Weighing a Galaxy Worksheet

Name: Marc DeJesus 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 λ obs − λ lab = v c λ lab (EQ 3) 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$4 x (C9-$A$4)/$A$4 Mass enclosed = B9 * $G$4 * $H$4 * $C$4 Predicted speed = SQRT($B$4 * F9/(A9 * $E$4))/1000 For example, if you were to write ∆ λ = λ obs − λ lab in Google Sheet syntax it would be: =(C9-21.106114) or =(C9-$A$4)

3) Insert a copy of your graph here in the worksheet: Analysis 4) I n 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. No, the observed and predicted rotation speed don’t agree with the chair because the space in between each point on the graph increases with the radius. 5) Now try playing with the mass to light ratio. At what value of the mass-to-light ratio does the data match best? 1.17 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