Weighing a Galaxy Worksheet.docx

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Name: Kenni Medvar Weighing a Galaxy Worksheet These lab activities have evolved over years of use in Clemson University’s Department of Physics and Astronomy general astronomy laboratory. Contributors include Tom Collins, Mark Leising, Neil Miller, Peter Milne, Grant Williams, Donna Mullenax, Jessica Crist, Keith Davis, Amber Porter, Lea Marcotulli, and David Connick. Please direct all questions, complaints, and corrections to David Connick (dconnic@clemson.edu) who is responsible for all errors and omissions. These constants and conversion can also be found in the “Weighing a Galaxy Data” file. They are included here for convenience when completing the calculations. Constants and Conversion Factors H spin flip lab wavelength (cm) Newton’s G (SI) Solar masses to kilograms km/s to m/s Kiloparsecs to meters Speed of light (km/s) 21.106114 6.67E-11 2.00E+30 1000 3.10E+19 3.00E+05 Calculations (EQ 3) λ ??? − λ ??? = ? ? λ ??? 1) Equation 3 from the instructions document is written above. Algebraically solve this equation for the observed speed, v, on paper showing as many steps as possible. Upload an image of your work below. 2) Using Row 9 in your spreadsheet, write the Google Sheets equations that you will use to solve for the following quantities:

Speed observed = $F$4*((C9/$A$4)-1) Mass enclosed =B9*$H$4*$C$4*$G$4 Predicted speed = SQRT(($B$4*F9)/(A9*$E$4))/$D$4 For example, if you were to write in Google Sheet syntax it would be: ∆λ = λ ??? − λ ??? =(C9-21.106114) or =(C9-$A$4) 3) Insert a copy of your graph here in the worksheet: Analysis 4) In many galaxies analyzed by scientists, the observed speeds are seen to be significantly larger than the predicted speeds, especially in the outer part of the galaxies. Do the observed and predicted rotation speed curves agree in your chart? Explain. They do not agree with my chart because one of them comes from Newton and one comes from observations. 5) Now try playing with the mass to light ratio. At what value of the mass-to-light ratio does the data match best? 1.2 6) You likely see that the curves still do not match well by just adjusting the mass-to-light ratio. Astronomers have invoked “dark matter”, that is matter that provides gravity but does not emit light like the stars, to explain the discrepancy in the data for decades. Focus on the outermost point at the radius 30.4 kpc. How much enclosed mass is required to have the predicted speed match the observed speed for this point? 6.845 goes in A 18?

7) Still looking at the point at radius 30.4 kpc. What is the ratio of the required mass you found in question 6 to the total luminous mass enclosed from your data? 2.87 ????𝑖??? ???? ???𝑖???? ???? = 8) In some galaxies the hydrogen gas is seen to be orbiting at 220 km/s at a radius of 100 kpc. How much enclosed mass is required for the predicted speed to match the observed speed in that galaxy? 6.85 is required to match the observed speed for this point? 9) What is the ratio of the required enclosed mass at a radius of 100kpc to the enclosed luminous mass from your data? 2.25E+42/2.425e+41 ????𝑖??? ???? ???𝑖???? ???? = 10) Based on your chart from question 3, does the galaxy studied in this lab require dark matter? Explain using details from your chart and the analysis you performed. I think the galaxy does need dark matter because it counts as the difference between predicted and actual speed. 11) If we use dark matter to explain the discrepancy, how would the dark matter be distributed in the galaxy? Could it all exist at the center of the galaxy in the form of a black hole? Would it be evenly distributed throughout the galaxy? Think about what each scenario means for the enclosed mass. For this galaxy it is more towards the edge because but in general it would be more towards the center. 12) Based on what you have heard about dark matter candidates like MaCHOs, WIMPs and more recent propositions, share your thoughts on dark matter and what it might consist of. I think it would consist of different particles.

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