Ellipse
MGA
(information posted 10-3-2019)
We
will introduce this assignment in class during Week 7. It is due during Week 9. A help session will be available in Week 8. You will need the following for the MGA:
·
this handout
·
a couple feet of thin, strong string (like kite
string or fishing line or heavy thread)
·
two push-pins or other pins
·
paper
·
a soft, flat board (such as soft wood, dense foam
board, etc.)
·
some tape
·
pencils
You will complete the assignment on your own.
Elliptical
Orbits
Kepler discovered that
planets move in elliptical orbits, not circular ones. An ellipse
is a curve defined by two focal points (which will be push-pins
for us) and a constant overall distance (which will be a loop of string for
us). The ellipse curve is all those
points such that the distance from one focus to the other focus to the curve
and back to the first focus is constant.
In this assignment,
you will construct seven ellipses in order to get a better understanding of
what an elliptical orbit is and what the elliptical orbits of certain solar
system objects look like. The first four
ellipses that you construct will not represent any particular object’s
orbit. Rather, they will familiarize you
with elliptical orbits in general. The
last three ellipses that you construct will represent the orbits of three
specific solar system objects: the planets Mercury and Mars, and Halley’s comet. In
constructing these, you will get a better sense of what the orbits of actual
solar system bodies look like.
PART 1 – SET-UP
Make a loop of string
whose length (when looped) is approximately
10 cm. The exact length is not important
– the 10 cm value is just so that it will fit on a piece of paper.
Note that 10 cm is the length of the loop,
not the length of the string used to make the loop.
Get a flat board (such
as soft wood, dense foam board, etc.) and a piece of paper. Tape the paper to the board. Put in two push-pins.
PART 2 – BASIC
ELLIPSES
Ellipse #1) Loop the string around the push-pins and
draw an ellipse using the method shown in the figure below.
There is also a YouTube video that shows how to do this
(click here).
Now measure the
distance between focal points and
measure the major axis of the ellipse
as shown in the diagram above. Calculate
the eccentricity of your ellipse:
(see
Chapter 11 of The Known Universe).
Draw in the Sun on the
ellipse (at one of the focal points) and a planet (anywhere on the ellipse
itself). Also
mark on the ellipse the point where the planet will move fastest, and the point where it will move slowest.
Ellipse #2) Get a new piece of paper and draw another
ellipse, only this time change the distance between push-pins. Measure the distance between focal points and
measure the major axis of the ellipse.
Calculate the eccentricity of your ellipse. Add the Sun, a planet, and where the planet
will move fastest and slowest, as in #1.
Ellipse #3) Get a third piece of paper and draw a
third ellipse, again changing the distance between push-pins. Measure the distance between focal points and
measure the major axis of the ellipse.
Calculate the eccentricity of your ellipse. Add the Sun, a planet, and
where the planet will move fastest and slowest, as in #1.
Ellipse #4) Get a fourth piece of paper and draw a
fourth ellipse, but this time use only
one push-pin. What is the distance
between focal points, the major axis, and the eccentricity in this case? What is this shape called? (Put your answer on the same page as your
one-pin ellipse.) Add the Sun and a planet.
PART 3 – ORBITS OF
SOLAR SYSTEM BODIES
Look up the
eccentricities of the orbits of the following objects (you can find these on
the web or in a reference book):
Ellipse #5) Mercury
Ellipse #6) Mars
Ellipse #7) Halley’s Comet
Set your push-pins to
draw each of these orbits.
(Unless you know something about ellipses from a math class, this is mostly a trial-and-error
process to get the right eccentricity.
Looking at the four ellipses you drew in Part 2 should give you an idea
of where to start the process).
You should end up with
an ellipse for each – Mercury, Mars, and Halley’s Comet (each on a separate
sheet of paper). Add the Sun, the planet
(or comet), and where the planet (or comet) will move fastest and slowest, as
in #1.
Turn in your seven
ellipses. Make sure your name is on
them.