Parallax and Uncertainty Worksheet-1

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Parallax and Uncertainty 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. Student Name: Marc DeJesus Lab Section:__________ II. Measuring by Hand 1) What is the inherent uncertainty of the ruler provided? (use metric units) The inherent uncertainty of the ruler provided is .05 mm since the ruler has 1 mm lines. 2) Fill in the table with your handmade measurements for the apparent shift in position of Star A and Star B. Star First Measurement Second Measurement Third Measurement Average of Measurements A 1 ⅞ In 2 In 1 ⅞ In 1.91 In B ⅜ In ½ In ⅜ In .41 In 3) What is the deviation of your measurements from the average? (this is experimental uncertainty) Star A: + or - 0.09 Star B: + or - 0.09 4) Which of your uncertainties is larger (inherent or experimental)? (Denote which method and the value) The experimental uncertainty is larger. Its value is + or - 0.09, which is .04 larger than the inherent uncertainty. 5) Write your answer for the apparent change in position of each star with uncertainty
attached. (Example: 5.2 +/- 0.2 cm) Star A: 5.3 +/- 0.09 cm Star B: 1.4 +/- 0.09 cm 6) When measuring distances in the sky we use units of arcseconds to denote changes in position on the celestial sphere. Using the scale provided for the images determine the conversion factor from centimeters to arcseconds. Conversion factor (arcseconds per cm):: 1 cm = 0.8 arcseconds 7) Using the uncertainties in your measurements, determine the range of possible position change by completing the table. Star Min change (cm) Min change (arcseconds) Max change (cm) Max change (arcseconds) A 5.21 cm 4.168 5.39 cm 4.312 B 1.31 cm 1.048 1.49 cm 1.192 8) Write the change in position with uncertainty attached in units of arcseconds for each star. Star A: 4.24 +/- 0.072 cm Sar B: 1.12 +/- 0.072 cm 9) Which star has the larger change in position? Star A has the larger change in position. 10) What is the minimum difference in the change in position between the two stars considering the uncertainties in measurements? The minimum change between the two stars is 0.072cm 11) What does the change in position of each star tell you about their distance from the
Earth? Which star is closer to the Earth? The change in position of each star tells us the distance from Earth. Star A is closer to Earth than star B. 12) Multiplicatively speaking, how much farther away is the more distant star compared to the closer star? Star B is 3.78x further away from Earth than star A. III. Uncertainty in Data 13) Calculate the average redshift of Star C. 215.3 micrometers 14) What is the uncertainty in the redshift for Star C, state the uncertainty from all sources. (inherent and experimental) 2.7 micrometers 15) Provide the redshift of Star C with uncertainty. 215.3 +/- 2.7 micrometers 16) Use the conversion from redshift to radial velocity to find the radial velocity of Star C with uncertainty. (remember you can use maximum and minimum values to carry uncertainty) 305.9 +/- 3.8 km/s 17) Calculate the average redshift for Star D. 211.7 18) What is the uncertainty in the redshift for Star D, state the uncertainty from all sources. 2.3 19) Provide the redshift of star D with uncertainty. 211.7 +/- 2.3 micrometers 20) Use the conversion from redshift to radial velocity to find the radial velocity of Star D with uncertainty. (remember you can use maximum and minimum values to carry uncertainty)
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300.8 +/- 3.3 km/s 21) What is the range of values for radial velocity for Star C? [212.6, 218] 22) What is the range of values for radial velocity of Star D? [209.4, 211.7] 23) Does this activity support the hypothesis that the radial velocity of stars should decrease as they get farther from the center of a galaxy? (Write at least 3 sentences using the data you collected to justify your answer) Yes this activity does support the hypothesis that radial velocity of stars should decrease as they get farther from the center of the galaxy. We see this through all of the data we ended up collecting. Therefore, the hypothesis is correct.

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