| RANDY L.
    PHELPS  This is the
    "Determining Your Latitude" Exercise The following
    Applet was written and provided by Walter Fendt and is copyrighted by him.  The right
    of commercial use remains with that author. Purpose: The purpose of this
    exercise is to illustrate the differences in the sky as observed from various locations
    (latitudes) on the Earth.   By changing the latitude interactively, the student
    should see the correlation of the observed sky with the observer's latitude.  The
    student should also see how, by observing the altitude of the celestial pole, the latitude
    from which the observations are made can be determined. Procedure:  
      Recall what the definition of
        latitude is: Latitude is the
        angle, as measured from the center of the Earth, between the Earth's Equator and another
        location on the Earth's surface.Do each  "Exploration " outlined in
        the first column below.  Before you actually do each "Exploration", answer
        the questions posed in the "Anticipate the Result" box for that
        "Exploration".  After you have done this, determine if the actual result
        was as you expected, or somehow different.  If the actual result was different,
        determine why before you proceed to the next step.At the end of the exercise, you should have
        answered the "Anticipate the Results" questions, which are also many of those
        that appeared in the lecture note portion of this module. 
      
        | Exploration | Anticipate the Results | Instructions/Sugestions
        to Help Answer These Questions |  
        | 1. The Appearance of the Sky at the North Pole of the Earth                         | 
          Where is the North Celestial Pole as seen by an observer at the North Pole?
          Where is the Celestial Equator as seen by an observer at the North Pole?What star should be located near the zenith?What is the altitude of the North Celestial Pole at the Earth's North Pole?What is the latitude at the North Pole?               | 
          On the figure on the left hand side below, place the cursor at the point where
            the arrows intersect, which is on the circle representing the Earth's surface. The arrows indicate the directions, as seen by you on the surface of the
            Earth, to the North Celestial Pole, the zenith, and your northern and southern horizons.While holding down the left mouse button, move the cursor to the desired
            location on the Earth's surface.  In other words, move the cursor to place the
            observer at the North Pole.Note as you move the cursor (your observation point), the direction to the North
            Celestial Pole does not change, but the angle between the Celestial Pole and your horizons
            does change.Note how the view of your sky, illustrated in the right-hand figure, appears at
            this new location. |  
        | 2. The Appearance of the Sky at the Equator of the Earth         | 
          Where is the North Celestial Pole as seen by an observer at the Equator?
          Where is the Celestial Equator as seen by an observer at the Earth's Equator?What is the altitude of the North Celestial Pole at the Earth's Equator?What is the latitude at the Earth's Equator? | 
          Repeat the procedure outlined in Exploration 1, but this time move the cursor
              to place the observer at the Earth's Equator.Note how the view of your sky, illustrated in the right-hand figure, appears at
            this new location.   |  
        | 3. The Appearance of the Sky at an intermediate latitude on the
        Earth         | 
          Where is the North Celestial Pole as seen by an observer at an intermediate
            latitude? Where is the Celestial Equator as seen by an observer at an intermediate
            latitude?How does the altitude of the North Celestial Pole change as  the latitude
            changes from 0o to 90o?What would the altitude of the North Celestial Pole be here in Sacramento? | 
          Repeat the procedure outlined in Exploration 1, but this time move the cursor
              to place the observer at an intermediate latitude on the Earth's surface..Note how the view of your sky, illustrated in the right-hand figure, appears at
            this new location.     |   
    
     Critical Thinking/Applications:   Now try to explore the following.  First
    think about the question, and then determine what parameters in the applet need to be
    changed to help you explore the concept.    
      
        | Exploration | Anticipate the Results | Instructions/Sugestions
        to Help Answer These Questions |  
        | N/A | Not yet implemented | Not
        yet implemented |  |