University of Michigan - Department of Astronomy

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Version: Worksheet


The Analemma and Time

Part 1: The Analemma

The program steps forward one month at a time. Since there are 365 days in a year and 360º in a circle, you can treat each dot on the ecliptic as approximately equal to 1º.

  1. Sketch the position of the Sun each time the projector stops in the box below. Note the approximate dates when the Sun is highest, lowest, farthest east and west for both loops, and the cross-over positions (i.e. the top, bottom and middle of the analemma - 8 positions).You will get a chance to doublecheck this latter, but it is best if you get as much information as possible during this run.graph

Now the program will run forward smoothly. Check your figure as it runs, then answer the questions below.

  1. What direction, eastward or westward, do the stars move relative to the Sun?

  2. What is the total height of the analemma in your sketch in degrees? Does this match the number in the introduction?

  3. What is the maximum width in degrees?

  4. Convert the maximum width to minutes. Show your work.



  5. The average day is exactly 24 hours 0 minutes long. What is the minimum length of day (baed on your observations above)? Explain how you arrived at your answer.



Part 2: Sundials

SUndialAt the right is a picture of the sundial on the roof of Angell Hall, taken on June 1. If it is sunny and you have the time, your GSI may take you to the roof on Angell Hall to see the sundial. If that is the case, record the date here, and draw a sketch showing the position of the shadow in the space beside the picture.

  1. What is the local solar time displayed on the sundial (click the image for a bigger version)?




Concluding Questions

  1. Is the Sun on the meridian at noon on the solstices? Is it on the meridian at noon on the equinoxes? Explain how you determined this.




  2. If you were on a planet with a perfectly circular orbit and no tilt, what would the analemma look like? Explain.




  3. Which day(s) is the time zone correction the only correction you have to make to get the civil time from the sundial? Explain your answer using the observations from part 1.




  4. Use your sketch from part 1 to determine how many minutes you need to add or subtract to adjust for the analemma for the date in part 2. Explain your answer.





  5. Convert the local solar time from part 2 to the current civil time. Show your work.





  6. In part 1 you were asked what direction the stars moved relative to the Sun. Explain why this direction makes sense using the relationship between sidereal and solar time.

Updated: 9/30/10 by SAM

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