded automatically, but as a double check against your scoredisappearing into a black hole:My score was.If you like, you can comment here on the tutorial:12. Recession velocity of Per AThis is the observed spectrum (Kennicutt 1992) of NGC 1275, also known as Per A, thecentral galaxy in the Perseus cluster of galaxies. The name Per A is because it’s the brightestradio source in the Perseus constellation.(a) Wavelength of HαMeasure, as accurately as you can, the wavelength of the Hα line (Hα is the leftmost ofthe two close prominent emission lines at the right of the graph).The observed wavelength of the Hα line in Per A is nm.(b) RedshiftDeduce the redshift z of Per A, from the redshift formula z = (λ − λ0)/λ0, whereλ0= 656 nm is the laboratory wavelength of Hα.The redshift of Per A is .(c) Recession velocityHence deduce the recession velocity v of Per A from the nonrelativistic Doppler formulaz = v/c with c = 3 × 105km/s the speed of light.The recession velocity of Per A is km/s.23. Cepheidsh & χ Persei is a pretty double open cluster of stars. The clusters contain several Cepheidvariable stars which are used to calibrate Cepheid luminosities. Here is a table of their periodsand luminosities:Star Period Luminosity(days) (L)UY Per 5.4 2600VY Per 5.5 3660VX Per 10.9 5450SZ Cas 13.6 76600510 1520 2530 3502×1034×1036×1038×1031041.2×1041.4×1041.6×1041.8×104Period(days)Luminosity(Lo·)(a) Luminosity-PeriodPlot these Cepheids on the above graph of Luminosity versus Period. Draw a straightline as fairly as you can through the the origin and through the h & χ Cepheids (the line willnot pass exactly through all the points because there are observational and other errors anduncertainties in the precise positions of the points). The straight line expresses graphicallythe proportionalityL ∝ Pdiscovered by Henrietta Leavitt in 1907.(b) Hubble’s Cepheid Number 1The first Cepheid variable found by Edwin Hubble in 1923 in M31, the Andromedaegalaxy, had a period of 31.4 days. Plot the expected position of Hubble’s Cepheid on yourdiagram. Read off the plot the luminosity of Hubble’s Cepheid.The luminosity of Hubble’s Cepheid Number 1 is L.3(c) Distance to M31The observed flux from Hubble’s Cepheid is F = 1.1 × 10−15W m−2. Use the inversesquare law of flux with distance to determine the distance to M31 in pc? [Hint: 1 L=3.9 × 1026W; 1 pc = 3.1 × 1016m.]The distance to M31 is


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