Yearly Rotation of the Sky
Goals of the Lab
To observe the apparent motion of the stars across the sky over the course of a few weeks.
To attempt to make sense out of the observed motions in terms of what is really going on with the Earth, the Sun, and the sky.
To measure the difference between the length of the Solar day and the Sidereal day.
Requirements: your observing log, colored pencils or pens, a watch, and an observing location with a clear view of the sky on all four horizons.
Part I: Yearly Rotation Observations
Note that while you are welcome to perform these observations during your regular lab meeting, that is not necessary. Because you need to make observations spaced out over a few weeks, and because you can't count on the weather being good on any particular day, you would be advised not to do the observations within the locked lab facility, but elsewhere on the roof of the 25th St. garage; you can only get into the lab facility while the lab meets, but you can get to the top of the garage at any time.
Pick a location where you have a relatively clear view of the sky down to the horizon either in the East or in the West.
Make a fairly careful sketch of the horizon in the direction you have chosen to look.
Draw the stars and constellations over your chosen horizon (East or West). Your drawing should include at least 10 stars, preferably more. Draw stars up to at least 45° off of the horizon
Measure the angular distance of each star off of the horizon, and indicate that either on your drawing or in a table off to the side (see How To Measure Angular Distances). Also give a horizontal angular scale for your drawing. Label the drawing with the date and time of the drawing, Indicate which horizon you are looking at on your drawing!
Between 5 and 10 days later, repeat step 3. This drawing must be done at exactly the same time as your first drawing. Draw the stars on the same drawing, but in a different color. Draw as many of the same stars from your first drawing as you can. Label the date and time of this second drawing in the second color.
NOTE: If there is a daylight savings time change in between observations for this part of the lab, you need to correct for that. In the Fall, drawings made after the time change must be performed one hour earlier. In the Spring, drawings made after the time change must be performed one hour later.
Between 5 and 10 days after your drawing of step 4, draw the stars you see on the same drawing in a third color. Again, this drawing must be done at exactly the same time of day as your first drawing. Correct for daylight savings time again as necessary. Label the date and time of this third drawing in the third color.
Part II: Yearly Rotation Analysis
How would you describe the motion of the stars you observed?
How fast (in degrees per day) are some of the stars you've drawn moving? Are some stars moving faster than others? If so, can you predict how fast a star is moving based on where it is in the sky?
Why do you see the stars moving as they do?
From your observations and the calculations above, you can measure a fundamental property of the Earth. What is it? Make an estimate of it based on your observations; how close is your estimate to what you know the "real" value to be?
Suppose that a given constellation that you wanted to observe rose at midnight. How long (how many days, weeks, or months) would you have to wait for that constellation to rise at 10PM?
Part III: Sidereal Day
Pick a spot where you have a view of a bright star in the Southern sky near the equator (between 40° and 70° off of the horizon). There must also be a clear landmark on the horizon, such that you can tell exactly when this star is directly over the landmark. Standing so that the star will pass behind the edge of a building or behind a light post is ideal.
Observe the time when your chosen star passes your chosen landmark. Note down your location, the star you are looking at, the landmark you are using, and the exact date and and time when the star passes behind the landmark.
Between four and eight days later, return to the same spot. Stand in exactly the same location, facing exactly the same direction. To be safe, arrive about 1/2 hour earlier than the time when you observed the star pass the landmark in step 2. Again note down the time when the star passes the landmark. Be sure to date this observation!
If you want to repeat the observation again several days later, please do so. You will be able to get better results by combining multiple observations, although this is not strictly necessary.
Answer the following questions:
a) Does the star pass the same spot in the sky as observed from Earth earlier or later each day?
b) The sidereal day is defined as the amount of time it takes the stars to complete one apparent rotation around the sky. The mean solar day is defined as exactly 24 hours, or the amount of time it takes the Sun to complete one apparent rotation around the sky. From your measurements, how long is the sidereal day? (Hint: working through the tutoral on page 11-12 of Lecture Tutorials in Astronomy may help you answer this question! We will not be doing this tutorial in lecture.)
c) Why is the length of the sidereal day different from the length of the mean solar day?
d) Calculate how long the sidereal day should be given that there are 365 days in a year. How close is this to your result to question (b)?
e) Can you relate the results of your measurements and calculations with the seasonal shift of the constellations and the results of Parts I and II of this lab?