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.