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. 
Description: Description: p1.gif 
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.