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Astronomy

Lab: Observing differential rotation

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Astronomy Lab Instructions

Astronomy Lab: Observing Differential Rotation

Goal: to measure differential rotation using Jupiter features or Sol sunspots

Because it is generally difficult for students to secure telescope observations of Jupiter with sufficient detail to measure the rate of motion of the bands, it is recommended that students use solar observations of sunspots to determine the difference in rotation speeds of gas materials at different latitudes in a planet or star. However, if you have the opportunity to directly observe Jupiter, or you can get a timed sequence of photographs, you may use Jupiter information instead.

Background

The first in this sequence of Four Earth-based observations of Jupiter shows what appear to be two “red spot” type storms in the middle of the white equatorial band, on either limb of the planet. As time passes, however it becomes clear that the right most and paler spot is really a moon, and the other darker spot is the moon's shadow on the surface. Notice also that change in location of the spots over the two-hour period during which the sequence was shot. Here is the entire sequence as a time lapse movie.

For this exercise, you will follow the linear path of at least two sunspots across the solar disk, or two identifiable storms across the face of Jupiter.

FeatureJupiterSun
Equatorial Radius71492km
Polar Radius66854km
Equatorial rotation velocity12.6 km/sec
Materials
Procedure
  1. Watch the weather, and pick a time frame when you will be able to observe every night for at least a week (if you are doing Jupiter), or every day for at least a week (if you are doing the sun).
    Be sure to use appropriate equipment when observing the sun.

    Never view the sun directly, especially through binoculars or a telescope.

    For details on solar observations, see the SunSpot Lab.

  2. Using the same diameter for each observation, draw a large circle to represent the face of the sun or Jupiter.
  3. Sketch as accurately as possible at least two surface features that you see on your object. These should be selected so that at least one is close to the equator and at least one is significantly distant from the equator. Label them “A”, “B”, etc. so that you can compare the different observations you will make. Be sure to note the date and time of your observation.
  4. Identify the North and South Poles of your object.
    • Jupiter: use an online map or photograph of Jupiter with north and south poles marked to identify the poles of the planet in your drawing. Clearly mark these.
    • The Sun: use an online picture taken the same day as your observations to identify the poles of the sun in your drawing. Clearly mark these.
  5. Collect at least five time-stamped observations of the same surface feature.
  6. Using a piece of tracing paper, draw circle the same size as your observation pictures.
  7. Mark two opposite points on your tracing paper circle as “North” and “South”.
  8. Overlay each diagram of your observation with the tracing paper, and align the Northpoint of the diagram with the North Mark on your tracing paper.
  9. Copy the location and size of your observed surface feature to the tracing paper. You should wind up with all of your observations on the tracing paper, in sequence according to the time of the observation. [If your observations appear to be out of sequence, then on your object has rotated all the way around between two sequential observations.]
Data Analysis
  1. Measure to the nearest millimeter the length of the straight line for the sunspot or identifiable storm near the equator. This is the apparent motion of the feature across your observed disk.
  2. On a piece of graph paper, draw a line which is exactly this length.
  3. Using your compass, find the midpoint of this line and draw a semicircle connecting its ends.
  4. Use a ruler, and transfer the sunspots positions from the tracing paper to the baseline of the semicircle.
  5. Draw a vertical line from each observation to the semicircle. The positions on the semicircle represents the position of the observed phenomenon on the spherical surface of your object.
  6. Draw a line from the center of the baseline to two widely spaced observations.
  7. Using protractor to measure the angle between the two lines you drew in the previous step and record the angle measurement on your diagram.
  8. Determine the length of time between the observations of the two positions, and record the results in the angle measurement.
  9. Calculate the sun's angular velocity in terms of the number of degrees of your angle divided by the time between the two observations.
  10. Repeat this process for the object near the pole.
  11. To determine how long it takes the object to make one full rotation as seen from earth (its synodic period), divide your angular velocity by 360°. [This value should be approximately 27 days for the sun and 10 hours for Jupiter. You may be off by as much as two days, depending on the accuracy of your measurements.]
  12. To determine the synodic period of the object you observed, use the formula P = (365.25)S/(365.25 + S), where S is the synodic period you determined in the previous step in days.
  13. Compare periods for the phenomenon closest to the poll with that of the phenomenon closest to the equator. Which is longer?
Report

As usual, you should describe the materials you used, your actual observations including the date and time, your data and calculations, and your conclusions. For this lab, you may find it necessary to scan in your drawings. Please remember to reduce the size of your drawings for upload.