Return to Physics IndexOrbital Motion

Eleanor Kopsian Franklin E. Frazier

4027 West Grenshaw Street

Chicago, Illinois 60624

(312) 534-6880Objectives:

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'sLaw 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 aphelionMaterials 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 IHave 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 IIRepeat 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 IIIRepeat activity II substituting 8 cm on each side of C.Activity IVRepeat activity II using 10 cm on each side of C.Activity VRepeat 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 hisLaw ofElliptical Orbitswhich states:The planets move in orbits which are ellipses and havethe 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 focilength 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'sLaw 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.