Earth's Orbit Lesson
Overview
One of the first questions students often ask when they learn that the
force of gravity exists not just on objects on the Earth, but between the
Earth and the Sun, is "why doesn't the Earth fall into the Sun?" The orbit
of the Earth is a balance between the Earth's momentum and the gravitational
pull between the Earth and the Sun.
Preparation and Materials
The teacher should be familiar with the GalaxSee application
(for those unfamiliar with this software, there is an online tutorial),
have it loaded on a Power Mac, and have some means of displaying the monitor
to the class.
Objectives
Students will
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use a computational model to explore how the orbit of the Earth might change
if its velocity were different. They will see how a slight change in a
circular orbit will produce an elliptical orbit.
-
practice accurately observing and recording data from a scientific experiment.
-
communicate and defend a scientific argument while collaborating with other
students.
Standards
This lesson fulfills portions of the following standards and curriculum
guidelines:
Activities
-
The students should have learned the features of the solar system and that
the Earth revolves around the Sun once per year.
-
Make the following points about planetary orbits:
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The further a planet is from the Sun, the longer it takes to get around
the Sun, and the lower the speed at which it travels.
-
None of the planets travel in a perfect circle around the Sun, but the
Earth travels in an almost perfect circle.
-
The pull of the Earth on the Sun is just as large as the pull of the Sun
on the Earth, the Sun is just so massive that the same force does no produce
as much of a change in motion. (The same is true of the pull between the
student and the Earth, the student is pulling just as hard on the Earth
as the Earth is on the student.)
-
If we are to accomplish anything in science, it is extremely important
that we are careful observers.
-
With the monitor displayed so that the students can see it, open the Galaxy
Setup and choose 2 stars. The distribution should be either spherical or
disc. The other fields will be changed later, and the value is unimportant.
Create a new galaxy, and make sure that the scale is set to solar system.
Open the list by selecting "Show List" from the Galaxy menu.
-
Set the initial position, velocity, mass, and color of the sun by clicking
on the first object in the star list.
-
Consider having the students look up the mass of the Sun in Earth masses.
(330000)
-
Show a picture of the orbit of the Earth from a top down view, with the
Sun at the origin. Ask the students what the coordinates of the Sun's position
are. The coordinates of the Sun's velocity? (All should be zero)
-
Define for the students the Astronomical Unit (AU) and ask them how many
AUs the Earth is from the Sun. (1)
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Using a diagram of the Earth's orbit, show the Earth 1 AU from the origin
on the x-axis. Ask the students to determine the coordinates of the Earth.
(1,0,0)
-
(Note: There is a slight discrepancy in the current versions of GalaxSee
for Macintosh and Windows. On Windows, the z-axis points out of the screen
by default, the x-axis points to the right, and the y-axis points up. on
Mac, the y-axis points out of the screen, the z-axis points up, and the
x-axis points to the right. The following directions are for the Macintosh.)
-
Do not ask the students what the velocity of the Earth should be, but ask
them in what direction the Earth would be moving at the point at which
it was on the positive x-axis in the diagram. (z direction in coordinate
system used on Mac version, y direction for Windows)
-
Put in an initial guess of 1 AU/day for the velocity.
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Save the model. (this will save you a lot of time recreating the input,
trust me)
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Have the students watch carefully as you run the model. (The planet shoots
off quickly, the velocity is too large)
-
Have the students run the model repeatedly, with different values of the
initial velocity. What velocity will make the Earth travel in a perfect
circle?
-
Note: This is a numerical solution, and can accumulate numerical error.
For objects that make a close approach to the Sun, sometimes inaccuracies
can make the object appear to move into a small circular orbit around the
Sun. If the students find this happening, have them run the same model
with a smaller time step and compare the results. On the Mac version, the
trace option can be useful here as well. For more information about detecting
and controlling error, see the section about the info window in the GalaxSee
tutorial on the Shodor Education Foundation web site.
Discussion of the Simulation
Ask the student to describe in general what happens when the initial velocity
is increased or decreased. Have the students run a model with a much larger
timestep. Is the model still stable? Have the students discuss why a model
with a larger timestep might not be as good of an approximation, if the
model assumes that the force of gravity stays the same throughout a timestep.
Discussion of Observation
Ask the students if they can come up with a way to test if their result
is correct. One thing they may come up with is to compare the circumference
of the Earth's orbit (2 pi AU) with the Earth's revolution period (365.25days).
Does this result agree with theirs? Also, what is the sensitivity?If the
Earth were moving a little faster, what would happen to the orbit?A little
slower? If it was further out? Closer in? Moving at an angle?
Assign them to write a clear and accurate report of what they observed.
Emphasize that it is important that they know what software was used, and
what parameters were set. Be sure to go through the setup procedure again
so that they can record this information.
Collaboration
After they have polished their reports, instruct them to prepare and post
a note to WebCaMILE for another group of students to see. If possible,
have the other group of students attempt to repeat the experiment as described
in the note, verify the findings of the first group, and provide feedback
about their methods and conclusions.Encourage both groups to ask questions
of each other's procedure and observations. If another group of students
is not available, you could split one class into two large groups and require
them to communicate only through writing.
Extensions
Further Experimentation
Have the students try to see if the mass of the Earth changes the solution.
Does it require a large change or a small change? Does it matter if you
make the Earth larger or smaller? Does changing the mass of the Sun make
a difference?
Thinking Harder
If the students solve for the acceleration of the Earth, they will find
it does not depend on the mass of the Earth (aEarth = G MSun
/d2). Why then does the result of the above simulation change
if the mass of the Earth is made to be comparable to the size of the Sun?
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Last Update: Dec 12, 2000
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