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Solar System Trial 2: Ellipses
[ideas:
Planets travel in ellipses, which are squished or stretched circles.
Ellipses are characterized by two foci. The sum of the distances from the two foci
is constant.
Note that Earth's orbit is elliptical – but it's closest in January and farthest in July!
So it doesn't explain the seasons.
In an elliptical (non-circular) orbit, a planet moves faster when it's closer to the
Sun.
ACTIVITY NAME
Solar System Trial 2: Ellipses
DESCRIPTION
In this activity students use a computer model to study the elliptical orbits of planets
around a sun.
DISCOVERY QUESTION
What shapes are planetary orbits?
ELLIPSE2.JPG
ELLIPSE-1.GIF
MATERIALS
PhET flash model "orbits"
http://phet.colorado.edu/simulations/orbits/orbits.swf
SAFETY
There are no special safety concerns in this activity.
PROCEDURE
For other PhET (Physics Education Technology) models, go to the University of
Colorado website: http://phet.colorado.edu/web-pages/index.html
This unit addresses NSES standards for…
PREDICTION
What shapes are planetary orbits?
Our Solar System consists of many types of objects circling around the Sun, held in their
orbits by gravity. Name all of the objects you can think of that orbit the Sun. Write down
what you know about each one.
This activity will look specifically at planets, which are relatively large objects circling
the Sun. You will run a model and study the different shapes of planetary orbits. Before
you start the model, make the following predictions.
Are all orbits circles? If not, what shape are they?
COLLECT DATA
Open the PhET model "Orbits". It begins with a single planet going around a sun. Use
START, STOP, and RESET to control the model. This picture shows how to adjust the
model.
In the drop-down menu on the upper right, select the "ellipses" model. Click START and
observe the model. Three orbits are shown. What do you notice about the shapes? How
are they similar and how are they different?
Is the speed of each planet constant as it travels around its orbit? You can measure
differences roughly by using the clock. Start and stop the model and compare the time for
the half-orbit closest to the sun with the time for the half-orbit farthest from the sun.
What is the difference?
ANALYSIS
An ellipse is a special shape a bit like a distorted circle. It has two foci (plural of focus).
It is defined as all points for which the sum of the distances from the two foci is constant.
http://images.google.com/imgres?imgurl=http://mathworld.wolfram.com/images/epsgif/Ellipse4Points_1000.gif&imgrefurl=http://mathworld.wolfram.com/Ellipse.html&h=2
17&w=423&sz=4&hl=en&start=8&tbnid=olXtrQ6JHxxdbM:&tbnh=65&tbnw=126&pre
v=/images%3Fq%3Dellipse%26svnum%3D10%26hl%3Den%26client%3Dsafari%26rls
%3Den-us%26sa%3DN
If the two foci are in the same place, what will the shape look like? Explain why this
statement is true: "a circle is always an ellipse but an ellipse is not always a circle".
Since the Earth's path is an ellipse, its distance from the Sun changes a bit during the
year. You may be surprised to learn that the Earth is closest to the Sun in January and
farthest in July! Do you think this elliptical shape can explain the seasons?
CONCLUSION
Johannes Kepler (1571 – 1630) discovered that the planets travel in ellipses, with the Sun
at one focus. He also discovered that they move faster when closer to the Sun. Isaac
Newton was able to demonstrate that a gravitational force coming from the Sun would
have these two results. This was very strong evidence that gravity exists between the Sun
and the planets, as well as planets and their moons. After this it was generally accepted
that the planets revolve around the Sun rather than the Earth.
FURTHER INVESTIGATIONS
An ellipse can be drawn with two pins, a loop of string, and a pencil. The pins are placed
at the foci and the pins and pencil are enclosed inside the string. The pencil is placed on
the paper inside the string, so the string is taut. The string will form a triangle. If the
pencil is moved around so that the string stays taut, the sum of the distances from the
pencil to the pins will remain constant, satisfying the definition of an ellipse.
Try drawing ellipses on cardboard.