Solar System Lesson
Overview
Students often have a perception of the solar system in which the planets
all travel in perfect circular orbits, all in the same plane, and can even
have a perception of all of the planets in a line. The goal of this lesson
is to have the students build a realistic model of the solar system in
GalaxSee.
This lesson is expected to follow the Earth-Sun lesson, and is somewhat
more advanced. To justify the need for an accurate model of the solar system,
consider framing the lesson within a case-based problem, where the students
are required to provide testimony in a dramatic court case as to the location
of a planet on a given night.
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 or PC, and have some means of displaying
the monitor to the class.
If the teacher wishes to use a helper spreadsheet,
Excel should also be available on any display or student machines.
Objectives
Students will
-
use a computational model to discover possible answers to a question about
a natural phenomenon
-
practice accurately observing and recording data from a scientific experiment
-
communicate and defend a scientific argument while collaborating with other
students.
-
Be able to describe accurately the motion of the planets.
-
Be able to describe elliptical orbits.
Standards
This lesson fulfills portions of the following standards and curriculum
guidelines:
Activities
-
If the students have not previously studied the solar system, be sure the
students understand the properties of the planets. Two sites which cover
this with great detail using the latest images are Solar
Views and Nine Planets.
-
If the students have not studied why the Earth orbits the sun, consider
doing the Earth-Sun lesson before this
one.
-
Make the following points about the solar system:
-
The distance between the planets is much greater than the size of the planets
themselves.
-
The planets do not move in exact circles.
-
The sun contains 98% of the mass of the solar system, and is the dominant
object in controlling the motion of the other objects in the solar system.
-
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, set the scale
of the model to Solar System.
-
Make sure that the Galaxy Setup is for a spherical galaxy
of 2 stars. Other options do not matter, as we are going to change them.
Generate a new galaxy. Open the Star List. Change the options for
the first object, and give it the mass of the Sun (330000 earth masses)
and position it in the center of the coordinate system. Have it be stationary.
You might want to start off by checking to see of your students can correctly
state that an unmoving object in the center of the coordinate system is
represented by (x,y,z)=(0,0,0) and (vx,vy,vz)=(0,0,0)
-
If the students have not learned about ellipses, familiarize them with
the terms semimajor axis, focus, eccentricity, perihelion, and apihelion.
-
For the second object, give it a mass for Mercury, and position it on the
x axis at the perihelion distance (r=a*(1-e)). Give it some guess for the
initial velocity. A good first guess might be to take 2*pi*a as a "order
of magnitude" number for the distance Mercury travels around the sun, and
divide it by the time it takes from the table below. The direction of the
velocity should be tangential t the position. On the Mac, this will be
in the z direction. On windows, this will be the y direction.
-
Have the students save the model as a starting point for each trial.
-
Have the students notice that the shape of the orbit changes depending
on what they use of an initial velocity.
-
Leaving the star list open, run a model from the beginning until almost
halfway through the first orbit. Stop the model, and step through one timestep
at a time until the halfway point is reached (z=0 on Mac, y=0 on Windows).
The star list will show the x value of Mercury. Compared to r at apihelion
(r=a*(1+e)), does the planet overshoot or undershoot the observed
value of the planet's position at perihelion?
-
Have the students adjust the initial velocity, running models with different
initial velocities until they find a perihelion velocity which gives the
proper apihelion distance for Mercury's orbit. The student can then determine
from the star list what the velocity is of the planet at apihelion.
-
Once the students have the perihelion velocity, the next step is to determine
what this velocity is in the reference frame of the Earth's orbit about
the sun. For students who have not studied trigonometry, they may consider
using the helper spreadsheet.
-
The values of the position and velocity at perihelion are now known for
a coordinate system with perihelion occurring on the -x axis. The perihelion
longitude in a standard reference frame for all planets in the solar system
can be found in the tables below. In the standard frame, we can express
the object at perihelion in either x, y, and z coordinates, or in terms
of distance (r), angle around the plane of the solar system (longitude),
or angle up off of the plane of the solar system (latitude). At perihelion,
the latitude is at a maximum, and is given by the inclination of the orbit.
We can express the x, y, and z coordinates as
-
xperi=r*cos(perihelion longitude)*sin(90-inclination)
-
yperi=r*cos(90-inclination)
-
zperi=r*sin(perihelion longitude)*sin(90-inclination)
-
The velocity can be determined quite easily. We know the tangential velocity
at perihelion. Since the latitude (angle off of the plane of the solar
system) is at a maximum at perihelion, the planet is not moving up or down
in the y (z on Windows) direction at that exact point in time (vyperi=0).
