Parallax2 and Uncertainty Worksheet.docx

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Parallax and Uncertainty Worksheet Student Name:___Jacob Cubides_____________ Lab Section:__3________ II. Measuring by Hand 1) What is the inherent uncertainty of the ruler provided? (use metric units) The inherent uncertainty is .5 mm. 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 5.50 cm 5.70 cm 5.60 cm 5.6 cm B 1.7 cm 1.6 cm 1.9 cm 1.7 cm 3) What is the deviation of your measurements from the average? (this is experimental uncertainty) For star A the deviation is +/- .6 cm. For star B the deviation is +/- .7cm. 4) Which of your uncertainties is larger (inherent or experimental)? (Denote which method and the value) The uncertainties for experimental are larger as for inherent it was half of the smallest unit so .5 mm and the uncertainties for experimental were .5 cm and up. 5) Write your answer for the apparent change in position of each star with uncertainty attached. (Example: 5.2 +/- 0.2 cm) Star A: 5.6 +/- 0.6 cm Star B: 1.7 +/- 0.7 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):: . 75 mm per arcsecond. 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 5.5 cm 7.333 arcseconds 5.7 cm 7.6 arcseconds B 1.6 cm 2.133 arcseconds 1.9 cm 2.533 arcseconds 8) Write the change in position with uncertainty attached in units of arcseconds for each star. Star A: 7.466 +/- 0.8 arcseconds Sar B: 2.266 +/- .933 arcseconds 9) Which star has the larger change in position? Star A. 10) What is the minimum difference in the change in position between the two stars considering the uncertainties in measurements? The minimum difference between the two stars is 3.9 cm. 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 one that changed position the most, which was Star A, means that it is closer to the Earth.

12) Multiplicatively speaking, how much farther away is the more distant star compared to the closer star? Star B is about 3.5 times farther away than Star B. 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, stating the uncertainty from all sources.(inherent and experimental) Inherent uncertainty is +/- .5 micrometers and experimental is +/- .3 micrometers. 15) Provide the redshift of Star C with uncertainty. 215.3 +/- .3 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) The radial velocity with uncertainty is 305.94 +/- 0.43 km/s 17) Calculate the average redshift for Star D. 211.7 micrometers 18) What is the uncertainty in the redshift for Star D, stating the uncertainty from all sources. Inherent uncertainty is +/- 0.5 micrometers and the experimental uncertainty is +/-,7 micrometers. 19) Provide the redshift of star D with uncertainty. 211.7 +/- .7 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) 300.78 +/- . 0.95 km/s 21) What is the range of values for radial velocity for Star C?

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[215, 215.6] 22) What is the range of values for radial velocity of Star D? [211, 212.34] 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) This activity doesn’t support the hypothesis that the radial velocity of stars should decrease as they get farther from the center of the galaxy. There is not enough data/information for us to be certain of an answer. The ranges for Star C and D have very similar ranges and there should be more data/information that would determine which one is faster and we don’t know where they are in the galaxy.

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