Orbital Motion

Eleanor Kopsian                Franklin E. Frazier
                               4027 West Grenshaw Street
                               Chicago, Illinois 60624
                               (312) 534-6880
Objectives:

In this activity the students will:
  l.  compare a circle with an ellipse,
  2.  communicate an operational definition of an ellipse,
  3.  understand that as the foci of an ellipse are moved further apart the 
      minor axis becomes shorter,
  4.  understand that as the foci of an ellipse are moved further apart the
      major axis becomes longer,
  5.  communicate a definition of the eccentricity of an ellipse,
  6.  be able to use a formula to measure the eccentricity of an ellipse,
  7.  be able to state Kepler's Law of Elliptical Orbits,
  8.  predict the solar energy received at different positions in a planet's 
      orbit.

Vocabulary:

      revolve    circle    major axis    ellipse         perihelion
      orbit      focus     minor axis    eccentricity    aphelion

Materials Needed:

For each team of two students the following materials are needed:
  one foot square foam board, string, thumbtacks, pencils or pens, metric ruler,
  paper, masking tape or scotch tape, marking pen, data table, graph paper. 

Strategy:

Divide the class into pairs.
Activity I  Have the students press a thumbtack into point C at the center of 
              the paper where two perpendicular lines intersect.  These lines 
              are identified as the major axis (horizontal line) and the minor 
              axis (vertical line).  Place a string loop under the tack head and
              place a pen, point down, inside the loop.  Then move the pen 
              outward to stretch the string.  The string should stay under the 
              tack head at all times.  Hold the pen firmly against the string 
              and move it in a rounded orbit.  Paste the completed drawing on 
              the wall. 

Activity II Repeat activity I except have the students press a thumbtack 6 cm 
              from the center on each side of C along the major axis.  Again,
              using the pen and the string loop draw a shape.  The string should
              stay under the two tack heads at all times.  Paste the completed 
              drawing on the wall. 

Activity III Repeat activity II substituting 8 cm on each side of C.

Activity IV Repeat activity II using 10 cm on each side of C.

Activity V  Repeat activity II using 13 cm on each side of C.

Complete the data table by measuring and recording the distance between the foci
and the length of the minor axis for each shape one through five.  Make a bar 
graph showing the relationship of the distance between the foci and the length 
of the minor axis for each shape.  Discuss Johannes Kepler and his Law of
Elliptical Orbits which states: 
          The planets move in orbits which are ellipses and have
            the sun at one focus.  (The other focus is empty).
Discuss the perihelion, the point on the elliptical orbit where the planet is 
closest to the sun.  Discuss the aphelion, the point on the elliptical orbit 
where the planet is farthest from the sun.  Discuss the amount of energy the 
planets receive from the sun at the perihelion and aphelion. 

Hand-Outs:

Worksheets review the concepts of where the aphelion and perihelion are located 
on the elliptical orbit.  They review vocabulary words and use sentence 
completion to review the concepts learned. 

Conclusions:
  
   1.  The greater the distance between the foci, the greater the flatness or 
       eccentricity of the ellipse.  The eccentricity can be measured by using 
       the formula: 
                             e = distance between foci
                                  length of major axis
       
       When e=0, the shape is a circle and when e=1.0, the shape is a straight 
       line. 
   2.  The planets move in elliptical shaped orbits with the sun as one focus 
       and the other focus is empty or just a point in space as stated in 
       Kepler's Law of Elliptical Orbits. 
   3.  A planet would receive the most amount of heat from the sun at the 
       perihelion which is the point closest to the sun.  A planet would receive
       the least amount of heat from the sun at the aphelion which is the point 
       farthest from the sun.  

Evaluation Questions:
     
   l.  How many centers were used to draw a circle?
   2.  How many centers are needed to draw an ellipse?
   3.  How is an ellipse similar to a circle?
   4.  How is an ellipse different from a circle?
   5.  What happens when both foci are placed directly on top of each other?
   6.  What is the shape of the orbits of the planets?

References:

Delta Science Module.  Solar System.  Delta Education, Inc.  
Hudson, New Hampshire, l988.  pp.6-9.
                            
Hewitt, Paul G.  Conceptual Physics.  Addison Wesley:  
Menlo Park, California, l987.  pp.59-62.

Rutherford, Holton & Watson.  Project Physics.  
Holt, Rinehart & Winston Inc.: New York, New York, l975.  pp.43-46.