The x and z coordinates of the velocity can be chosen such that the velocity
is at right angles to the position.
-
vxperi=-vtangential*sin(perihelion longitude)
-
vyperi=0
-
vxperi=vtangential*cos(perihelion longitude)
-
Once the students have used the model to determine the perihelion velocity,
and have used either a helper spreadsheet
or the above trigonometry to then translate the position into the standard
reference frame of the solar system, they still don't know WHEN the planet
is at perihelion. The tables below give the last time each planet was observed
to be in perihelion. We would like to be able to find out where the planet
is at a specific time, perhaps January 1st, 2000. If the student can determine
the number of days between the desired date and the known date from the
table, the student can then run the model from the known date (last perihelion)
to the desired date. If the known date is more recent than the desired
date, use a negative value for the time step to run the model backwards.
-
NOTE: To ensure accuracy, you might keep the info window open. A good check
on the accuracy of this simulation is to see that the energy is conserved.
If the time step is too large, errors will quickly accumulate, resulting
in a change in the energy. If the energy of the model is changing, you
know your time step is too large.
-
For a large class, consider breaking up into groups so that different people
can determine the exact location and velocity of the planets on January
1st, 2000. When the class has completed their individual tasks, they then
can combine their data and have a complete model of the solar system, starting
from January 1st, 2000.
Tables
Planet |
a (AU) |
e |
T rev (y) |
I (deg) |
peri longitude |
Mass |
Mercury |
0.387098 |
0.205635 |
0.241 |
7 |
77.45 |
0.0558 |
Venus |
0.7233 |
0.006773 |
0.615 |
3.39 |
131.57 |
0.815 |
Earth |
1 |
0.016709 |
1 |
0 |
282.94 |
1 |
Mars |
1.5236 |
0.093405 |
1.88 |
1.85 |
336.06 |
0.107 |
Jupiter |
5.20256 |
0.048498 |
11.9 |
1.3 |
14.33 |
318 |
Saturn |
9.55475 |
0.05546 |
29.5 |
2.49 |
93.05 |
95.1 |
Uranus |
19.18171 |
0.047318 |
84 |
0.77 |
93.18 |
14.5 |
Neptune |
30.05826 |
0.008606 |
165 |
1.77 |
44.63 |
17.2 |
Pluto |
39.48* |
-NA- |
248 |
17.2 |
-NA- |
0.01 |
planet |
perihelion v |
last peri. |
day (2000) |
Mercury |
0.0292 |
3/27/00 |
87 |
Venus |
0.02029 |
7/13/00 |
195 |
Earth |
0.0172 |
1/4/00 |
4 |
Mars |
0.0139 |
11/25/99 |
-36 |
Jupiter |
7.54E-03 |
5/6/99 |
-239 |
Saturn |
5.58E-03 |
1/19/74 |
-9477 |
Uranus |
3.94E-03 |
9/15/66 |
-12160 |
Neptune |
2.74E-03 |
2/24/1881 |
-43409 |
Discussion of the Simulation
Ask the students to discuss the motion of the planets. Why is it that the
planets have almost the same plane of motion, but not exactly. What might
that tell us about the formation of the solar system?
Discussion of Observation
Before the Copernican revolution, mankind thought that the Sun and all
of the planets orbited the Earth. A series of scientists noted that it
made more sense if the planets and the Earth orbited the Sun. As scientists,
we want to be able to observe, understand, and predict. Newton's law of
gravity (the same thing GalaxSee models) was the first time anyone had
ever been able to not just predict the motion of the planets, but to do
so with a simple explanation of why it might happen (gravity).
One of the key observations that scientists were trying to explain was
the retrograde motion of planets. From viewers on Earth, planets would
move in one direction across the sky, but occassionally backtrack for a
period of time, and then start forward in their original direction of motion.
The planets were evened named because of this wandering across the sky,
the word planet literally means "wanderer".
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 determine whether there are any planets reasonably close
together in the night sky. The planets that are observable with the naked
eye are Venus, Mars, Jupiter, and Saturn. Check your local star charts
for times to observe.
Have students try to use their model to predict how far apart Jupiter
and Saturn will be as viewed from Earth. Have them try to actually observe
this in the night sky.
Thinking Harder
Pluto was originally found by a scientist who claimed that he knew where
to look by a wobble in Neptune's orbit. How massive would pluto have to
have been for this to be true?
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Last Update: Dec 12, 2000
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